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Applications Of Bioacoustics To Musical Instrument Technology

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A 8B:DC(0&$3(E:DFG# / $ ) }@G |i~ 7 @ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) < 7 r ~ ^~ ) ) ) ) ) ) ) ) ) ) . ~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) H ~ 7 6L~D JI # : ~> ) ) ) ) ) }@ }Q 8 ~ ~ ~R [L~ 7 r~ 5 ~> ) ) ) ) ) ) ) ) ) }@ }Q 8 ~ - 7 ~ 19 & 7 !. |i~ 7 ) }@ 0&8 7 ~ 0 7 m`~ ~ 7~ 35 R 1 ~> ) )K= }@ }Q ~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) > }@ < 7 r~ ^~R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) >) 9 ~ ~ NM . ~ 6 7 r ) ) ) ) ) ) ) ) ) ) ) >) }@ }Q 8 ~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) >) }@ 0&8 ) ) ) ) ) ) ) ) ) ) ) ) ) )O? }@ < 7 r~ ^~ : ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )O? ) }@ < [ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )O? ) }@ < ' ~>~> u r ) ) ) ) ) ) ) ) ) ) ) ) ) @ < : 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) # "7 ? -1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) > ? @ L L D > > > /= P? 8B: ) }@4&" ~ 3 ~ 7 [ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 0 < r : 7 8 < 7 r~ i~.- m~ 7 9 & 87 !. [i~ 7 ) }@ < 7 r~ ^~.- 7 ~ 19 & 7 !. |i~ 7 ) ) ) ) ) ) ) ) ) ) ) ) }@ |i~ 7 [~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )K= [ ~ 7 !I : < 7 [~ ^~R 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) > < : 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )O? 6 $ 7 [ 7: ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) < A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) B8 :DC 10&$ (E: # C< #&+ ) }@ 0 7 ~ % r~ }M~Du ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) }@ G 7 " ~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) ) < ! ~> 7: # ' . $ < ~ ) ) ) ) ) ) ) ) ) ) : ) ) }@ 9 [ 7 ( | 7 G 7 " ~ ) ) ) ) ) ) ) ) ) ) ) ) ) : ) ) 7 !I 7 " ~ [ 7 r~ ) ) ) ) ) ) ) ) ) ) ) : ) 7 !R: ; r 9 7 ~ }M~D: [~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) ) ~ ! 7 : 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) ) }@^ " $ ' ' ~>~ `r~> [ 7 ! * 7 ) ) ) ) ) ) ) ) ) ) ) ) ) : ) J:[u 7 ~ }4 ~ : 7 7 6 7 r ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) : ) J:[u 7 ~ , ~ 7 ' L~ 7 ~ 0 ~ 7 : )K=) ~ 1 6 7 r ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : ) > }@ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : )O? < : 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) : :&P#%)FG1!!###( # !#1 C #' 0!# #( =) 0 7 & 6 *}@^ !~ ' $ < ~ ) ) ) ) ) ) ) ) ) ) ) ) ) =) 0587 ~ 7 !7<0~ : 8 * 7 7 ! 7 $ 7 u u $ } 7 7 ! ~ ) ) ) ) ) ) ) ) ) =) % 6 * 9 ri~ 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) =) < [ % 6 * ; ^~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) =)K= 05: 7 ! 6|~ r 6 * ~ < ~D 7 u -) ) ) ) ) ) ) ) ) ) ) =)K=) }@ H ~ 7)$ ~> 7 < ~> 7 u ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) =)K=) U 7 !8: 18 0& 7 !R 6|~ r 9 [~ 7 ! 5" =) > < : 7+ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) " 77 L ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) /> = P> = =/= /= = => =L =L ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) > >/> > ? >L ? ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ @D P@ = @ ? @L L L= L@ ') #% :& GF (* 1! ')PP"1 :& C < #&+ >) }@G : 7 7 7 ) ) ) ) ) ) ) ) ) ) ) >) t~B" 7 7 & 7 S ) ) ) ) ) ) ) ) ) ) ) ) ) >) 7 7 0 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) >) < : 7 + ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) FG1 !0&#(&9 $ 0&0& : ? ) < : 7 + ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ? ) 6 '& ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) G0#!$&&%D: FG1' 0&#% C:!# #!#P FG ) P* 9,!##(%1; :*< - ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) /> L ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ? @ - A - A - A " 78787 -(- "7 ) @} 7 ~ 8: * R~ # 7 7 7 ~ 8 ~ [ ~ 7 u [~ 7 ! ~ .~ # - 78 ~ 7 ! 8 ~ ~ (~ rI 8 & 87 ! # [~ ~ : 7 7 ~ 78 ) }@ 7 ~ 7 !D [r|~ 7 ^~D ~ u :I ~ 7 ! 8 & 87 !Rr` ir|~ 7 !R~ . # 7 7 ! ( [u)1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) = ) "^~D : ~>~> rr ~ @.~ 7 9* 7 r~ i~ | 7 L ) $ ~ ~IR~D'& 6* 7 7 ~ & 7 >D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) :) = ~ : ~ ~ 7 ~ ~ ~ D / > @> < 2 / = ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) >/@ =) "^~D : 5 ~ m ~ ! ( ~D 7 ~ 8 # ~ 7)$ ~ 7 2 ~D 7 uQ / . &l~ ~D ~ & / ? 2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) L @ >) "^~D : #< " ~ ~ 7 [~ ~>~> u r 7)( r 8 7 3 71 )}@ !D 7 7 r~ [ 7 7 [" ~DR i~ 2 m~ 7 ! 8 + 8 I r 7 [~ ) ) ) ) ) ? " " 7 ) }Q 7 [~ r~! < & 7 !R : 7 r~ 7: [u /@ = ) ) ) ) ) ) ) )K= ) > )O? ) @ ) L ~D 7+ | P + 7 7 ~ : / &* 7 2 > 7 # B@BD B @ ~ ;@B )F @/= ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ 8 7 7 ! 8 & ~ 7 ! ~ J * ~R : [ M [ 7 m : 7 r~ 7+ ) ) ) }@ : 8 7 ~ | 7 # 7 r~ ^~) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ~ !D~> 8 7 r~ i~ * 7 !R r~ 7 # 7 . 7 $ 0 7 : 7 7 > 8 ~ / # *2 7 r ~> 9* B 7 r 7 # :G~ 8 2 i ~ :~ [ ~I~ ~ 8 7 ~ ~ 7 ~#) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ ^~> ~ 1 u # ~ [u 7 [~ ^ [i~ 7 [~ ~ ~D : 7 7 ~ 7 $ [ 7 8 S 7 [ ~ 7 8 r9 * |~D 7 r "> ~ ~ ~ ! 7 ~ / ~ 7 7 20~ ~ ~ ~ ! # R~ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ~ !D~> # 8 ~ + * 7 ! 7 7 # !8 r~ 2 78: 0 7 : 7 7 7 # * 7 . [u2 : 8 ~ : ~> ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ H" [ 8 & 87 ! "! 7 9 * 78: 7 !m~ 8 & u` )B}@ 7 ~ !D~> 78: ~ ~ 7 7 @ 7 ! 7 7 ) 0& 7 r~ i~8 ~Du 7 : * : G 8 ~ : ~> 7 * *0~D 1) I 7 : 7 #~ !D~> : 78 7 &8 & ~ 7 7 ! 5 7 ~ !D~>- 9 * 78+ ~> 8: & ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) |~ 7 ! ~ / 2 ~ 7 & [ !D~> / 8 2 # 8 & 87 ! " / ^~> ~ 7 8 @ 2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ~ ) ) ) ) ) ) ) ) ) ) ) ) ) *0~D 8 & 87 !. 7# ~I 8 ~ 78 rm~R t~ ! 7 8~ i~ # : G9 * B$ + i9 * B$ 1 [ 8 7 ~ ` ~> 7 : [ ) }@ I . ~ $ u 7 u2 >/ =M3 1 / * 7 (~ ~> 87 !R ~> # D D 2 ~ S I* @:)) ) ) ) ) ) }@ 7 7 ! ~ J * 7 #~ ! ~D 7 r~ i~. * ~> ~ ![ # ~ : r ) 05 7 : 7 7: 7 r [~. 7 ~G 78 8 & )B+} * ~ : r / 2 ~ / 2 [~D! 0~> ~D" 7 ~D ~ 8 ~ *2 7 7 r 7 ~ 7 + rO : 7 ! 7 @~ 8 ) "[ ~ ~ : [ / 2M~D ~ ' : " 787 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) = > ? D ) !}@ *0~ 8 I m 8 ~ / 2Q~ ~ [ 8 7 ! ~ Ri !D ~ 35 R 1 . ~ * 7 ~ I &L / 7 : 2@~ ~ I # @ / 8 20 7 !G 7 r~ ^~.- ~ 8 7 ~ ~ 7 ~#) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 0 u " - : 7 r~ i~8 7 : ' 7 )) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 0 ~ " / ' 2 ~> 7 : : [ : ~ + 7 7 7 :~ : 7 " :# &! 7 .~ R ~ u[~ ! 7 7 ~ : ) ~ : ![H~ R ~> : ( 8 7 ! ~ : 7 )) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) " 8 ~ &. ) +} * B$ i~ ~ 7 r~D 7 * 7 }@ r r 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ BAC #) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ [H - 8 & 87 !R 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ " ~ : 7 ~ 7 # : . 7 ! 7 ! 8 & 7 !+)) ) ) ) ) ) ) ) ) ) ) ) )K= 0 : 7 !. 7,BAC 7,4- & + ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) > }@ 8 : !r - 7 !! m: R~ ! 7 7 * 7 *2 7 : r 7 ~ 8 G 78: )) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 8 & )O? }@ 7 ! ~ 7 7 7 ! 7 7 B :3m~ ( | : )4}@ $ 7 !8~ 7 7 ! $ ~D R~ & : ~ 7( r 7 ~ 7 !I 7 7 8 ~ 7 ~ 7 ! ~ 7 ! 7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ }@ 7 ! ~ / ~ 7 * 8 ~D & !D : 7 2P~ r ~ 7 ! ^ !DG 7 ! ~ 7 7 7 !G 7 7 7 6 7 ! :)K? 7 ! 5 r !D ! r~ 8 8 D #4@ ACEDF ~I 78 )+) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) L }@ 7 ! ~ / ~ 7 * 8 ~D & !D : 7 2P~ r ~ 7 ! ^ !DG 7 ! ~ 7 7 7 ! 7 7 7 6 7 ! :)K? 7 ! 5 r !D ! [ ~> 8 L>?#4@A)EDGF # ~I 78 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , " 8 8 ~ 1 7 ~ r 8 & 87 !R~ 7,BAC 7, 78 ) ) ) 0 # ~ * r~ 8 " : 7 / 7 8 ~ & !D +2 7 ! .~ ~l 7 !+) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) }@ 7 ! ~ ! r~ 8 ~ r 7 # ~ * 8 & 87 !:@~ [~ . 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'! +) $1.-- [u 7 M : [ 7: Q 7 " 7 ~D 8 [r~ : 7 ~ | # .~ $ 7: 7 [ ~ 7 7 # - r & ) = ~> ~ | 7*7 + 7 r ~ 7: 2 7 ~8 |~ : 7 !R : 7 [~ 1 ) r M | 7 : 7 7 7 + 7 ! 7 ~ ! 7 ^ / 2+* 7 7 ~>~> rr ~ * 7 ! i~ ! 7 [ 7 )8}@ ~ 7 # R 57 + . ~ rr 7 8 8 : i~>~Du r # : . ~ 7 +: .~ 7 ) }@ r 7 )7: [~ .~B& r 7 7 78 787 7 r : "z rp~> 7 + 78: . ~l) 4m~> ~ K : [ 7: * 7 8 ~> 7 ~D : 7 r ~> *2 7 &i~ ~ 887 #"^ 7 . 7 ~ ~l~ 8 787 ~ *2 7 z : 7 7 ~ : i~ " : ~ 7 7 !+ ~l 7 !~ r [ 7 !:)R}@ 7 7 r i~ : m [~ + 7 7 . 7 / Q & 8 [ R~ 7 7 ~ 7: *2 7 ! 7 ! * # : ) 9 [r~ : # 7 7 7 8+ : ~ 87 (~ 7 ~>~> u r 7 r~ 87 ! i~ ~ r : ~D 7 | 7 ) 0 ~> !! 7 (~ [ [~ ( 8 [ z ~ 7 ~ #" 7 7 ! r ^ !~ [ 7 ~ 7: L~ ~D 7 r r 7 1 ~ 7 r~ 8 [i ) 0 78 ^ ~ * 8 ~ & # 7 r, * 7 r" 7 | 7 7 )7 * 7 7 ~. : [ 87 ~ ~ #" 7 7 !I *2 7 8 7 7 S #" 7 7 !. : 7 [~ 7: ) ! 7 "[ ~ : [ ' 7 r~ 87 !i~ 8 " 7 ~D ! ~D ~ | 7 7 8 87 8 8 + [ ~ I : 7 7 ~ : )4}@ 7 7 % r i~ : 8 |r~ + 7 r~ K ~l ~> ~ & 7 !G + [ ~ . : 7 7 ~ + ~ 8 2 #" ~ I 7 #" 7 7 ! / # 7 7) [~ 87 G.B : |~ : : r6 * : 87 & 8 7 [ 7 r2 + 7 7 ~D" 2)H}@ !D 7 7 [ * *2 7 I : r ~ z~ #" 7 7 !( : 7 [~ 7: 7 7 " : 7 7 | 7# + 7 r~ 7: G | !D 7 8.~l 8 8 7 ~ |~> I 8 [ #" 7 7 !8 ~ 7 7 ~ 7: ) }@ !DS 7 r~ u 78 7 7 * ' & ~D 8 ~ #" 7 7 !I~ + 7 [ r ~> [ * 7 5 *2 7 . .~ : 7 r~ 7 r~Du )B}@ rR~> ~ 7 .~ . 7 [i~ 7 ~ 7- ~> 7 ~> : |i~ 7 # 7 [~ ^~R~ ! 8 7 3 ) 7 ! 8 ~ ~ ~ . ~ 8 7 ~ ~D : 7 m ~ )O}@ 7 r~ i~ : ~8 ~ 7 " ~ ) }@ 7 : 7 R~ 7 r 7 !S~ . 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[ i 7 / / 7 7)( r 2 )}@ 7 7 R~> 7 7 8 ~l [I !~ 7 .~ r [ 7 M r 7: a~ * 7 ! 7 M : r : .:8 ` ~ 7 8i~ ! 7 ! ~ r: [@i~ 7 r r .$ ( . ) [~ S [ : (~ r~ .~ ! / ~> 7 !![ 2 8: . 7 7 R~ - 7 / 8 ~D ~> 7 8 u9 *" : ~l rR~ . . " ) E : 8 [ | ~> [~ . R~ z~ + . ~ I .~ 7 . L~ 7 Gr~ 8 7 & z ! 7 ^ ! r [ 7 .~ 7 !+) A) 7 B( r 7 !p~ ~ ~ ! " 8 ~D &p [ rR~ &~ * 7 ! 8 ~l 7 #" r ~ 7 r" 7 ) }@ + # ( r 8 ~ 7 r~ i.~ - /. 7 7 ~ 8: & 7 ! |i~ 7 7 '! +) $1.-- ? u r 7 =*2u rGS |i~ 7 *2 7 &~ * S 7 [~ ^~ : 7 rr 7 : ~ 7 78 ~> 7: # 8 ~ ~>[~ 78 : ~ ( [u 7 8 ~I .~ : ~l 7 !I~8 + 7 r~ 7: ) t~ 7 ! 7 ~ 7 / 7 7 7 !I + 7 r~ 7: ~ 7 ~D .~ ~ ~ : ` r i~ : 8 |r~ : 7 7 : 8 7 7 ! 8 & i~ .r~ . [~ 7 : 7 r~> " 7 7 !z~ : 7 7 $ *2r t R~ 7 ! + . ~ ~ 7 7+ 7 ! D ! 'AEA ) ~D : 7 7: ^: 7 7 7 8 u9*" : . -! [ ~> ~ : ( r 7 i~D [2 7 > i~ r : ~ & u [~> 7 !.~ 7 & 8 u9*" 9* 7 ~Du 7 r~ #" 7 ) E 8 (~ . / : R 7 +2 L~ R r [Ri~ ~D =& * ! 7 ~ - r ) E 7 ~t~> [ [G i~ .r~ #" ~ 7 7 7 # | 7 r~ r .~D : 7 ! r 7 ! . u 7 # 7 NM [ 7: )I}@ 7 " # r ~ 7 7 ( 7 | ~> [ 7: [ . ) ~ r 7 7 ( / 7 M 7: ~ 87 0 8 ~ *@~> * 7 NM [ 7 [~ 7+ ( | @: 7: 2~ 7 ! / 7 # H[~ 8 - " 8 ~ r r ~ 7 ! # 7+ - > D D4 7 3 2) 9 [[~ : r 7 z~ 7 !D [u 7 8 r9 * : 7 8 7 ~ 7 r~ ! 6 7 ~ 8 787 t[~ 8 " ( ^ !( 7 ~ ~ [ 7 7 7 h~ 7 7 !S~ ) 7 ! 7) r~ ! ~ 7 6: r 7 ( 7 7 u [ 7 7 ! 7 7 7 I ~ 7: 7+ 8 $ # 9 *@~> I * [ 9*" : 7: ! # r r : 7 ~D ~D u [ ~ 7 ` [~ 7 7 7 7 G~ : ~D 2 r5 ~ 7 . ~D $ 1) 6^ 8 .: % H [ r ) 6 #"^~> ~ $ B$ 2R~ 7 !: *2 r 2 r : 9 * |B~ &I~ & 8 ~ 8 r rH~ 7 ~ [ ~>~> u r 7 7 K & [ : r 7+ ) 8 : [ / 7 7 7 7 @ }@ 7 & ~> ! 7 7 7 ~ r~ 78 ~D[ : 7 : 8 R.B~ & 7 ! 7 r G*2 r m 7: ~>~> r r ~D + 7 !8~ 7 ! ! ) ~D ~D r [ : 7: # |~D r8~ ~.~l 8 7 ! 7 [~ 87 7 8 S ~>~> u r ~ 7 ~ *@~lt i~ * - 05: : | ~> 7 G r : 7 ~ 87 ) 0 7 ~ 7: ~ ( | 7 Ri~ 9 * : ~>~> u r 7 ~ ~> 87 / 7 ^~ 7 ! 7 7 +2 ) r~ !D [~> [~ & ~D 7 u :r~ 8 8 ~ 7 7 8 7 7 !I 9 * ~>~> u r rQ 7 7 !R~ r .~ " ) ~ 7 # 7 ~ : *"r r ~> 7 [ ~ 8 78 7 ~ ~D ~D r [ L~ A 8 ~ ( 3 7 ~ 7 ) ~D ~D r [ ~D 0R~ #~ ! I ^ !D ~ *7 7 7 m.~ 7 !G *"r : r * 7 7 & 8 [ : 7 !I~ 8 3 : . r r ) [' *2: > ~ r u r 7 7 ! 7 & ! 5 ~>~> r r . 7 r~ # ~> u r ~> ~D ~D r [ #" S i~ ~ 7 r~ |~ 8 u [ 7 1) 0 ~R [~ : .~ & 7 !R G @ !"#$%&'!( ) * +,-/.10 8 7 3 87 & / ~ ~> 7 ! 7 *2 7 : ~l[Mr~ : " 7 ~>2 |0 7 r~ 78 ~ [ 3 8 7 . ! rr 7 l~ [B 7 K @9* 7 .~> G ~>~> rr > ! ~ : 7 7 78 ~ 7 ! ~ ) 7 ~ [ 7 7 ~D" 7 7 + 78 rr 7 G R ~ ! # ~ & R ~>~> u r L 7 ~ i~ !a~ *2 7 : 8 7 3 $ 7 &)K}@ 7 7 .~> 7 7 r : 7 ! 7 7 !R.~ 7 ! ~ ! 7 ) / +,')+/ /- * 4 7 r~ > :P ~ 7 [~ 7 ~(" : 7= ~ 7 7 !( 7 7 ~ 7 . < r 7 r~ * 7 * ) : 7 ! 8 u 7 " = ~ 7 887 :~ # ) [ 7 [~ 8 & - 7 " m~ * 7 r2 [~ 7 !R~ 7 [~ }@ * 7 ! ~ ~! / ~& KACEA F L 2 7 ~ ~D ~ 8 * 7 ! * 7 ~ ~ ~ 7 ~> 7 ~>M* 7 ! # 7 r~ i~) ER~ = ~ 87 - i~ M [ : ~ !D *2 7 :* 7 ! ~ 7 . I~ *7+ ~> 7 ~ 8 m 7 7 ` 7 8 8 # ~> ) ~8 7 7 ~ [ ~D" r 7 S~I.~ * 8 4~ * 7 , #"~ 7 ~D 7 7 ~ 5 ~ r u~ 7 !2 7 ) 6 M~ ~ 7 : ~ 7 8 7 3 *2 . 2B~ 8: [ * 7 ! |~ ~ ^ 7 ~ 7 .L~ z 7 l~ . ! r( (~ + ~ * 7 r ~ 7 m r 8 [~> 7 ~ ~> 7 u # * u 8 *2 7 ( 6 . ! ) .~ i~ :[~>I~ 7 r~> . !z . 7 + B~ 8 7 ! ~ 8: [u 7 * 7 t~ 7 ! 8 . .~ 18 7 3 u r~ 7 ) ~> 7 p~ 8~t ~ ~ r3 8 *2 *0~ 8 * 7 ! 7 ~;& 7 # * * 1> : `~ * 7 ! 7 0~ ~> 7 r 7 &M*2 7 m 7 ! 7 : !r ~ 8 7 7 ~>Q ~ 8 7 3 ! 8 7 ~ 7)( r 2 u 1) ' .1H1" 8 7 8 7 ~ ~ 7 7 4 !~ 8 8 ~(r~ 7 #"^i~ ! 7 J ~ u z L~ i~ " "r2 8+ S2* "[2i~ . 7 ) 9 [~ 7 1 7 !Ii~> 7 " 7 # ~ *& r # 7 ! : 7 [~ ~ * u ! |~> : [ 7 S ~ 7 ~ ~D 7 : # "u 7 ! * 7 *~ ) .~ 4 7 r !t.~ 8 ~ 8+ * ~ * 7 ! :8 r 0 rS~ * 7 | # * 8 7 ! ~p [ : !~ 8 :~.~ r 8:8 7 !I 7 : !r 7 ~> .: 7 ~ ! 8 r i~ 8 8 [~> 7 !7* 7 ! # *0~ .+ ) i~>R: ;& * * 0 7 * [ ! H* H 7 7 u 7 + 7 ~ 7 7 7 2 + * ~ 7 " 7: #" r 7 i~ / . [~DS 7 . * [ 7 *"rG~ : : ^ 7 7 ! 8 " ~ * 7 8 87 RL~ 8r 7 &r [ 7 I: 7 < * 7 ! !r [ ~D 7 ~> ~ [Sr~ JLS~ ~ ) r ~ 7 !G , 7 DG 7 ! (!" ! ,-/.10$ ! L h~ [m 7 .~ i~ t 8 87 i~ I*0~l 5% 7 ! : #" 7 L 7 ! r 7 7 ! ~ " ~ 78 8 ~ r 0i~ r @i~ 7 !Gr~ 7 7 L~ ~I 7 r~ i~ ~ 7 7 7 7 7 [ 8 ( 7 ! 7 7 ! 7 * 7 ! hrR 7 7 7 7 : r~ i~ 2 r 7 8+ ` @~ [0 7 !:) 0 ~ 0 7 ~> ~ : r : ~ * . 7 i~D 87 !~> 8 [~ (2 7 & 7 ! 7 7 !D 7 78 ~ 7 P | 7 -8 [~ & [ 7 [ 7 " 7 ) 9 u [~> m: m & : 7 !Ii~ 7 7 " ` 2 ^~ . ~ : % " 7 ! ~ *@~l 7 87 5* 7 7 7 . i~ 8 7*0~ 7 ~ 8: R u r 7 5*2: u: r ! L~ 7 ! 7 ~ 7 87 !~> ) 0& 8 t 7 " [ 7 " . 7 & * ! *@~ 7 / " L~ *2 ~ & S * . * [ u [~> S: : S ~ : *r0 r~ i~ m~ !D 2& *~ * *0~l : 2*0~ . i~> .~ #" 7 *2 7 *r : ~ ! 7 ~ 8 ) & * -8 : 7 . = ~ 7 = ~ 87 7 7 #1 r [u 7*7 .~ + [ . ) 0 : 7 : 7 r~ 7: r 8 }@[zi~ r *2 7 1 7 7 ~D 7: |i~ 7 B~> #" r z . : 7 R 7: I~ :ri~ ~ 7 |~ . ~ 7 ( -7 ~D 7 ~ i~D ~ [ 7 7 8 ~ $ 87 7 7 ! ~ )-E 7 : * [ 7 7 7 / H #" ~ K r -7 # : 7 [~ 7: / ~ * 7 : + 7 r~ 7: 8 7 ! " 8 0 t`B~ "S~ *2 ~ ~Ri~ #~ ! 2 ) E 7 5 *"r 7 .~ r ~ .~ : 7 i~ - #"^ 7 : 7 | !D #" 7 ) }@ [ I~> [~ + 7 r L~ + I : 7 r~ ~ 87 7 . z~ : 7: ~ [i~ 7 : 8 G~ 7 .~ 7 7 ! .~ : ~ 7+ | > 1) E 7 % [" ~D rK i~ - %8 ~ &~>3 / 7 87 r~ 2O |~>K i~ : 7 ! 7 7 7 *0~ 7 ! 7 ~ ~ & ~D . " 8 : 8.~ (~ 7 .~ 7 7 7 7 ! * -7 " ) 7 &2 : 7 [~ 7: > u 7 [i~ 7 ~D ~ r 8 7 r9 * 7 * 7 : I*@~l 7 *2 7 ( r(~> 8 / * 7 7 r~ [ 7 | 7 7 ! : 7 ! r 2) 0& | &8 7 ! 7 [~ R~> [ 7 ~ . &~ L~ : 7 ~ ~ 7 7 ~> : I~ [~> : ~ : I.~> r 7 ~ 7 : 7 r~ 7: / !D " 7 7 [~ 8 # R.~ r 7 ~ 7 | r 7 7 [~ 2 )% ~ 7 7 ~ 7 R~ ~ 7: | : # + ~> H ~ & 71 :* 7 ~ !D [~> [ : # 7 |~> 7 = L ` ~ 7 !G~ #" 7 8 7 7+ i~ @r~ .~ &2 r 7 / 2 ) ' 7 ~ 7 : 7 i~ " 7 7 " "^~> / 2[~ 8 [~D 8 7 ~D : 7 u 7 |i~ 7 i~> r~ 8 7 [u ~ 87 ~> R~ ^~ 0: 7 !8 : 7 r~ 7: Q [ )$ ~ ^ 7 8: ! 05 ^ "R~ | 7+ 7 ! ~ 7 7 6 7 ! ) ~D I !"#$%&'!( ) * +,-/.10 i~ [ . . 7 7 ^ + 7 r 7 ! 9* 8 ~ ~ : 8 7 3 0- 5 7 " ) 7 8 ~ : 7 [ 7 ~D 7 ~> 7 r~ i~.- E2*0~ 7 r 7 0 .~ ~ 8 7 7 u #' ~ ~745* = 7 [~ i~> 7 8 ! r~ 8 : 7 !. [i~ 7 r~ . ~ # ~ 8:.11 7 ! 8 u :8i~ ! 7 !. ~ # 1) 9 S~> ~ 7 !I 7: [u ~ 7 &S~ 7 ! 7 7- # : 1L"r ~ 7 i~> 7 8 [ 8 pi~ ! 7 !7 ~ L~ # [~ [~ 7 ~ [ 7 7 7 ~>G ~l 7 !t~ **2- i~> ) # /&"* # "! / # *" }@ 8 7 ~ . [ 7 # 7 r~ ^~) }@@ 7 r~ i~ 7 i~D ~ r 7 7 ! / 4 |~ ~ 7+ | > 2 : 7 ! ~ [ 7 7 ~> |i~ 7 7 *2 7 r !D ~ #" r ~ m ~ 7 !. : 7 [ : [! : 7 ! 8+ ~ [i~ 7 r~ ~ R~ ~ : 7 / 83& I 1 2K . ~ > ) ~ D 6 7! ) > ($ * !$ 87 ! # [i~ 7 r~ ~ (~ : 7 ~ 7 G r : 8 m : 7 r~ 7+ 7 7 ! 8 7 ! ~ 6* 7 9 ~ * @: 78 ~ 7: # ~ 7 .~> . [i~ 7 [~ ~> H ~ !~>^ ! : 7 !I~ 7 2~ |~D .~ [~D) }@ 7 [~ ^4~ - % 7 .~> G [i~ 7 r~ . ~ 7 r~ 8:L 7AD~ 8[~> @9* r~> 7 : r 7 7: [uH- ~ 8 / 6 7 ! ) 2)K}@ 78 ~ 7 !G 8 ~ ^ 7 :6 MED A B *2 7 ~Du ~ [ ^~D~D : 7 ~> )@}@ ~ !> # ! ~D ! : ~ 87 ~Du I 7 [ i~> z~D : 7 R ~> )S}@: ~> ! [~D ` K>4D 7 R: ~ r R^ !D *2 7 z 7: [ - . !R~lz ~ 7 ~ ) }@ ..~ 7 +$ 8 7 [~ ^4~ - & . 7 !. [L~ 7 - i G 8 ~ ^ 8~ 8 ~ ~ ~ 6~> 5 7: ~ 7 6 7 ! ) ) Tymbal Abdominal air sac Opercula (controls sound output) 6 7 ! @) > 0 7 7 7 ~#! ~D 2 7 r~ i~ * :m 8 ~ / # *2 7 [ ~> 29* 7 r ~ ~ 8 7 ~ ~ 7 ~D) Tympana (inertial element of the Helmholtz resonator) 7 r ~> 7 7 % 7 r "> ~ 8 2 ~ ~:D r ~ ! : # 7 # / / t~ 8 7 ! 7 r~ ~ I : 7 r~ : ~> 8 ` 7 ~ "> 78 ~> 7: i~ H~D 7 7 7 ~ ~ : ~ 7 8 ( r 7 7 I $ "` 7 ~ 7 ~ ~ ~ 7 ~ rt~ i~ ) , " :r 7 ~ "` 7 ~ 7 [i~ 7 77: ~ / ~8 |i~ 7 8 7*2 7 r !D 7 7 :2 ^~D ~ u 7 ~ 7 # : [ 7 r~ 0 [i~ 7 r~ & ~D : 7 . ~ 7 rr 7 8 : 7 r~Du 7# [~ 7 [ > ~ ~ ~ ! # : 7 ~ " / ~ 7 7 20~ ~ ~ ~ ! # .~ ) 6 7 ! m ) 2 :mr~ ~D 7 ~ " 7 m 7 ~ [ ~ [u 7 [~ 7 7 / * ~ 7 ~ ~ ! + : ~ J 7 : Ir~ 7 7 2~D : 7 / 35 R 1 24 . ~ / * 7 . r # 6 7 ! . ) 2~ 7( # ~ 7 ! 7 ~ |i~ 7 r~ % r / * : (,, 7 ! 7 6 7 ! ) 2) 7 &* 7 > 7 u ~ # [u 7 [~ : r 7 ~ ~ ! : [& # 35 R 1 . ~ @~ : R~ 7 ~I |i~ 7 [~ . ~ ) a.c source fluid−filled cavity capacitor inductor mass liquid neck resistor mouth pressure ELECTRICAL spring force ACOUSTIC MECHANICAL ) > }@ ^~D ~ r ~ | 7 r~ ` [i~ 7 r~ ~ ~D : 7 7 ~ 7 u[ $ : 7 [ ~ 778 u9*" [~ 7 [ > ~ ~ ~ ! # 87 ~ " / 5 ~ 7 7 20~ ~ ~ ~ ! # .~ ) 7 ! 7 6 8 ~Du 7 r~ 7 ~> ^ r !D 7 ~ 7 7 7 7 ~ 8 t~ 7 : & 7 7 ~ / ~ #"^~D : L35 R 1 ~ 328*2 7 [~ : ~> 87 #( 7 ~ 7 [r~l #" 7 ~ )4}@ i~D : 1 0 . ~ 7 7 7 r~> 8 ~ 87 ~Du I 0 . ~ ) }@ I # ~ . ~ r 7 ! 7 8 I ~> 7 I . ~ u : 9 8 ~ * 7 `L~ 7 / ) 2 I 8 ~ * ~ 7 ( ~> $ u9 I # . ~ 7 7 !D1 [ ! * 7 8 ( : ~ ~> * [ 8 ~ &~ : : 5* 7 8 rQ ~ ) 7 &* 7 7 BI 7 * $ 7 7 : : #"^ 7 : . ~ 2 * 7 8~ * 78 ~> 7: [~D~ M .~ 7 ~ 7 ^~D ~ u ! : !t -8 [ " 7 ~ L~ 7 !~ 7 1 ) ~ r a: . . 7 ! . * 7 8 R r : 7 7 ~> ) # ! ( # " # / / }@ 7 A 7 ( 7 r~ ^~.- 7 .~> p ~ E 7 ~ .~ Hi~D $ i~ r ~ * 7 (~ ~> ~ S~ r 7 R " 7 7 . #( ) ! 8: / 6 : : 8 #! : ) ! 8 ) 2 ) Resilin hinge Tymbal plate * 77 R [u@ 7 7 ~ 7 ~ >~ ~D G ~ * 7 ! ) >&0 . Resilin pad Long ribs 6 ($ * !$ : 8 % ! 7 7 # !S r~G 78+ I 7 r~ ^~ ~D )7 8 ~ : L:G 7 ! 8 ~ ~ 7 &: 7 *0~D : ~ 7 ! ~- * *0~D " [ # 78 *2 7 7 7 | 7 . 78 ~ : 4,@BA 7 ~ K$ i~ ) 7 m~ m 78: ~D : [u * 7 S~ . 7 !D !~ 7 Q 7 7 G*2 78 ~ : 7 7 7 !D 8+ 7 !8 78 ~ ~ 87 ~ 7 7 ~> * *@~>3 "[~ : 7 ! 7 2~ ~ + )B}@ 7 7 7 ~ m 78: / 7 ! * - r !D 7 [~ 8 : 78 2 7 : 8: & 7 7 7 ~ 7 !~ .: ~ 7 7 ! 78 ~ 7: 5 8 8 ~ 8 & 87 ! # # 9 * -8 & 87 ! 78: ~ " 8 t r ! 7 # . 78 7 * 7 ~ ) 0 6 7 ! )K=) 78-8 & : r !D 7 : ~ 7 787 / 8 ~ - 87 ~ 5 r 2 7 [~ ~ p S 8 ~ ~ ~ ! * 7 8 & 78 8 "! 7 78 ~> )z}@ S 8 ~ ~ 7 & ~IR~ ~ 7 ! [ / " [u 7 ) 2* 7 |~D 7 & [ 8 7 !8 .~ 8 ri 8 ~ ~ / ~ S~ . 78: i~>m~> 8: & :20~ 7( # 8 ~ - ~ # )I}@: 8: & 7 ! # |~D 7 7 7 ~ 78 78: r~ ( | 7 78 ~> 7 !R~ : * %0" ) ! -(,, = 2 1 Tymbal plate = Vibration 2 1 2 Ribs 1 Hinge = }@ [ & 7 R 7 9* 7 7 R~ & r K}@ 7 ~ D~> * Q 7 ~ ~ 7 7 4 7 7 7 0 7 r~ ^~m ~Du 7 [ Q ~ ~ * @~> R 7 7 ~ D~> 7 7 & ~ 7 R 7 7 ~ ~D * 7 9 * 7 ~> & 6 7 ! ) > " : 8 ! ! ! 8: : 3 ) #! : 8: 8: ) 8: ! 8 ) & 0 8 8 ) 5 #! + 8 ! - #! 8 ~ ~ 7 !.~ 8 & r` / }4~ 8 ) 2 ) }@ 7 7 u [~ 7 : ~>- .~ ~ [O~ 7 *@~>3 8 & 87 !m 78 r~ : ~& [r|~ 7 ^~D ~ 78 ~ 7 !I 8 ~ ~D[ 7 !8 : ~ 7 u : *2[ 7 7)( & ~Du L~ 7 :8i~ ! 7 !..~ ) $& 7 !S~ 8: & Iu` :r L:r 7 ~ # 7 7 ! ( [uu [~> 8 S~ .87 !D * 7 [r|~ 7 r / 7 78 7 6 7 ! ) >2 ) }H 8 ~ [ t~ ~ ~ 7 7 78 8: & 78+ 3 78 * / ) 2 * 8 8 =/=> /@D D @P= @ =/= =/>= / ! 2 } ~ 78 ~ 7 !.t~ D = L = /=> ==D / ! 2 i~> ~ 6^ u 6 / &3 1 2 )K= ) P ? ) > ) @ >)K= }O~ 8 S ) > }@ 7 ~ 8 * R~ # : 7 7 7 ~ 8 ~ r ~ p 7 u [~ 7 ! ~ .~ & 78 ~> 7 ! 8 ~ ( ~>I~ [ 8 & 87 ! # |~D~ 7 7 ~ 78 ) }@:G 7 ~ .87 ! |u [~ 7 ^~D ~ u ~> 7 ! 8 & 87 !8r `u [~ 7 !8~ . # 7 7 ! ( [u) > ($ * !$ Four Clicks of the Isolated Tymbal 1 Rib 2 Rib 1 Rib 4 Rib 3 Amplitude 0.5 0 −0.5 −1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.01 0.012 0.014 0.016 Time (s) Frequency (Hz) 15000 10000 5000 0 0 0.002 0.006 0.008 Time (s) 7 ! ) > > [~ . 7 8 @ 2) 6 0.004 ~ / 2I~ 7 | ! ~D 7 ! / 8+ 2 # & 7 ! 8 / ^~ ~ " }@ ~ 7 & 7 R 7 7 "` 7 ~ 7 [L~ 7 7 [~ ^~ & 7 7 ~ L~ *2 ~ * *0~D 8~ 7 ( ~ #" i~ 8[~ 7 7 |~> 7 7 ~ [~ i~ [ M~ 7 [~ 7 O? 7 *2 G 7 [~ ^~R ~ " 7 ^ 7 7 7 ~D& *7 7 7 ~ L~ |~ `. & ~ ~ 7 H B 7 & [ 7 57 R 7 ~ 7 7 r ~ G @ ~ ~ 7 7 ~ 7 .i~ 7 ~> 7 7 ~ K}@ 7 r~ ^~G[~ i~ m ~> 87 7 I ~ 7 t~ D .}@ D [~> [m #" 7 R ~ P |~ [ ~D [ I 7 . & 7 *2 7 ~> ~ .~ #" ~ ~D 7 r D |~ (~ ~ D }@ 7 ~ 7 87 R 7 r~ ^~R i~ u ! : #! , " 8 "! : : : 8 / " 6 + 8 8 ) # ! ! ! / : ! 8 8: . ! : 8 ) #2) 5 " : # - ! ! 8 :) 9 ! ! : 8 8 ) ! 8 " # 8 : ! : 2 8 . ) ) " ! 8 8 8: / ! ! # 8 ! 8 :2 ! : ! # : * %,$ , ),( ) (,, ? F 6 O? *0~D 8 & 87 !R 7-# ~8 8 ~ 78 r ~. ~ 7! ) > 78: 7: 7 :M ,> [i~ 7 7 A) / u 78 7 7 i~ 7 G + I ~ 7 i I 7 [~ ^~ !u ~ " / ~S . 7 *@~>3 / ~I . # 8 9*@~>3 8 & 87 ! 0 78: 20~ !M* 7 S: ~> 8 r ~ & : 7 ! 8: r !DL~ : ~ 7 78 ~> 7 # R 8 ~ ) E 7 7 8 & 87 ! 2 )R}@ 7 R ~D 7 / 7 : # [ ! i~>H~ * | 7 % 7 [~ ^~ + ~~ 7 " 7 u u 7 : ~ [ " ~ .+ ~ 7 S ) }@ p 7 r~ i~i~ 9 * 8 ~ r~> 7 r 7 7 ~ 8 *2 7 r~ 8 7 8 7 r~ ^~ > ) 6i 78 ~ 7: # |~Dz 8 ~ [r~lt~r 3 7 ! / ) 2) 9 8 ~ ` 7 ~ 8 7 ~ ~ 7 ~7 *2 7 [ ~ R r 7 8 u9 *" 7 7 7 ~ 8 ~ 78 ~> 7: : [ : 7 ~ ~> * [ 8 ~ h~> 87 (~ 7 : ~ 7 ~ 7 i !DS ~ 8 - ~ :~ ) # *"/&!$ ) #% ! /& # /& / }@ 8 ~ ^ 7 ~ | ^~> S~ 8 7 ~ ~ 7 ~D *2 7 t[~ 8 (~ ~535 R 1 . ~ ) 0& * '7 6 7 ! ) :^~M3& R 1 ~> @ : 7 # ~ `~ [& ~ ~ t ^ !D *2 7 .~l ~#!~ ? ) }@8 [~ 7 r :I~ 8 7 ~ ~ 7 h . : 7 ~ " # .~ 8 - I~ 7 r ~ # I ~ ~ |~>3 ` / ~D# ~ r ^ !D=*2 7 . ~#!~ 2 u[ 7 ^~> ~ u # . ~ " ~D[ 7 !8 : * 7 ! ~> 71> / ) 2 *2 [ 7 . " # 1 *2 [ 7 : ~> [:~ 7 !D [ & / ~ 8+ i~ t ~> 2R~ 7 : # r~ 7 ) : zr~ # : 7 r~ ^~ <*2 7 i~ 9 * ~ ~~ t r I9 * 7 R~ r a: ( | 7 ~> [~ 7 8 7 ~> [~ # + + @ ($ * !$ :G9* ~ ~) }@ [& I~ 8 7 ~ ~> 7 [~D i~ . ~ 82 7 ( [ 7 !> S r 7 [~ ~ ~D[ 3 7 !8 > + 8+ / ) 2 z~ 7 ~ + ~ 7: #( ~ ~ ) }@ 7 r|~ 7 ~> 87 # 78 ~> 7 ~>H: i~> ~ : u ~ I ~>m~>*2 7 8~i~ ! [ 7 r[ 7 8 ~ 87 ~ I # 0 . ~ / " 7: 7 : 7 [u 7 ) 2 )4}@ ! 7 + 7 ~ 7 :*0~ ! 7 7 / ) 2 [6I ~ 35 R 1 ~ 7 ~ . ! 7 78 / ) =2 I *2 [ 7 G 8 7 ~D |~ # 9 * ~ 7 : 8 / ) 2 ) 4 i~ I 7 .~ : 8~> [:~ 7 .~ ( 7 & ~> !) ~ 87 ~ 7 [~ ^~ $ 87 & [ ~> !L*2 ~> 7 / ) =2 7 ! : ~ [L~ 7 r~ ^~> 7 ! * 7 7 8 ~ ~ 8 7 ~ *@~ @ ) }@ !D!: ~ 8 7 ~ ~ 7 ~ 7 ! r~ ! ~> ^~D ~ 5 u ~ : 8 ~ @~ : r~ 8 t.~ 8 " 7 !p t~ 8 ~ : 7 t~ : 7 ~ r ) }@ t 7 ! z 8 ~ ~ : ~ 8 7 ~ [ 7 ~ ~Du 7 : ~ # R 7 ! : ) : R9 * . ~ ~D * P .~ 8 7 ~ ~> 87 r~> 7 [ G |i~ 7 r~ 78 ~> 7: # 8 ~ ) ~ 7 7 O S~ 8 * 7 R 7 7 *@~ : 8 8 ~ - : I~ 7 ~ z~ R u 7 i~>2 * 7% 7 & z 7 ` 7 ~ t 7 !m 8 ~ ) }@ ( [ # ~ ~ + 7 ~ r 8 u9 *" : * 7 7( [ I ~ 7 5 * 7 : m~ 7 6 7 ! ) ) *2 [ 7 + + # !0"! @} -#" [ : 7*2 7 & t 7 r~ ^~ 7 * 7 ~ ~ 7 8 7 r 7 ~ r # :3& I 1 . ~ ~D! [~D ` K>4D M*2 7 7 m~ 7 ~ r i !D=*2 7 ~!~> )B}@ ~ ~ 7 ! ~> # ~ 7 [ ~ * ~ : [ : u 7 78 ~ 7 ! 7 r~ 7 ! [~ 871 ~ 7 ~ 1 7 ~ D : 7 7 7 7 7 7 L .B~ & 7 !8[ @ 8 ~ .~ 7 S~ 7 ~ ) H ~ ~m~> ~> !rMi~ 8 ~ / 6 7 ! Q ) 2a[ 7 @~D : 7 9 [[~ : K: 7 i~ " .~> 7 ! 8 u9 *" : 7: [u@~ : 7 !I~ 7 )B}@ 7 ~ * . ~ 7 ~ ~ 887 !8 7 r~ ^~8 | ~ #" [ ! ) ) =2 ~ / ) 2 m ~ ~8~ : ~l ~ 7 + ~ @ 7 u r 7 7 ! 8+ S I 0& " 8 / ~ ^~D ~ u # I~ 8 7 ~ ~ 7 ~ 8 (i~ ! 7 !R ( [u 7 ~D" G~> [:~ ) !"$#% &'(#)* +( +, -.(#/+( 0%12 $3!( 4+(( "05(0 "+"#% 0)76 98: ( ( ; 9" <" ="#>( ?(#@+" 0 [~ # . 7 m~ r ~ : : u ~ I # . ~ ) : # + *" /0*"#% }@. 7 r~ ^~S : 7 #8 & 7 ! 78: M~7 78 ~ 7 !S 8 ~ ~ z~ 35 R 1 . ~ ~ 8 7 ~ ~ 7 ~D) , Q u @ 8 ~ ~ G ~ 8 7 u[ 7 : 7 ! / ) 2O~ / ) 2 i [[~ 8 7 : ~> + 7 ! ~ 7 9* B$ + 9* B$ 1 [ ~ & 7 ! 7 ~ 0 : [) 8[~ # : ~ 8 *2 [ m 7 ! 7 7 ~G 7 !D:r 3 r : r 7 : 1)B}@ 7 r~ 8 7 [ 8 ~D 7 ! "r~ . : [ 7 [ 7 ) }@ ~ : . r u 7 ~ 8 ~ ~ M . ~ : [ *2: r : ~> S 8 ~ #" !~ ~ 7 ? 7 ! 7 78 / 2 / / 2 / 2 / 2 2 [[~ : 8 r~ G~ : 7 ~ 8~D ~ `~ 7 7 ~ 7 O 7 M : [ 7 # r~ z~ #4 'B : r 7 ~ # 4 ?> )G}@R + 7 !7 7( r " ~ 7 7 ! 7 8 / ) > 2 / 2 / 2 / 2 / 2 / 2 }@ m~ 7: # [~ + 7 u@~Dr 3 7 ! 7 8 ~ * 7 I . ~ : 7 ! : * 7 !R~ " 7 .~> ~> 7 ? / )K?2 *2 [ 7 8 ~ * 7 `S~> $ 9 7 3 1 / 7 ~ 7: 7 I 7 ! 7 7 ) 2K~ 7 ~> 87 ! ~ ! u r 7 : ^~> ~ uS~Dr 3 7 ! r 7 ) }@ / )@ 2 }@ 9 * .~ 7- ~D ~D r [ @ : [ : ^~> ~ u ~ GI / ~ r ~ $ 7 `: 8 ~ .* 7 + 2 u r 7 i~D ~ [ 7 7 . ~ 2~ [~ 8 8i~ ! ~D[ 3 7 ! [K ~D ~D r [ 47 [~ )$ 7 >.~ & 7 ! 7 ~ #/ 7 H~ 7 [~ 7 : [ ~ 7 r $ .~ " 7 ~> 7: ) ~m ~ M 7 QL~ 0 / ~ 47 2r~ O 0 8 ~ 7 : 7 ~>~ / [~DR 2 * 7 . r~ 8 *&2 D 7 # 4 : r r~ 8 ~ : [ ) 8 7 !I " 9 ! $#&% > ($ * !$ Two−pole, two−zero resonant filter with a frequency of 2205 Hz and a Q of 18 Magnitude (dB) 50 0 −50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Normalized Frequency (×π rad/sample) Phase (degrees) 100 50 0 −50 −100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Normalized Frequency (×π rad/sample) 7! 6 7 Q) @ > t~! 7 Q~ i~ # Q9* B$ + r9* B$ 1 [ 8 7 ~ `~ 7 : r )4}@Q . ~ u r2 DD/=I3 1 / * 7 t~ ~> 87 !I~ # D2Q~ I @:) }@ [ @~> H9* 7 O 57 @ [~ [u @ ~ * 7 8 i~> ~ 7 |~>K2& 3 1 7 .~ 71 2 ~ ~ I r 0 ~> 7 .~ r [ ~> 7 r R 7 7 ~> 7 ~ 7 7 7)( r R r 7 7 ~. G "~ 7 ^ t~ 9* B$ 7 7 ~ *@~ 7 ~S R r 87 r ~ ~ *2 r 7 ~ 7 [ 7 9* B$ 7 7 m~ r [ 0 ~ [~ I9* 7 7 7 ( 7 S9* 7 ~ `~ 7 r 7 ~>~ | }@ ~ 7 [~ m9* 7 ~ }@ i~> ~ r 2 ~> 57 r~ ~> 8~D[ 7 B 7 0 2.~ 47 r r 7 8}O~ m D r 7 7 .~> 7 8L~ 7 7( ~D ~D r [ ) = ! : # : 8 ) 8 ) . . 8 # : + ! # -) ! 8 # : & ! : : / 8 3 ! : # / ) 2) 8 # # 8 ! " : : 2 ) : : ! : 8 . 8 ! : # : 8 8 8 8 8 8 ) " ! ! * %!$ ,$ 7 &~ R . ~ >: 7 ~> 7 ! 8 ~ 7 7 ! " # [!i~> 7 7 8 5 ` 7 8 . +& 7 # #"^ 7 ~> 7 [i~ 7 -)O}@:r 7 3 [ K 7 ~ " . S:r : 8 2& 7 #57: *2u r 7 8 : ~ r2 ~ 2~ 7 7 7 ~ 7 ) @9 * 8 7 ~ ^ ~> 7 : [ 7 7 7 ~ ~ ~> 7 ~ 8 * 7 Ii~>R 7 ! 7 7 % B^ !D 87 !m H 8 ~ [~ 7 0~ 788 & )B}@ 7 7 % #"^ 7 ~ 7 7 ( ~ r 7 / ~ 7 : 7 8 ~ ~ .~ 7 78 ~ 7 ~G ~r ~> " # #"^ 7 ~> 77 ) 8 & 87 ! 7 ! $ 3 *"r D i~DI 7 ! 7 : 7 & 7 7 ~> 7 ~ ~ ~ 7 2 8 ~ ~ =* 7 : I* 7 ~ 7 ! # 7 R~ & ~>~> r r ^: 8 7 ! " (r~ i~ ! : 7 [ ~ 8 ) 6 |~D A / r 7 !2 " #+8 & 7 ! 78: 8 0 : Q ~Du 7 2 : i~ ! 7 !.~ ~ r }4~ 8 m ) 7 : 7 r D~ 8 : rH #/ 7 ~> : ^~> ~D[ 7 ! ) 9 [r~ : # ~ ~ 8 ^~ ~ 7 8 9 r $ < ~D' & @ 7 *0~ & 78 r r 7 : 5 ~ : I 7 8 u9 *" [~ 7 # 8 & 87 !G~ I ~ 7 ~> : %# r !D8 |~ 8 |~D 78 7 8 & 7 ! / 6 7 ! S ) >2)7 [ R: 8 & 7 : ~> ! [ ~> (~r 3 7 !. 7 ^~ 5~ *2 7 : 7 ! r i~ .~> 7 ! 8 u9 *" |~D 8 & 87 ! *@~ # 8 ~ ~> @r~ 78 " ~>0 -# 6 7 ! ) : ) 7 ) 05 #"^~D : K }@ #A [ +-7 : B~ "`~> 7 *2 78: 5 7 ! 8 ~ &. 7 m #" i~ ) }@ 7 r 7 & (~ S IR~ # ~> 7 : 7 r~ : ~> 7 ! : r ~ @ 7 7 ) ~ . H ~ 7 ``6* 7 > > }H [ ~ ~ ~ * 7 ` 9 9 ! 0 #( 8 % + . 0&8 ! ~ ~ ~ 7 & 3 ( | 7 ~ 7 |~ & !D~>7 ~[~ ~ 7 ~ D . [~> 7 r ~ r u >}H }O~ 8 8) > "`~D ~& >D ) A EA; 'A = ? > @ ? # $ L K?> > => +) 'B =BDGF A K= > @ ? @ >? = ) + ; 7 R R R I u R R && 33 11 ~>~> u r& ~ m .~ 7 9 * 7 [~ ^~ [ 7 L ) $ ~ ~ .~>,& * 7 7 D ($ * !$ &% "')(* ! "$# L }@ 7 7 ~ J * 7 ~ D~> # 7 [~ ^~t * ~> ~ ![ # ~ : [ ) 0& 7 )7 7 r |~D 7 G~R 78 8 & )Q}+* ~ : [ / 2@~ / 2 [~t a>~ ~D 7 D~ ~ 8 ~ *2 7 r~ . ~ : [ / 2 >~ ~D 7 [ 7 D~ 7 r@ : 7 ! 7 : ~ 8 ) 7 6 7! ! ) > ! : " " : * %!$ ,$ Tymbal Output Amplitude 1 0.5 0 −0.5 −1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.014 0.016 0.018 0.014 0.016 0.018 Time (s) Tympana Output, Q=9 Amplitude 1 0.5 0 −0.5 −1 0 0.002 0.004 0.006 0.008 0.01 0.012 Time (s) Tympana Output, Q=18 Amplitude 1 0.5 0 −0.5 −1 0 0.002 0.004 0.006 0.008 0.01 0.012 Time (s) 3~ R 7 ~ ~1 7 }@ ~5 *@~ ~ L* 7 !~D I JL z7 . G~ ~ ~ I ~ 6 7! ) > & . 8 #) 8 / : 2 8 / 2 /8 # @ ~ ~ r 8 7 ! ~ ^ !D 2G 7 !( 7 r~ i~.- ($ * !$ }@ Q ~ 7 O ^ G~ 7 7 ~>B ~ r K# 4 4 87 @~ 7 ~ ~ 7 ~D 7 r@ 7 7 7 ^~I 7 D r [ r 7 ` 7 7 9* 7( [ | 7 7 r~ ^~~ 7 }4~ ~ ~ 7 t r~ r~ ~ p~Dr 7 = }@ I ~ z ^~> ~ u 7 I ~ ~> [~ ~ [ i~ 7 S~ ~ p~ 7 t [ ~ ( | 7 7 u [~ 7 . 8~D |~ ~ ~ t~Du 7 * 7 7 7 [ 7 I r / 7 ^~D ~ t ~ 7 7 [ & z~ : ~D u M 7 ;*@~ 7 |~ ~D 7 ~ * ~ 7 7 7 r~ r ~ G r * 7 H* [ 7 7 7 7 7 7 7 8 .i~>m 8 ~>:*2 7 |~D 7 7 7 ~ 7 & 7 7 [ 7 * 7 ~ '7 r |~ 7 I ~ 7 ~ ~> #) # : . ! / : # ! # ! " 2 8 : ) / ) 2 ) / : + ! ! 8 # : # 8 8 ) # # : ! : 8 2) 9 ! : ) 8 : ! 8 " 8 2 ) 4 8 88 3 3 ! . ! : / 8 8 : : ! : : ! 8 # ! 8 ! 8 8 " : ; ! 6 8 ! ! ) ! : # 8 ) # + *" "! # & }@ 7 r~ ^~ 7 7 [ ~ ~ ~ "r ~ :8 [ / 7 < !D~>R 7 ! ~ ! ~!2 * 7 7 ~ 7 [ ~ 7 . 9*0~D 7 [~ ' / ^~> ~ 2 @@ ) 0 r # :8 7 r~ ^~ 8 [u 7 ' 7 * 7 6 7 ! m) )O}@ 7 7 *@~ [u 7 |~ $ 7 7 r~Du 7 7 7 7 u ~ r ~ * 7 ! m ~> 78 787 =* 7 [ 8 [ ~ S r~ [~ 2* 7 *2 7 7 [~ 8 : 8 + 7 7 ~ : 7- 7 : 7 r~ [ .~ ) }@ 7 ! 7 ~ [ H 7 [~ ^~I*0~ ~ ~ 7 [ 7 5! *2 7 ~ * % 7 R .$ 7 r~> 7 7 ~ $ G* 7 R 7 r~ i~ 8 | 7 ' 7 / ~ r m 7 [~ ^~ 8 [u 7 7 7 7 * '7 6 7 ! ) 2 )B}@ 7-# [~D : !r 7 : ! `~ * ~ ::" [~D i~ 1 7 7: 5* 7 S~ : 7 ! 7 6K )`}@[ 7 ~ ~D 7 ~ 8 5 ~#! / 8 u9*" $ = 2 [~D : :*2 7 7 7 ~ 8~D ~ : 7 ~ + ![ ) }@ 7 ~ ~ ! 7 ! ~ 7 ~D : : 7 !I~ ~ ~ ! 7 ! 7 ~ rr / 0 /? 2 8 8 7 ! 0 9 ~ 7 I ~D / ~ !D~>R.~ 8: 7 u B$ r 2 )m}@: 9 ~ 7 8~> 7 * i~ : 7 ! ~DR I | 7 ~ " ~ ^~> ~G | 7 - i~ )O}@: : ~ # : ~> 7 ~. 7 : [@ $ @ ~ ! * 7 t~. $ 2i~ 5 [~ 6K ~ ~ l~ @ 7 7 r~ 7 ! I~D . G~ 87 ( i~> + . ) }@ 7 7 [~ 8 8 u9 *" ~ ^~> ~ 7 .~ S ~> 7: ~>~> u r # ) ' ?- 7 718 [ m~ /= 6* %!$ ( + 6 7! r ) >%0 - # 7 [~ ^~I 7 ' 7 ) @} ^ 7 + ~ ~D ~D r[ *2 7 ( 78 : ~ G 7 r~ ^~.- ~> ~ # ~D 7-# : 8 ~ : L: # : 8 ~ *2 7 7 : 8 r # 78+ 5 8 ~ ~ 7( # ~ ~>6~ 7 ! 8 r9* : 8 ~ ~ : ~ 8 7 ~ ~ 7 ~D D ) ( 240 /!# GF 1* #(& $ 7 ! : | 7 < 7 [~ ^~:D ~ # + m ~Du 7: [~ ~> R~ !D [~> [~ ) 3 *"r 7 | 7 *2 7 7 57 8 ~ h ! 7 r~ -#"^ 7 t + R ~ 7: r~ [ ~ ~ ? 7 [ | ) }@ 7 ~ 7 # #" r ~ G~ 8 r 7 ~ 8 7 7 ~ .~ ) }@ ~l[ | 7 G~ # ~D 7 : :r L~ G [mi~ G u 7 7 > 7! ($ * !$ @ t ~" ~> 7 r : ~>Q : 7 7 7 ~ G . 7 : + . ) r ~ 8 7 .~ 8 ~ " u r ~ ! 7 7 ~ 8 ~D& D~ 7 R~ 87 / ) 1 > 0 ' 2 : : ! " # ! # . 8 ! ) ~ 6 8 & 87 !t 78: * 7 . ~ ~ + . 7 7 !:)t}@ 7 |~ : ~lr ". r 7: ~D ~D r[ ) : ~l 7 !I 7: 2:r ^ : ~lr 7 5 &" | - " 7 [ : . ~ 7 ~ ? : ~ 7: & r | ) , # : .~ 7 " # r2 : 7 7: 7 i~ 2 .~ 7 78 ~ & r~ 8 : [) # C 0& 0& (E: 8 <' ! }@ # 8 ~ [ 7 R~D 7 z ~ # 78: / *2 7 * 7 ~> 7 !"` 7 ~ 7 7 ! ~ *2 |~D! 78 8 & 2I~ 8 [ # 78: 8 ~ / *2 7 ~> 7 8 r9* 7( [ [ 7 2 ) 0& 7 ~ 7 : 7)( : ~ ~>) }@ m l~> 7 78: 7 ~r 7 : :8 R~ * 7 ! : rH i~ !@ i~ 7 7 ! : 7 !D~ * 7 `1 # GL~>R 7 ! 7 : i~ 7 G 8 ~ [~D 7 I~ 788 & ) 9 m A) S r *2 7 5* 718 u 78 7 8 : 8 & 87 ! # 78 2 )}@: 8 [ # 8: & 7 ! 78: 7 ~ . ~ i~ ![~ 8 ~>~> u r ^ ! #" r 7 * [ ~ 7 1 7 8 [ 8 : : [R u [~>t~ 7 [ 7 ! ) 860&#% }@ ^~> ~ u 8 ~ . ~ 7 u r 7 8 / ) 2) |r~ L~ 2: 8 ~ 8 ri~ 187 &@~ .~ ~ 7 ! [* 7 8:Q [~ 7 r (8 7 !0.~ 0 8 ~ : ~> ~ 7)( % @ 8 ~ - ~ )K 7 @: 8 & 7 ! # [~ 7 7 7 ~ 78 78 ~ 7 u [~ 7 r~ R~ # ( 8 ~ 5: ~>~r 7 ! }4~ 8 ) 0 ^~D ~ u 7 u r 7 7 .~> 7 8 : 7)( / *2 7 7 8 : ~lr 2 ) 9 7 % 7 : i~ ! 7 !I 7 1 ^ 7 * 7 . 7 + . ~ @ 7 !6* 7 [ i~> ~ 8 7 ~ ~> u [~ 7 !R~ ~> 7 ~ 8 #" 7 7 ) }@ : ^~> ~ + r # ~ 8 r~ 8 8 .i~ ! 7 ! 7 [H ~D|~ 2 ~ ~ / 7 ~ D 7 ! [ ~ 2 5 # ~ 8 7 ~ ~ 7 ~ # : ~D[ 7 ! / ) 2)K}@ r : 0~ 7 r~ ^~ i~ ~ 8 787 8 2 + 2 u #7 . ! ~ & 7 ! 7 !D ~ : # .~ 8 7 ~ ~ 7 ~# 6: 7: [ 7 8 (.B ) =2 7 7 i~ ! 7 ! ~ 8 r 8 Ri~ ! 7 ! : 7 7: [~ ~> m ) 0 / ~ ~~D |~ * 7 ~ ( [ 8 I # ~ 7( [ )p}@ 7 ~ : ~ r 7 [ 7 ! # [Q ) }@ . 87 ! : R 8 ~ ~ 8 7 ~ ~ 7 ~D h z : ~> u 4~ * )5 ~ 7 7 7 r |~ 7 !R L: [ ^~D . ~ ~ 7 ! ~ [ r ! ~ ~ + r 7 u u : : 7 R~D . ~ / "6 7 ! G ) : ) }@ ~ # . t[~ 8 .i~ ! 7 ! 7 r~ 8 t~ r 7 ! 8 7 ! 89 * . ~ ~ 7 ! : 7 ~ 7 r L | ^~> S~ 8 7 ~ ~> < * 7 L~ G~ ~D 7 ! ( [u 7 ! . ) / +/& }@ !D: . # Q 7 r~ i~@ 7 [ 7 [ 7 ! ~ "r ~ 7 mi~ + 7 r~ #+ 7 ~ C ~D 7 ~D *2: ~> 7 ! K 7 ! 8 u9*" :K 8 ~ ~ Q~ 8 H 7 & 7 !m~ . [u # 7 u 7 [i~ 7 7 / 7 r * 7 *2 7 7 r~ ^~ 7 ~ 8 I : .~~ 7 #(8 & 7 !R 78: u [~> [ " ~ .+ ~ 7 ) }@ !DI ! 0 r 7 r : " : 7 ! ~D ~D u[ . ~D2~ 8@ 7 ! 7 7 / 7 " 7 !8 7 ~D 7 ~> 7 [i~ 7 -) t~ 7 ! [~D # ~D ~D u[ : : " i~ 1 0 ~ : ![ 7 ~I ~>[@ 8 r .~ 7 ! ~ "! ~ 7 @ ($ * !$ : : [<* 7 (~ 7 7 7 : *2i~> M 7 87 !+) }@ 7AC 7 D 8 [u ~ : ` 7 47 8 : u 7 !~ [ *2 7 7 : [ 7 * 7 ~ 7 7 ! ~ i~ 2 7* 7 S: - 7 m~ + 7 r~ 7 7: ) : r # # #%* / + / & / # }@[ 7 ~ ! " 7 # : [ ~ [u 7 8 : 7 I u [~ : ~ 8 7: * 7 7 *2 7 R : 7 7 ~ : ~ R~> 7 r~ 7 [ ~ * 7 R: ~D 5 ~ I 7 ~ 7 8 7 ! K* 7 ~ + 7 7: )K}@ ! 7 ! 7 ~ | !8[~ 8 &[ r * [ 7 ! 8 I~ * 7 ! + 7 7 ~ - u [~> 7 7 I #" ~ 8 r : ~ 7 7 8 7 [~ |~ 87 . ~ [ # ~> 7 :m .~ ~l[ 8 ~ 8 ( | 7 7 [ ~ 8* 7 . & 7 ~ 7 r~ [~ 7 8~D 7+ | 7: ) * 7 + | 7 : 7 r~ 7: }@[[ 7 @D `i~ ~ 7 87 7 , # 7 7 ! h~ 7 7 t ~>~> u r ~ 7 t * 7 Gi~ (~ 2* 7 ( r~ & " 7 6 7 ! :) # ~ ~. . + 7 7 i~ ~ * ~l [@ + 7 7 7 ! " : L~ 7 + 7 ~ r : 7 [~ )1 7 # 7 l 0}@ r r 7 7 /. 7 & u 7 7 71 7 " ~ G ~ & 7 ! L~ 7 " 8 ~D &*2 7 .B~ & 7 [ ~l * 7 [ 7 7 ) 7 7 .~ r * [ D . 8 I }@ [ [ 7 `~ [ : ~ r p~ < ~>~ & 8~ 7 ~ ~ 7 ~ a r t G ~ 87 # 8 7 7 ~l ~ 7 7 ~ ~D : 7 7: ) }@ 7 7: 7 ~D .~ r t * [ h~ z~ ~ 6 + 7 " 8 2}@ [ [ 7 7 (# 7 7 8 "[ 7 ! $ 7 ! ! 87 ~ 7 ( [u ( 9 7 }@: r r 7 7 "r ~> # 7 + ~ " # ~ ! 7 " 7 " 7 `~D & )}@ #187 7 : ~>~> u r ~ ~ *7 7 7 R~ 7 ! *2 7 7 * 7 ~ * : ~l [K : " r@ + 7 r~ 7 7: ) ~> ~ ~ :: ~ 7 S r i~> 7 7 7 + . 7 M }@ 7 5 7 [~ ^~ r 78 7 ?#4@BACEDGF 8 & 87 ! 78: i~ ~ 8 .: ~ 7 78 ~> 7 # : L D } 6 7! * }+* $ i ~ " D~ " 7 [ ~ 7 * 7 }@[[ :) > 7 9 0 9 0 ) [i~ 7 R ~& 7 ! u 7 7 # 8 & r` 2 / 7 ) 7 i~ r D~ r~ 2 +# : 78+ 7 u [~> ~ 7 + ~ ~G : 7 [~ r 7 [ ~ . : 7 7 #" 1) / / +# "+ # * # "! # + *" " +* '. 1 - ! [ ~ ( 7 i~ ~lr 7 :: r !D : ~ 7 ~ ~ 7 7 : 77# ~> *2 7 8+ * 7 !R~ 7 ! 7: 0: 7 : 8 * 7 ! 7 : ~ 7 ~ ~ * 7 7: ) $ 7 u u #"^ 7 ~> 7: [L~ 7 (~ & 7 ! L~ 5 [[~l ~ r2~ [ 7 # 7 ) 05 !D 7 2.~l 8 R ~l 7 & 7 ! ~ ~ 7 I r 7 ~>m~ .: ~ 7 I ~ 7 ~ 7 R 7 ! # ~ .~ 87 D 7 7 [~DS~ ~D &I 7 7 ! ~ 7 ~lr- ~>`~ [ ~ 7 7 r r #"^ 7 ~> 7 * 7 7 [R~ 7 ! 7 ! 7) [~ [ ! ~ 7 7 ) : 7 r~ 57: * %!$ + , (1. ) & 7 ! |i~ 7 i~> 7 7 7 ~ ~ .+ ~ 7 |i~ 7 [~ 78 ~ 7: i~ 8 : 7 7 .~B&r ~ [ . R~& 7 ! 7 r r 8 r 8 p~ 7 7 ~ : 7 r~ 7: ) }@: 7 # 7 [L~ 7 7 R 7 r~ i~ 87 8 7 M*@~lI [i~ 7 ?*2 [ 8: & 7 ! 78 r~ + 8 R : . ~ 7 r~ 7 7 7 ~ ~ $ u 7: 7 ~ "^ 7 ~ 7: L~ (~ .*7 :G 8 I>?#4@A)EDGF*2 7 t~ * I 7 r~ i~I [~> ~Du 7 #" [ S ~ 7 ) 9 |i~ 7 78: / 7 r=* 7 ;*2 7 :G 7 r~ ^~ 7 7 7 ~> ~ : ~ 7: 7 ! [~ 871 ~ 7 ) }@ 7 i~ r u 78 ~p : 7 r 7: 7 8 7 r~ ^.~ - 8 & 87 ! |i~ 7 ) }@: A) *@~ " r [ 7 *2: u: rO 8 & 87 !m [i~ 7 8 : 8~ #/ 7 u r 7 8 I~ ^~ S 7 ( | 7 ~ ~R : 7 r~ 7: )@}@: 8 S~. .~ i~ *2 7 7 ~( [i~ 7 r~ : r 7 [ ~ : 7" 7 7 ! 7 # : S 7 r~ ^.~ - : Q~ !~ * + [8 R~ 7 ~ ( r 7 [L~ 7 u 78 7 : u 7 !~ i I 8 ~ 7 7: * 7 ~ ~ ~ ~ [ 7 : [u " 78+ i~> ~ : 4,@BA [.: ~ ~D 7 !8 : ? ) : 8 8 ~ + R ~ LI 8 ~ ~ 7 : 7 *@~>3 t~ ~ ~ * *0~D ~ ~D 0 78 *2 7 7 7 | ) }@ 7 7 / 7 @ r~ + 7 : ~ 78 8 & 7 *@~>3 ~ 7 ~ 78: ~> 7 8 ~ ~ 7 787 ^~ 7 7 ~> 7 #"r #" 78 7 Mr~ : 7 ! 7 -8 & ) $ 7 ! * " 7 ! r~ : 8 & 87 ! 78 B~ 8 r #5 .:8: G 78+ * 7 8 & 7 ~ 7: ( [u *2r |~D 8 788 & rG " # 7 7 !D 8 7 !( 78 ) $ 7 ! r 7 7 [ ~ 8 u9*" + 2 ~D 7: *2 @ 8 ~ : 7 ~ #|~DI 78 i~> 7 57 ~ 7 *@~>3 $ 8 & 7 7 ~ ^ 7 !8 78: . " r~ 8 |~ ) 7 ! 8 ~D &. 7 5 7 ! 7 ~ i~ ^ [ 78 7 8 & a R 8 ~ ~ 7 7 I 7 ~> r 7 78 ~ 7 ) 0 r }@ 8 & 87 ! #% . [ 7 !R 78: 5 : 7 [ * 7 8 # r !D ~ * 7 !8 78 ~> 7# : 8 ~ : ~> 8 .+ ~ 7 ) 0& # # " /0*"#% }@(}Q 8 ~ 87 8 ~: * 7 6 7 ! :) 7 7 7 ~>I ( 7 r~ ^~.- 8 ~ 7 i~> 7 : 7 # ~ #& . #" 78: [~ ~ 8 # 8 & 87 ! 7 ~p [~ i~ )&}@(~> ~ ![ ~ 7 * 78: 57 ~ 7 [ 7 7 # <&r ( ~ & ~ 87 8 ~ * 7 |~DI 78I 7 ! ~ 8 i~ ?- + + ![ ~D 7 ! 8 u9*" 78: 8 7 ! ~ : ~ 8: 7 2 + [) r@: 6 7! } * 9 0 9 0 }@ 7AC 7 ) :) > : r ~ : 7 ~ / 7 * *@~>3 I ~ 78 7 8 & ~ * 7 6 7 ! :) :) }@7 [! 7 ! ~ ! r~ 8 7 7 * 7 ~ : 7 " ~ p7 7 # : : r - + ![) 0& * 7 p. 8 ~ 78: *2 + [ [ 7 NM [ : !r P + ( [u 7 r 7 !8: ~ 87 - * *0~D - 78: * 7 7 ! 8 ~&. 7 7 ! 7 ~ i~ ) ~ 78 7 ~ [ 8 .~D 7 S~ 7 7 | / 05 7 " 0 ~ r 7 7# : .~D 7 7 !t u 2 ~ . 7 ! [ 7 7 r~ [u ~D 7 R:7 7 pi~ 7 . . + : " 7 ) 0 7: ~ 7 6 7 ! ) : ^ 7 .~> 7 ! 7 !I : 7 7 78: 7 . 7 ! r 7 ~ . 78: 7 . 7 ! 9 2 ~ 7 7 !2*2 7 r~ 8 2 0 / !DR ( K * 8 7 8 & G 78 )H 7 ! 97 6 7 ! ) 7 ~ " ~ : 7 7( @ m 8+ 8 & 87 ! 78 ) 7 . 7 ! 9 m 78 * : R r.~ 7 7 ! +: 78 H 77 7 *@~>3 $ 8: & 7 7 ~ * 8 2 7 7 ! 7 ~ i~ 0 ~l r - + ![ 7 |~ ~ S * *@~>3 r ) - [ @: |i~ 7 [ ~> [ `~ i~ ! 7- 7 ! 0 / 7 R~D 7 ( [u 7 ! 7)( 28* 71 7 & 7 ~Ii~ ! 7 7 ! 9 / ~D 7 " : Q 78 8+ :2)O " r 7 ~ 7 7 7 ! r~ 7( [ : r *0~ 7 8 u 87 ! 8 7 ~ 77 7 ! i~> 7 : 7 !D " ~ +: 7 : " 7 ) : }@ !D& 7 ! ~> $ [ H [ 7 ~z |i~ 7 7 : ~ *2 7 !~ * : rI ~ : m 7( ~ 8+ / 8 2 # G 78: )0}@ 5 ,> * 7 6 7 ! :) =i~ *: [i~ 7 r~ 78: 8 : 7 ( [u 7 .i~ ! 7 ! ~ ! 7 0 ~ )(* : ~ ~. 7 [~ ^~I.~l i~ ! ~> : r !D [~ 8 S~ 8 & 87 !. 78-8 i~ ! 7 !I ~> 7 78+ r~ : : rmi~ ! 7( 5# |i~ 7 r~ 78-8 S~ : 7 !. : ~> [~( 78 ) u 7 ! : 5 : * 7 JL~> G 78 hR~ & 7 ! 7 7)( ~ [~ 7 rm 8: & 8 .B~ & 7 ! 7 0 8 r )4}@ !R 7 * 7+ m~ *rH~D : 7 7 : 7 0i~ 8 # ~ * 7 !8: : [2 ~l )7 ~ 7 r" 7 ) 7 &* 7 : 7 !.~ 7 *@~>3 7 u [~ * ) ! ,$ 6 7! }@ [H- 8 & 7 !. 7 ) ) > > } * 9 0 9 0 A A B B 6 7! }@ ) > " ~ 7 : ~ 7 . 7 ! 7 ! 8 & 87 !+) Rest Position Buckle Position : 7 S ~> # 78 O.~& 7 ! 7 87 ! 7 / G 8 & r ! r~ 7 !t~ 7 !D[ ~> 87 7 ! ~ ~ 7 8 & 87 !:)G}@ 7 ~ : * 7 i~I~ ( | : 7+ ~ 8 [[~ : : *@~l 7 ~D 7 r !D( [~ 8 ~ 8: & 7 ! 78 ~ " %# : 8 r # 78: L~ 8 & 7 " 7 i~ ~ ( [u r~ . ) [ 7 # 7 r~ i~ : .~lI ~DuQ~ .~ > 7 [ [ 1) $ 7 ! ! 7 r~ 7 7 7 ~ : ~> ~D 7: 7# 7 [~ ^~ ! 7 7 (~ 7 ! 7 [~ ,& ~ l~ #~ ! [ #~ ! 7 t .~ : !r ) E* 8 z~ 8: #" [uS~ .~ 8 & (: [i~ 7 r~ 78: * 7 ~p u 7 7 ~ t ~D ~ 8 S i~> # ~ 7: [ 2~ 7 [ ~ 7 * - : [ ( [ u 7 7 ~ 7 7 7 )@}@ [i~ 7 [~ [@[ 8 ! 8 : r~ r !D ! [ ~> 8 : 8: & 7 ! # K 78 D~ 8 ~ 7 7 ! ~ 2 r P= * ) ! ,$ 6 7! = 7 R: 7AC 7.- : ) :) > 0 : ! ~ r ~> " : " 7 ! r~ 8 ~ 7 7 ~ 8 & 87 !I 78: ) }@(~ 7 7 ~ ~ ~ ~! 7 7 ! 7 i~ ~ . 78: ~> 8 t 8 p : r ( | 7 7 7 !G : r<* 7 : 7 8 ~ i~ m[~ 8 - 7( r S~ : ~l 7 )%* : K~ 7 [~ ^~i~ 9* 8 ~ 9 7 [ 7 7 ~ 8 7 ~ ~ 7 ~ i~> r~ 78 G 6* 7 ~D ~> + ~ S S 7)( r u 7 :*0~ 7 ~ 8: L~ 2 7 ~ ~ ~ 7 ~ 8 2 : : r # }H 8 ~ 87 8 ~)B}@ 7 # 78: 9 .~ [~> ~ 8 . ~ 7 ! 8 & 7 ! " &! r~ 8 I : [Q ) 7 : r* 7 78 8 Ri 7 . 8 ~ Q~ )7 7 7 ~ & ~ 8: =* 7 & ( 7 # ~ : !r / 7 8 r # 8 " ~ 7 ~ r 7 # : G r 2 ) $ 7 ! * 78+ ~> .~ 7 r ! ~ 7: ~ ` R 7 ! : !r r ~ % 78: r~ r |~ ~ * 7 ~ ! 7( [ . ) [0~>m~ [~D #~ ! 7 7 * i~> : r 0 887 r + ~> 7# *r r~ 7 ~ 8 R : 7 # [i~ 7 7 !D~ 0 7 #~ ! : r5 *r )K}@ K*@~l 7 ! $ ~ 8 [i~ 7 r~ + I 78: Q~Du ~ 8 7 ! ~ . 8 ~ & ~> : r5 r 7 G [= *r 8 & (u [~> ~ ~ 7 .~ -#"^ 7 r 7 . 8 " 7 + ~ " 5 7 r~ 7 87 7 i~ 7 + [ 7 r ~D" 9 u 7 ! : r ~ [~D * *2 7 7 ~D@ # - r & 7 7 ! # : 7 [~ [ )K 7 7 [ : ~ 7 ~ : ~ 7 7 R 7 ! r~ ~ 8 787 7 #" [ 7 L~ * L~ 2 8+ 8 & 87 !+ 8: . 7 8 & 87 !: 7 ~ [ : :+ @ ~ 7 R [~ 7 ! )K}@ 7 7 . !! 8 I: r - i~ 7 6 7 ! ) >`r~ ~ 7 ) # ~ ~l > } * 9 0 9 0 ) > > }@ 8 : ![H- 7 . !! 8~#! 787 * 7 *2 7 : : r 7 ~ 8 & 78+ ) }@ ~l[ r~ i~ ! 7 ! ~ ! r~ 8 : 8 & 87 ! ~p 78 8 ~> 7 !p ! (~> ~ & L~ 7 8 &L~ ! 7 !z: 7 ~ M # : !r. 7 )!t~ : # ~D ~D r [ i~> 7 ! 7 [~ i~ !S : rR ~D- u r 7 ~ 7 (~ ~D & ) 6 #"^~> H 8 [ # 78: i~ 8 & 7 " 8 : ~ 5* 7 ~ 7 ! # ! [ ~> 7 7 S~> 87 ~ L~ # 7 7 7 7 ~ 7: )2}@ !DS 7 7 [ ( ~>~> u r R~l r 7 & ~R 7 7 ~ ~ 7 ~ 8 . : r 7 7 [ ~ 8 ~ ~D~ !r L *2 [ 8 z + [8 : 8 ~ *@~> # ~ ~ r, *2 7 !G 7 ~ 7 7 7 ~ ~>~> u r 8 z~ 7 ! 7 !-[~ + ![ / ~ *0~ 7 7 ! 7 ~ ! ( [ u 78 7 7: 7 u [ 7 7 r 8 z: [ 8 . ! ~DI .~ : 7 !:)m}@ G . 7 i~ : rm : : * , & 7 &# : ( + 7 ! " : ~l ( [u 7 ) u [~> 7 ! 7( r ! ~ [~> 7 !t |~ * 7 S 7 ~>~ 7 !D- : ~l r " 8 ~ *@~> #" 7 " [ ~>~> u r 7 ! [ .~ 7- [0 u [~> ~ * 7 ~D 7 u ( 78 . ) 7 6 ! 8 &# - / # *" & # ) /0*"#% ~>[Bi~ | ~ 0 % r !D 7: # + [ / ~ R~ G r [ ~ . [! r~ 8 . 78: i~ m~D 8 & 8 : r )K}@ 7 ! >: }H 8 ~ 87 8 ~ ~ 8 7 i~ 7 ! 2 7 ? + 1. %!$% 0 + -' ,$ R2 RIB 1 R1 C Vs R3 − R5 + 5+ R4 − + RIB 2 R2 R1 C Vs R3 − R5 + 5+ R4 − DOUT + ADC BS2SX DIN R2 RIB 3 R1 C Vs R3 − R5 + 5+ R4 − + RIB 4 R2 R1 Vs C R3 − R5 + 5+ R4 − + 7 ! )O? > }@ 7 ! ~ 7 7 7 !G 7 7 3m~ ( | : . )B}@ + : 7 ! ~ 7 7 !& $ ~D .~& ~ 7)( r 7 ~ 7 ! 7 7 8 ~ 7 ~ 7 ! ~ 7 ! 7 ) 6 @ } * 9 0 9 0 R~ [i~ 7 r~ r > [! 7 [ [~ -8 8+ 8 ~D&. + [2 7 l~ ~ 8 i~ 7 7 R~> 7 ~ ~ [~ . 8 ~ 7 ~ ~r ~> 7: 7 ! ~ ~ r r- 7 7 r~ ~ 7 8 ~ r2 ) }@ 7 7 ! ~ 7 8 ~ 7 8 : ~ 7 ! 3m~ ( | : 7 8 7 !D ~ *0~l [~ 78 ~ ~8.~#! u 7 [u : 78'7 ) $ 7 ! 8 & 87 !:.~#! u ~ r + . r~ : 7 ! 7 0 ~ ~ !m 7 ! 7 7 ~D"r .~#! u)K}@ 7 .: ~r 7 I~ ~ ! 7( [ 7 ~> 7 !S 7 7 7+ ~> 7 6 7 ! :)K?I 8 ~ 7 7 =*2 7 1 ~ ^ !Dt 7 ~ ~> [ ! r~ 8 : 8 ~ 7 [! 7 7 ! ~ : 7 " 7 r~ ) @ }@ 7 ! ~ / ~ 7 * 8 ~D& !D 7 20~ r ~ 7 !R ^ ! 7 ! ~ 7 7 7 . 7 7 7 6 7 ! :)K?G 7 !8: [! ! r~ 8 . D 4,@BACEDF # ~R 78 ) }@ ~! : / ~D 6 7 ! :)K?2 7 .: ~r # : 78: 7 ! 8 & 87 !+)t}@ | 7 7 !t~ 7 7 !t: $ ~> 7 6 7 ! )O?..~& ~- 7)( r 7 ~> 7 !( 7 7 ).}@ 7 . ~D"r ~#! : ~ i !D 7( r 7 ~ 8 ~ 7 ~ 7 ! ~ 7 ! 7 ) , " 7 7 ! ~ ~ ^ !D ~ ~ ~ ! 7 ! 7 ~ [ r / 0&$ < 7 6 7 ! :)K?2 7 7 8 8 z 9 ~ 7 ~> 7 r $ r / " 0& 7 " 0 9 ~ 7 ~> + ~D 7 7 7 ! ~ 2)@ 7 " 7 7 9 ~ 7 ~D 7 6~ 7 7 ~ 7 7 / " ~D S: 8 r ~D [~ 7 i~ ~ ~ $ < + 7 ! ~ ) 0& ~ ~ ! 7 ! 7 ~ [ $ ~> 7 6 7 ! )O?#2 7 : r [ [~ #~ ! ~ L~ / |~D 78 2~ 7 : 9 ~ 7 ~> / 9 iD 2 7 u rL *2 [ 7 7 7 [u 7 7 ! 7 ~ - 7 ~t [ 7 ~ B : 6 7! ) > ! + 1. %!$% 0 + -' ,$ L 7 ! ) L> }@: 7 ! ~ / ~ 7 * 8 ~D& !D 7 2@~ r ~ 7 !R ^ !S 7 ! ~ 7 7 7 !. 7 7 7 6 7 ! :)K?G 7 !8: [! ! r~ 8 . 7>04@ACEDF # ~R 78 ) 6 [) 6 7 ! :) @8~ ) L 7: ~ m 7 ~#! 5*2 ~ 78*7 8 & * *0~D .~ *@~>3 ~ [~ 8 ~ 7 / " 7 8 ~D& !D : # 8+ ! 2 ) $ 7 ! D 4,@ ACEDF#`~ : *@~>3 7 : ~ [~> : 7 7 6 7 ! :) @G~ 7 !5>?#4@BACEDGF r 7 ! *2 : !r 7 ~ 7 ~R 78 r 7 ~ [ |~>& * *@~>3 7 : 7 7 6 7 ! :) L ) 6 7 ! ) * 7 ~ *@~ 7 ! ~ * ~ ~ 58 ~ 7 * 7 7 ' ) }@ r 7 ~ ^~> ~ 7 7 [ ~ ~ S ~> u [~> ~ ~ 7 7 ! ~ *2 7 7 7 ) : ~ ~ 7 7 ! ~ : H 78: ) $ 7( r 7 ! $ 7( r * 7 7)( r ! : 58 & B * 7 7 7)( r #"^ 7 ~> 7 7 ! ~ ~ 87 &R~ ( . ~ * 7 p~ ~> 7 ! 7 "^ 7 ~ 7 [i~ 7 - r~ : 5* 7 ~> .~D[ 3 7 ! )( r~ # 7 r~ ^~ ~> 7 !G 0 |i~ 7 r~ 78 * 7 ~> 7 ! " 7 : ( | 7 !: Q 7 8 8 & 87 !&! : . ) 6 7 ! ) * ~ "^~> # I ( 8 8 ~ : ~> 7 : # [Q 7878 7 ! 8 & / R: * 8: & 7 7 * 28* 7 7 !D " m r )@}@: 7 7 7 ~> 7 ~ [[~l 7 7 r S~ ~> 7 B( 78: 7 7 !5*0 ~ - ) E 7 7 [ 7 ! 8: [ [r |~ 7 ~> 87 8 S: 7 : ~ 78 [ 7 ! 8 & 87 !Rr` ) 8 & 9 * 7 !R~ ~ ~D # [ ! 7 } * 9 0 9 0 Model Output After Buckling a Tymbalimba Rib 1 0.8 0.6 Amplitude 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 0 6 7! 0.005 0.01 0.015 0.02 0.025 Time (s) > , " 8 8 ~ 1 7 ) / +/& 0.03 0.035 0.04 ~ r 8 & 87 !R~ 7,BAC 7, 78 ) }@ Q} 8 ~ 7 8 ~ 7 ~ @~r ~> 7 7 ! ~ 7 r~ i~ ~D 8 7 ~> 7 $ 7 ! ~ % " 7: 8 7 ! : 7 7 *2 ~l 7 !~ : 7 [~ 57: >> ) ~> r r $ 7 1 # 7 7 !p ' 7 [~ 87 ! : ~ 7 7 7 7 ~ ~> 7 ~ 8 8 . 7 ~ 8 Q |~ $ 7 r .~ " )B}@ 7: . " R 7 [~ ^7~ u 78 7 *,+'!, 6 7! ) > 0 : 7 ! .~ ~l 7 !+) #( ~ * r~ 8 " 7 7 7 / 8 D~ & !D :2 : ~ #58 & 87 ! L~ 7 ~> : S ~D 7: / 7 8 $ ~> 7 ! # 8 & 87 !. 78: 2 i~> 7 r !D7 7)( r 8 u9*" 7 ~ 8: & 7 ! u` 8 u9*" : 8 & 7 ! # : ~ ~ 2 78 * + Q~ 7 [~ ^~ ~> 7 |~D # ~D ~D u[ 7 ! r~ 87 1 ~ 7 I: : r 8 ~ 8 .~ 7 ~ 7 [~ )$ 7 `~ ~ L~ 5 u r 7 : 7 [~ - " . ) ,& 7 7 7 78 S 8 ~ *0~D #& .~ 7 7 7 ~ ~>~> u r *2 ~l 7 !~ p : 7 r~ 7: / | 7 m~D : 7 2 u2 7 : m [~ 7 7 7 78 r-)m 7 " 7 7 ! r~ 7 ~ 8: @ [ u 7 ~ 7 ~ 7 [~ +8 7 7 ~> 7 ! 7 m}H 8 ~ 87 8 ~ 8 ~ 7: ~D ~D r [ ( 7: 7 ! 7 ! ~D 7 ~D ~D r [ : ~l r@.~l [~> 7 ~> 7: *0~l " 7)( r ) ! *2 7 }@ t 7 # 8 & 7 ! 78 ~ 7 ! ~ i~> 7 . : 7 r~ ) 6^ 7 7 7 ! ~ 6 7 r~ r 7 r ~>~> r r ~ * 7 7 ! ~ : 7 7 ~ )6i ! O S 8 ~ 7+ 7 .~ 7 ~ 8 I # 7 : r 7: *2 7 * 7 ( [u2 7 8 ~ : ~ 77 1)Q 7 |~D 78 7 .~ S ~ 7 1 R ~>~> u r ~> u r 7 8 . 7 u 7 .~ 7 [~ ~ 8 8 ~ 7 ) 7 " : r7 * 7 i~ ! ~ : 7 L~ ! ) 7 S 7 ~ ~ 7 : r+ * 7 " ~ [~> * ~D 7 !G 7 ~ [ ~ 5* 718 [ . ~ ~l 7 !8 7: ) }@ t}Q 8 ~ 87 8 ~ ! 8 r *MB( 7 !!r 7 ! 7 ) |~ 7 !z: [ ! ! r~ 8 7 } * 9 0 9 0 7 ! ) > }@ 7 ! ~ ! r~ 8 :~ [ 7 # ~ * 8 & 87 !: ~ [~ . : [) : [i~ 7 r~ r 7 z rS 7 r~ i~ * 7 $~ 7 7 ! ~ i~> ~D[ ~ : : r- ! ~ * ~ 8: & 7 !& 7 # 78: ) 4 : 7 87 7 ~ 8 ~ " # 7 ! r + 7 7 7 ~ ~>~> u r .~ ~ 7 ~> * 7 7 [~ 7 8~ * + [ ~> 7 ~ 7 ~l 7 !t~ . : 7 Ri~ 7 7 r ~D" *2 7 [~D 7 !8 7 7 ! 7 ! .+ ~ 7 S 7 r~ ^~.- r~ 7 1 ~> 7 ) 6 " # # / ~ 7 7 7: 7 ! * 7 ~ * + [G i~ !R : 7 ! 7 5* 7 0i~ G*2 7 87 ! 8 & 7 !8 |i~ 7 * 7 7 !D)(E 7 ~ " : 7 8 ~ : ~>R~ * 7 87 [~> " : 7 !S 7 )G [ 7 ~ !D 7 : : r [~ 7 [~ :G r [ ~D"r # 7 : 6K *2 7 7 ~ M* 7 ~ * : !r@ .87 8 r9 * ) r 7 7 !R 6 I* , &S.~l(~ *7 Ru [~ 7 ! 7( [ 71 5 :8 [) 6 #"^~D : 7 .~l 8 7 r 7 !S u [~ I~ r~ * r 7 i~> |~ 7 7 Ri~ P~ 8 & 87 ! r *2 ~ & ~ + ) 0& r~ r ~> 7 R~l 8 7 r |~ m 8 r 78: ^~ S [ m 71 . " 7 i~>m~ &r 8 ~D ~ ! 7 & .:+ ) # : }H 8 ~ 87 8 ~ * 7 . 0L~ . : 7 7 [~D 8 r 7 7 " 0 7 r 7 ~ ! 7 ~> * 7 p . 78: B~ & 7 !: ~ 7 ! ) }@: 8 & 7 !( 78+ i~ I: ( [u # i~ * 7 !G r 8 & R r ~ 7 5 * 7 : # & 7 ! * 7 (~ r 1 [H - : ![ "r@ [~ |~ 7 !8: 78 L ) ~l r [ 7 .~l 7 7 ! I 78: ~ *0~l 8 & 7 ! +-7 L~ ! : , : " i~ S ~ : 2 : 7 7 : 78: 7 ! [ .~ ) " )%E .~l ~ 8 78 : 05 i~ ~ *0~l &8 r 7 J 7 ~ : 7 7 ~ + ~ t~ ` I~ 87 [~ 7: & 8 7 ~ $ : 7 : 7 * 8 7 : r * 7 7 7 ! 8 7 3 r~ 7 1 ~> 7 ) }@ . : ! 8 7 7 # ~ 7 ~ 7* 7 7 !D $ 7 R # J ) }@ 7 7 #"r 87) 8 (:R 7 .~ * r + [ L~ ! 7 : 7 L* '& L~ [~> R: J r A?FG AEACED / }@: = + +2 $ 8:: - ED J a~ ~ 7 ~ 7 - J R 7 ~ - * , & 7 J ~ 7 ~ A D / 9 ~D& 8 7 +2 ) r :( L~ ! 8 7 3 7 : : 7 !~ #~ [ ` ~D 7 6 *2 7 ( [ / 7 & 7 J 28i~ 8 " * 7 = ? @ ) ~ r 7 Gi~ 8 " u r 7 zi~> ~ 7 ~ r~ ~D + ~ 87 [~D 78 ~> 7 ! r 8 ~ G~ 7 7 .~> 7 "^ 7 ~ 7 [i~ 7 - )m 7 &G r~ 1 7 8 R~ [~ ~ L: 7 !|~ r 8 ~ ~ 78 ~ 7 ! l~ i *2 7 7 : r 8 S ~D: [M~ *2 7 ~> 87 ~ ~ ~> " r ~ 7 ) # 2*@~ ! 7 7 u u 78 [ i~ 8 " 7: 7#" : 7 $ ~ m~ 8 " : 8 ~>^ ~ 0 l~ .1 7 7 8 7 . ! 71 7 !M* 7 7: ~ 1 7 ~ `i @ ) }@: 7 + 7 87 ! 8 7 3 0- [~ r 7 ~ 7 R ! ~> 7 # ~D : 7 $ 7 ~ 7 7 ~ : 7 r~ 7: + 7 ~ 7 7 ! ~ H** r : 7 r~ 7: 8 ~ ~ . S |i~ 7 L~ i~ ~ *0~l 7 7 ! .~ 87 [ ) 7 3 9 ! # + /0 }@ 8 7 0- ~ 7 '*@~l : 7 ~t ~[~;*2 7 7 7 7 R~ 7 ! 8 7 ~> 7 8 ~ ~ S~R r 8 ~ *2 7 ~ $ ~ |~>@: - |~D 8 : / " 6 7 ! :) 2) $ 7 !7 7 . !:L:G r 8 ~ ~> u 7 7 8 ~ 7 J * + 78 ~> 7 ! ~>~ u r r 7 ~> 8 . .~ ~ : 7 # r 8 ~ ~ ~D 8 R . ~ " : ~ 7 *2 7 7 7 [ P @ ) }@ ~ # : . 7 !8: 7 " 7 r ~ 7 ~D ~ 7 ~D<*2 7 r~ : 7 " ~ I 8 7 0- 7 ~> 8 |i~ 7 . 7 : D ~ !D [~> 78 * . 7 ~ 8 ( $ 0 .: 7 " / @ ) Trachea Interclavicular Air Sac Syringeal Membranes Bronchi Pressure from lungs 6 # &# 7 'J 7! }@ 7 " ) :) > * 7 7 " 7 ~ 7 ~> 7 ~ 7 " `.~ * 7 * 7 S 7 [~ 871 ~ 7 ! ~ ~ ^ !D 8 7 K~D|~t~ 8 [~B& ) , 7 *0~l4 S~ 7 'J * ~ ^ !: 8 7 ?- 7 .~> r~ 8 ! # $ 87 [~D 78 ~ 7 !R r 8 ~ *2 7 87 2* 7 7 [~D 8 7 8 7 : ! : : ~D: [~ / " 6 7 ! +) 2 ) 8 7 r ~ 7 : ~D0~ 7 ~D ~ ~ 7 # : $ ! 7 7- . 7 . 7 3 8 7 ~ 7 !|~ [~> 7 ~ !I ~ r &* 7 8 7 ! $ 7 !|~ : r~ : 7 ! ~ r~ % ~ 8 7 r . r 8 ~ .~ pu [~> 7 !~( + 7 7 7 8 7 ~ % / " 6 7 ! G:) 2)}@ 7 : 7 u 7 ~ !.: I [ 8 ~ 8u [~ ~ $ ~ ) : 8 7 3 7 ~ R : 7 !|~ r 8 ~ 7 7 r 87 7 [M J6~ *0~ 8 + 0 8 ! : * & 0 * 7 ~ = 7 ! 8 ~D 7 8 7 ~ / 7 7 u r 7 8 .: [ $ 8 ~ - 7878 7 7 7 7 7 7'7 ~ 8: # J *&2 ) - 7 ! 7 ! 8 "! 7: r 8 ~ 78 ~> * 7 7 r 7 ! 7 .~D 7 *0~D S: + 7 Ir~D 7 ~#! 7: *@~ ) 2 u [~> 7 !G~ :r ~> * 7 ! 7 : 8 + i !D7*2 7 . ~ 7 J * 8 : / " 6 7 ! m+ * 7 78 787 7 !8 ~ 7 ~ ~! u ) 8: ! lateral labium lateral labium rotates counter− clockwise membrane membrane 7 6 third bronchial cartilage 8 7 " 7 7 7 7 77 ! +) > , ! ) .~ . 7 ~ 7 7 third bronchial cartilage ~ R 7 ! 7 H - 77 }@ 7 7 ![~ r 8 ~ m[~ 8 r 78 8 I9* ^ " . ! ~ 7: . $ ~ 7 ~ : 7 :8 ? ):}@( ~ 7) [~ 7 # - ~ K !D r 78 8 6 r [ 7 L 7 u[ 7 8 z ( [ # ~ ~ 7 7 ~ . .~ : 7 7 :r )7 9* u / 2 ).}@ 8+ | 7 : [~D 8 ri~ 7 # 7 ~ : 8 ( ~ 7 ~ ~ 7 7 ~ :: |~> 7*2 7 | 7 * : |~> l~ ~ 7 7 " ~ ~ 7 7 ~ * : [~D ) 0 ~ # 7 ! 7) i~> 8 ri " " " " " /> ( $ 0 ~ + r *2 7 ~ ~ 7 ! 7 i~ 7 )K}@ 7 + u 7'7 [ : *2 ~ ~ 7 ! 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'.g0d !*- *- (% f "* ^&' -. h g F$ (' ' ' o " ' ] ) ' " ' ] *- Bc " 3 *-)"6E#- Bi)^d "6E#- a_.')3 # ^2' _ b ^ D(%*^= cH%#^ b ) 8 @ A -)"65 8 : : : : : y J 8 y F G 7; 7; J H 8 1_./ #+ _ * '.g *- Ah)%K * _.%( f "$1 '.g " Uh ^&% / `O#- MKh.(% # ^&' g F$ ;' / ` H= ) ' J @ 81#F G H : : =H) ' ' @ =H) ' @ ^ ,"6f h.%( # _)%K "5*- % < s5 * a_.')3 * ^&' ^&/ ,"6 ', ] / ` 7 27 = 7 ; 8 ; F 7 G 7>; = ; I H 8 F G H : : J : " ' ] )' "6fFf!`28 J *7 H= ) ' @ o /;3 *- 3 -)" % " 3 (% # 3 " ] b +*#" ')35 " ' ] ' $ ;% fF` %( f " ] ^ #- 3 -" % " 3 ;% * 3 7 = : d - (%K Fb h" ] " ')3 & - b ^ ] f ^&c *- #- %( hU^&% a _.'3 * ^&' d Ff!f %((3 F$ " ' '3J^ b '.gBh.%K * _.%(Ed " $ 8/7 8 ^&'1 " 3 - ^6c *- *- K% Oh^2% ^&',cH^2%b " 3 - ^6c *- >d ^ /.%#^&')3 -)T" ' ] #- % " 3 - " " ' ] d FfFf %( )_ %*' *- 3J^2%*%( h^2' ] '.g ^&_ g&^ ')gSh.%( # _.%K $"6f _, 8s7 y : 8 , . ! 301 2 *$01 6 !6 * ] F "6* ^&' f ^ # "6>#- A/ " k " %( " 3;3J^2_.' ] cH^&%e_ '.g "?f ^d7h " # f+ ;% 82#- A^&_ h._ ^6c d -. 3 - ',;g " ] ^ !b _ f " #- m%K;i)(3 * ^&'^6c " '^&h";'^;' ] _./"& KD$ ;' *- !b h f d "$ ;g2_ ] b ^ ] f ^&c " ' " 3J^&_ # 3 _)/ /";',9 cH%#^ b ^ b k ' ] ^&c f ^d h " # %(Ji)P3 * ^&' f! 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(' ]. cH%*^ b J ^ :8U*- Bh.%( # _.%( "6E#- P(' ] ^&c *- Sh h"Sd Ff!f /" #- _ b ^&c *- % g -2<" ' ] f Jc 7 % "$ fF ')gSd " $ "65*- m hU^ ' :81*-)"6< 8 H= ) '10 @ 7 = t @ G" ! y$#&%(' *) ! #&%(',+ ! #.- 2(/ 2 k(d *- $ ^ f _ b $ f ^K3 !a`"7#- +;' ] ^6 c *- m h h"md Ff!f /" : = t @ ; J J3 ^ b h f "&b h f!! _ ] 8 G ! y4#&% " ' ] ) ! #&% 8 cH^ fFf ^d '.g #- 7'.^ #"# ^2'^6c ' o + 86 ^ ')3 f _ ] End of Tube Reflection Frequency Response Magnitude (linear) 1 0.8 0.6 0.4 Phase (radians) 0.2 π/4 π/2 3π/4 Normalized Frequency (radians/sample) π π/4 π/2 3π/4 Normalized Frequency (radians/sample) π π 3π/4 π/2 g2_.%(0)Fo&o 8 - ?cH%( C_,(')3 ` %( h^2' 0^6c *- S%(J0 i)P3 # ^2' ) G / " ] ^&' #- " h.h.%#^ !bO"# ^2'Q=H @7" ' ] *- $"&f _)A^&c " ' ] g !$ ;'/ ` =H @e" ' ] = ) @>" h f ^ j ] ' 7 g2_.%(A!o J 7 " ' ] fF k;d #- !bO" g ' " % ` h " % = '= ) J @*@e g !$ ;'/ ` G =H) 0 @ o G / @e^ #- = ) @>" ' ] =H) 0 @e" %(Ah f ^ j ] ' 7 g2_.%(A!o J - ^d '.g *- `bO" k "6* c " 3 2^ % `" h.h.%#^ !bO"# ^2' ^ *- /" -)"$1 ^&_.%0^6c " ' ] _.h ^ *- 3;_ ^ cH%( C,_ (')3 ` B " FfFf _ % " ] ' .o 8 hM JIJ + - 3J^2%*%( hU^&' ] '.gScH%KLC _,;')3 ` %( h^2' Ag F$ (' / ` = ) & @T h f ^ * ] ' 7 g2_.%K!o2o& FHGAFGJI R _ [^VCW1 _ eHZf_ N Y 3["[* ZZfiV R N S RTOQVYZC_ F$ ;' #- f ^d h " # 3 -)" % " 3 (% * 3^6c *- %K;i)(3 * ^&'cH%( C_,(')3 ` %K hU^&' " 0 - ^d7' ' 7 g2_.%K)Fo&o 8! b %( " ^&' " / f ^ " * _ b *-)"6:" )% ^&% ] ;% f ^d h " *e - f c, f! (%?= 7 g2_.%KA)Fo @ 8 d !*- " g "6 ' 5 % < 0 * ^6ce^&', 8M" / " ' ] ] gg "6 ' ^&c$D(%*^ 8M" ' ] " % " ' !* ^&' cH%KLC_,;')3 ` = 7 @ g "6 ' ^&c 7 d FfFfDbO" 3 - *- ] "," dB fFf z z g2_.%(?)Fo 8 7 % ^&% ] (% - f cA !f ;%Ad - (%K = >@ cH(% C_,;'3 ` g F$ (' / ` 7 " ' ] = 7L@> g F$ (' / ` 7 7 J " @ " ' ] = >@ - )% 9 ^2% ] ;% % " ' c;%5cH_.'3 * ^&'cH^2% *- f ^d 9 h " #e - f c6 f! ;% g !$ ;'/ ` y8 = H1@ o o B H 8 H y 8 / 3 " ' "/ ;' cH%#^ b = ) @T#-)"7#- m/ " ' ] ] g g "6 ' D(%*^ 81*-)"6< y$# o o B ! 8 ! y$# =@ @ o Bo o 8 o " J - B3J_ ^ =H) @ / J c *- g "6 ' ^&') 81*- ;' *- 3;^X3 ;' < ^ f!$ ] / ` y$# o o B ! 8 ! y$# =J @ 5 o "'] o B8 B8 o / =H) @ 0 " > Magnitude of First−Order Reflection Filter 1 Modeled Magnitude Computed Magnitude 0.9 0.8 Magnitude (linear) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 π/4 π/2 3π/4 ωT Normalized Frequency (radians/sample) π g2_.%(<)Fo 8 - 7cH(% C_,(')3 ` %( h^2' 7^&c *- E%K;i)(3 * ^&' f! (%Td - (%K 7 3J^ b h._ ] "e" "&b h f! '.g?% " ^6c &o JJ 8 %K(h.%K (' * '.g " ' " 3 _ "6f cH%( C_,(')3 `$"&f _,m^&c>o .Fo kD2 7 L^ ^ fF$ AcH^2% *- c ] / " 3,k3J^X O3 (' B 88K*- $"&f _,^&c = >@ "6K 7 = o 7 @ y$# o B ! y4# o 8! 3J^ 7 ')3 H sB 8 3J^ 7 H B8 7 7] ;% b ', ] / ` H H / =H) 5 @ '.g *- $"6f _,cH^2% g F$ ;' '= ) @ 8 =H 5 @ /"(3J^ b =ao B 8 sB 8 @ = J3 ^ 7 @ 7 B 8 6B 8 3J^ 7 @ =jo =H) J @ % < 0 * Magnitude of First−Order Transmission Filter 1 0.9 0.8 Magnitude (linear) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 g&_.%()Fo; 7 π/4 π/2 3π/4 ωT Normalized Frequency (radians/sample) 8 π - ?3;^&%#%K hU^&' ] '.g0cH%KLC_,;')3 ` %( h^2' E^&c #- % " ' b # ^2' f! (%( d -. 3 - 3 " '/ m%( ] _)35 ] ^ B 8 =ao 3J^ 7 ^&% d - (%K - $"6f _,m^6c *- 7 @ sB 8 =ao 3J^ 7 7 3J^ 7 @ =jo 3;^ 7 7 @ J B 8 6B 8 o J o 3J^ 7 7 J3 ^ 7 o 3;^ 7v 7 / +f ;%:3;^ 3 ;' B 8 = ^ f!$ ] _ '.g #- CC_ " ] % "# 3EcH^2% b _ Ff "C@> #- ; ' g F$ ( ' / ` B 8 o / =H) Ko @ =H) @ =H) @ =H) @ 010 " > - % " ' +# ^2' Hc %KLC_,;')3 ` 7 :] (% b ', ] _ '.g #- C _ " ' *!a` B 6" <*- B3J_ ^ cH%KLC_,;')3 ` = " h)h.%*^ bO" ] / ` B J / @e" ' ] g F$ ( ' / ` =H) @ 7 J / B zH d - (K% z #- "6b h fF '.g"h ;% ^ ] 8 #- h ] ^&c ^2_.? ' ] " ' ] B *- S% " ] _ ^6c #- 0^2 h (c ' ;' ] ^6c *- _) / 2 - bO" g&' + _ ] "B*-)"6 cHK% ? L2)_ ;')3 `&8 7 8D O] ;% b )' ] _ '.g *- bO" g2' + _ ] ^6c = G @ g !$ ;' / ` =H 2 @ $"6f _ " ] " G J / o2# - bO" g&' + _ ] B^6c #- )% 9^2% ] (% - f :c f+ ;% = H1@ 84b ^ ] fF ')g *- (% J)i P3 # ^2' "S*- 1;' ] ^6c #- % " 3 - " = d +#- " % " ] _ ^&c . bb@ 8D g !$ ;' ' 7 g&_.(% !o . - ] 3;K% (h " '3 ` / dd ;' #- A3;^ b h._ ] " ' ] b ^ ] f ] K% ;)i (3 * ^&E' f+ ;% "/ ;)' 3 F"&f '(% ] _3 '.g *- ] P3 ^6c "6fF " '.g 3 " 'O" / " # _ b ] *-)"6 d -)"6T '.^ K% ;)i (3 ] "D#- e(' ] ^6c *- % " 3 - " % " ' b!j ] *- %#^&_)g -*- "/ " kX - 3J^2%*(% hU^&' ] '.g % " ' b * ^2' % " ] F"6* ^&<' f+ ;% #- ;(% JcH^2K% g F$ ('/ `*- cH^ fFf ^d '.g % " ' c (% cH_.')3 * ^&'cH^&% "B-. g - h " * f+ ;% 8 y8 o o =j o B 8 HH y 8 @ 7 = H1@ o B 8 H y 8 B y =ao 8 H y 8 @ o B 8EH y 8 o = B 8 y 8 @ H o 8EH d - (K% *- <3JX^ 3 ;' 7" ' ] B 8>" (% ] )', ] ' =H @" ' ] =H 6 @ (% h P3 *F$ f!` ) - 5cH(% C,_ (')3 ` K% hU^&')3 ^6c *- % " ' b # ^&' f! ;% h f ^ * ] ' 7 g2_.K% !o() 01 -! !6 0 ! 'Nh.% " 3 * 3 "6f:!b h f b ;' ,"* ^&' ^6c " 3;^&_ * 3 _)/ _ '.g ] g !#"6f d "$ ;g2_ ] ` ' *- 85! ',P35 # " % ` ^ " 3;3J^2_.' cH^&% *- f ^ * " # ^13 F"6 ] d !*- $1 3J^2_ ] % " g " ' ] *- ;% b"&f 3J^2' ] _)3 * ^&' d -. 3 - ," k h f " 3 h.% !bO" % Ff!` d !*-. ' "*-. '/U^&_)' ] " % `fF"` ;% "&f ^2'.g #- 0/U^&%(0d "6fFf 5 8 h.h o Xo 5 + - ^&_.g - *- f ^ # " (% 6 @= r{ D= ~^ $ ;% #- f ;'.g *- ^&c *- _./" 81 ' " ] g !#"&f d "$ (g&_ ] Fb h f b (' #"# ^2' !> b ^&%(f O3 (' ^ f _ b h *- M (3 / ` @B0D=J 1p " 3 -)" % " 3 (% * 3 ] g !#"&f f+ ;% ^. " 3 - ;' ] ^&c *- md "$ ;g&_ ] B= " ' ] " ' ` ' (% $ ;' '.gB^&/ ;% $"* ^&' h^ ' @ o&o 8 o + 8)" FfFf _ % " ] ' 7 g&_.%()Fo K + ' @B;' " ] Bg F$ cH^2% b _ fF" cH^&%?3 "&f 3;_ f "* '.g *- Bh)%*^2h " g "* ^&'3J^2' ," ' ' " 3 `1f! ' ] % 3 "6f _./"O^6c " %#/ ! % " % ` % " ] _ 8K" ' ] h.(% ;' 5 !b h f " h.h.%#^ !bO"# ^2' 82$"6fF ] cH^&Y% +#- ;% f ^dNcHK% LC,_ ;')3 = " ' ] ^&% b"&f!f _) / @ ^2% -) g - cH(% C,_ ;'3 = " ' ] ^&% fF" %*g _. / @ 2L" ;% M;c + h.K% (' (h " % " -) g - ;'% 9^2% ] ;% " h)h.%*^ FbO"* ^&' cH^2% f " %#g " ' ] b"&f!f _. / E - Bh.%#^&h " g "6* ^&'3;^&' #" ' g F$ *- h -)" $ f ^K3 +a`R" ' ] *- "* ('C_ "* ^&' 3;^ 3 ;' ,' P53 * " % ` cH^&% ] g&' '.g *- f ^ # f! (% L= >@ d -) 3 - 3;^ bb ^&' fF` ] ;% !$ ] _ ')g #- f " %#g _."/ " h)h.%*^ FbO"* ^&' 5 8 h.h 5 + ' *-. (3 # ^2' 8TbO"6 ;% "6f h.(% $1 ^&_ f!` h)_./ fF - ] / ` 4 / f 8 b0`C#- " ' ] b+#-N ' o + h.K% (' ] 8 > * > * 0 −1 g2_.%(e!o 8 4 d "$ ;g&_ ] b ^ ] f ^&c " 3 `CfF ' ] % 3 "6fK _./ 7d !*- ;3 ^ bb _ ] d "6fFfKf ^ * f+ ;% 8 M = >@ 81" ._ h.h";% " ' ] f ^dd(% ] f "`fF ',m^2/ ;% $"6* ^&' h^ ' 8)" %(Ji)P3 * ^&' f! (% = >@5" ' ] S" % " ' b # ^2' !f (% 7 = >@ 7 d -. 3 - ^ ;% " _.' cH^&% b " h.h.%#^ !bO"6* ^&' ^ *- "* ('C_ "* ^&' " ' ] h -)" $ f ^13 +a` b ^ ] f ^6c@B;' " ] " ' ] M;c &@ " ] ^2' *-. _)' cH^2% b " h.h.%#^ FbO"# ^2' ! d " ^&/ ;% $ ] #-)"E*- f ^ * f+ ;% bB ' Fb _ b h -" " ' ] $ ;% "6fbB ' Fb _ b h -)" f! ;% ] g2' b #- ^ ]. " %(? $"6f _ " ] 84 ')3 f _ ] '.g " 3 " 3 " ] B^6c$)% 9^2% ] (% - f c f! (% d !*- h " % "6b ;% > h P3 ) ] / ` Fb h f EcH_.')3 * ^&' ^&c _)/ A% " ] _ 8C _./ f ;'.g *- 8K" ' ] "6b h fF ')g % " 2 4 fFf f+ ;% ] g2' b *- ^ ]. -)"$ O3J^ b h " % " / f " 3(3J_.% " 3 ` cH^&% " g !$ ;'^&% ] ;%m^&c ] g +,"6f f+ ;% 8 d -.Ff *- - f c f! (%A3 " 3 " ] -)" #- " ] $" ' #" g?^&c ] g&' Fb h f! 3 !a`R" ' ] ' 35 f!` h " % "&b (% D ] cH^&% *Fb $" % `1 '.g _) / ?g ;^ b % V XHZf_ bdNfPHR [.i9N h[ |N["["Zf[ R S ]HO RTSe_ R i 3O FHG KG N SehRQV [ 87 ' " 3 `1f! ' ] % 3 "6f 3J^2' ] _ !(8&*- 5d "6fFf 3;^&' % /._ "E$1 3J^2_ ] % " g ] ;h";' ] ;' ^&' *- 7% "# ^A^6c *- 7h h"7% " ] _ B ^ *- #-. 3,k1', * ^&c #- 1$ 3J^2_ /^2_.' ] " % `fF"` ; %5g F$ ('/ `#- mh " % "6b ;% I B y =H) 0 @ d - (%K *- ] ;' +a` ^6c "6 % 8 #- $1 3J^ ! a`" ' ] = *- m% " ] " ' cH%( C_,;'3 ` . o 8 h.h o 5 Xo 5 0 + 3 -)" '.g / dd;' *- "6 % " ' ] *- d "6fFf d !*- " 7 _.% = *- ;% f ^ # bO"` ^K3;3;_.% ] _, ^ "Q#- ;% bO"6f . B bO" g2' + _ ] ] ;h";' ] ;' ^&' #- % "6* ^^6c *- _./" % " ] _ ^ #- #- ;% bO"6f /U^&_.' ] " % `f "` (% #-. 3,k1', * g F$ ('/ `#- mh " % "&b (% y I B =H) @ 2 d - (K% *- *- (% bO"&f 3J^2' ] _)3 *F$1+a` " ' ] *- = h P3 3 - " ^&c "6 % " 3J^&' ," ' h.%( # _.%( .o 8 h.h o 5 Xo 5 0 + ) - d>^% "# ^ " K% (% f " ] / `*- C_ " (% E%#^1^ ^6c *- D% " ' ] #f 'C_ b /";% + 8K#-)"< 8 I I + / =H) @ "! 2 ! ! D"6f _, cH^&%7g " 3J^2' ," ' cH^2% "6 % " %(Ag !$ ;' ' " / f m) Fo& - $ P3 ^6c *- $1 3;^&_ " ' ] *- ;% b"&fDf ^ # f " ] ^ " ' "6j ;'1_ "# ^2' ' #- Od "$ h.%#^&h " g "6* '.g # 0; " > ] ^d7' *- f ;')g *- ^&c *- mh h"&$ - h.%*^2h " g "# ^2' 3J^2' #" ' 7 g F$ ;'/ ` = >@ = >@ d - (%K = >@< #- "j ; '1_ "6* ^&'3;^ 3 ;' (8 #- 0% " ] F" ' cH%KLC_,;')3 ` " ' ] ^6c d "$ ] _.%#/ " ')35 + @B;' " ] :g !$ *- AcH^ f!f ^d ')g " h)h.%*^ FbO"* ^&' cH^&%5/U^ #-*- Ah -)" $ f ^K3 !a` 3J^X O3 (' = >@7 ' *- f!Fb+ ^&c b"&f!fL" ' ] fF" %*g _."/ ?% " ] _ /^2_.' ] " % ` fF"` ;% I I = > @ = >@ ? o o I o =H) 0 J @ ! I o =H) 0 o @ ? I o ? D"6f _, = ! # ! `1b U/ ^ f &" % ] (' !a` $1 3;^ +a` T% " ' ] *f % "# ^B^6c h"(3 U3 - "6 cH(% h " 3 ^&_)' ] h" ] I o/ o = o @ E_ " ' *!a` = >@e" ' ] #- "j ;'1_ "6* ^&' *-. 3,k1', # % "6* ^ + 8 I o o = o @ ? I = >@: #- Sh -)" $ f ^13 +a` = >@ =H) 5 @ o / o o J yy o/ oJ J / o o2 J / o J ? " / f )Fo 8 " 3;^&' #" ' cH^&% "& %R $"&f _ " ] "6 JJ = 0 ' ! g 3 b g K= 3 bO@ 3b / 0 @ + L hU^ # / f ^ " 3;3J^2_.' cH^&% "* ;'1_ "6* ^&' ] _) ^Ed "&f!f2f ^ * L Fb h fF` / `b _ f+# h fF`1 ')g ] fF"`Af! ',>^&_ h._ / O` " '.g f A3J^X3 (' 0 8 h " g< 010 + 7 ^2% "? _./"E^&c f ('.g #- " ' ] % " ] _ B 8 d !*- ^&/ ;% $"# ^2'Oh^ ' "5#- +; ' ]) ^6c #- m_.h.h";% " ' ] f ^dB;% ] fF"`fF ', 81*- ?3;^&' #" ' -)" *- A cH^ fFf ^d '.g " h.h.%#^ FbO" $"6f _, 8 w o H w o J y B =H) 0 @ d - (%K *- " h.h.%#^ !bO"6* ^&' $"6fF ] cH^2% _./" < _ 3 ;' #f!` - ^2% 5#-)" ', " %7^&',2 ')35 f ^ * " %(?cH%( C_,(')3 ` ] (h (' ] (' P8X*-. 3J^X3 (' ^2' f!`R" %*^2_.g - *Fb"6 2 ' .h % " 3 # 3 8U*- !b h f fF" %*g I Kh.%( # ^&' " %K<3;^ bb ^&' fF` _ ] ^ ] g2'Bd "6fFfKf ^ # f! ;% cH^&% b _ 3 "6f d ' ] ' %*_ b (' > * > * 05 h -1` 3 "&f b ^ ] f = 8 2 g 5 8 h " g o 5 + @E" ' ] g F$ (' #- %K fF"6*F$ fF` f " %#gB/^2%K ^&c b ^ m ' %*_ b (' 8 *-) fF k fF` " ' " 3(35;h #" / f " h.h.%#^ FbO"# ^2' - c Kh.%K * ^&' bO"` ')^ (87- ^dd $ ;% 8 / _ 3 ;' #f!` " 3(3J_.% " BcH^&% b"&f!f ;% _./" fF k *- ^ ScH^2_.' ] ' ^ b O/ ^ f ^2g 3 "6f ^&_.' ] h)%*^ ] _)3 * ^&' b (3 -)" ' b m _)3 " #- ?/.%#^&'3 -.M" ' ] % " 3 - "B ' / % ]. o 5 + - ;%(JcH^2%K 8K ' ^2% ] ;% ^ -"$ "b ^&%( $ ;% "*Ff " 3J^2_ # 3 _./ b ^ ] f98 !? h.(% Jc (% " / f 0cH^2% #- Od "6fFff ^ # f! ;% ^ b" kB_ B^&c " '.g f f # %K % 3 #!$ P 1h)%K * ^2' cH^&% h -)" $ f ^13 +a` " ' ] "* ;'1_ "6* ^&' ^&') #-)"7 3J^ b h "# / f d +#- "6fFf4 _./" D " ' ] cH%( C_,(')3 >SR ~N _ b FHG KGJI "_ N`HR b $VYR N S ~N _ Y X 3[^Z ZO1NKi,RQV6] 3Se V.V.ZSh $VYR N S Modeled and Limiting Phase Velocity 0 Phase Velocity / c 10 −1 10 0 1 10 10 Boundary Layer Thickness Ratio (r ) L g&_)%K)Fo 7 008 R^ v ] f ] _.' cH^&% b h -)" $ f ^13 +a` = ^ fF ] @5" ' ] *- fF!b!* '.gO/" -)"$1 ^&%?= ] " - ] @ - " `1b h ^ * 3O/" -)"$1 ^&%?^&c5h -)" $ f ^K3 +a`" ' ] 6" j ('1_ "# ^2' cH^2% f " %#g " ' ] bO"&f!f I g F$ ('/ ` =H 0 J @ " ' ] =H 0 o @ 6 - :cH^ fFf ^d '.g ')g f fKh.%( # ^&' " ._ ' cH^&% b " h.h.%#^ !bO"# ^2'0cH^2% #- :h -" $ f ^K3 +a`28 J " > Modeled and Limiting Attenuation −3 Attenuation / Frequency 10 −4 10 −5 10 0 1 10 10 Boundary Layer Thickness Ratio (rv) g2_.%K!o 8 ^ ] f ] _.' cH^&% b "6j ;'1_ "# ^2'= ^ f! ] @5" ' ] #- fF!b!* '.gO/ -)"$1 ^2%?= ] " - ] @ 7 $"6fF ] Hc ^2% " ' ` I 8 I QI = >@ o G G I =ao = ) I )@ .@ 8 g !$ ;' / ?` o ) o o = o @ @ + d - (%K *- mh " % "6b ;% 5G " ' ] ) G =H) 0 @ ! dB;%( f (3 ] ^ b"6 3 - *- fFFbB!* '.gOh - " $ f ^K3 !a` / -)"$1 ^2% " ' ] *- m h " % "6b bO" %#k #- m% "* ^ I ] fFFbB!* '.g #- bO"&f!f " ' ] f " %#g _)/ ?%(;g ^2' =H) 0 @ ;% =H) 0 @ > * > * Ko FbBFf " % f!`" _)' cH^2% b " h.h.%#^ !bO"6* ^&'cH^2% *- 6" j ;'1_ " # ^2'3;^X3 ;' 7 *) I = >@ I G o QI = .@ =H) 010 @ d - (K% #- ?h " % "&b (% @ ' = ) 5 @ g F$ *- A h";%e_.' !ef ;'.g *-"j ;'1_ "6* ^&'O^6cLd "$ h.%#^&h " g "6* '.g "6f ^&')g " ' ' )' ! fF`Qf ^&'.g _)/ " 3 * '.g " "R % " ' b * ^&' fF ')& 4 3;3;^&% ] ')g fF`&8 *- cH^ f!f ^d '.gRcH%( C_,(')3 ` %( h^2' " h)h.%*^ FbO" *- "6j ('1_ "# ^2' " ' ] h -)" ] f "` ^ $ (% "0 _./"?^6c f ('.g #- 8 ! y 9 : ' ! y 9 : '9$y # 9 9 : : ' / =H) 0; @ 9 b ^ $1 '.g " h)_.%K ] f "` ^6c ] _.% "* ^&' 8D#- ] %K ] d "6fFf7f ^ # f+ ;%OcH%( C_,(')3 ` %( hU^&' 8 M= >@ 85 ^&/ #"6 ', ] " ' ] g !$ ;'/ ` L= >@ ? ! y 9 : '9y$# 9 9 : y : ' / =H) 0 5 @ B<^ * '.g *-)"6>#- "j ; '1_ "6* ^&' = >@> ')3J%( " d !*- *- C_ " %(:%#^1^ ^6c cH%( C_,(')3 `281*- Ad "6fFfUf ^ # f! ;% L= >@L ( ' ^ -"$ " g( ' *f f ^d h " # 3 -)" % " 3 ; % * 36, -) f ^d 9h " # 3 -)" % " 3 ;% * 3 b ^2%Keh.%#^&'.^2_.')3 ] d !*- ] ( 3;%K " ')g _)/ % " ] _ B ^&% '3J%( " '.g _./" f ( '.g #- :8M" FfFf _ % " ] ' 7 g&_.%( !o " ' ] !o 5 %( h P 3 *F$ f!` '.^ A` 3;^&')% b ] " ' "6fF`C* 3 "6fFfF`&8 'C_ b ( % 3 "&f %( _ f! ' ] 3 " *-"A*- S d "&f!ff ^ * f! ( % L= >@: N-.Ff B b ' !b _ b h -)" & E ' #- L C_, f98M!0 " # _ b ] #-. h.%#^&h"; % a`R- ^ f ]. 8L" ' ] 3J^2' ] ( %m^&' fF`R#- ^ ] g2' b #- ^ ]. d -. 3 - h)%*^ ] _)3 bB ' Fb _ b h -)" f! ( % p # +/"! "-0p -' F$ ; ' *- ] %K ] d "&f!ff ^ # f! (% % " ' c;%:cH_.')3 # ^2' L= >@ Kh.%( # ] ' ( % b ^6c #- ._ /"h " % "6b ;% " ' ] h -1` 3 "&f 3;^&' #" ' 8 d -" %K b"& ' ^3J^ b h._ *- m3J^X O3 (' ^6c " ] g !#"&f f+ ; % " h.h)%*^ Fb"6* '.g *- ] %K ] % " ' c(% Wall Attenuation Magnitudes for a 20cm Long Tube with Different Radii 0 −1 a = 0.5 a = 0.4 −2 a = 0.3 Gain (dB) −3 a = 0.2 −4 −5 −6 −7 a = 0.1 −8 −1 0 10 1 10 Frequency (kHz) 10 g2_.%(S!o 8 "6fFf f ^ * f! (% b" g&' ! _ ] L= >@ 8 - ^d '.g B " f ^d 9h " * 3 -)" % " 3 (% * 3 *-)"6m b ^&%(Sh)%*^I '.^2_.')35 ] d !*-R" ] P3J%( " '.g _./"m% " ] _ =H% " ] _ $"6f _, 8 8 g !$ ;' ' @ 7 ? Bd ;%(0_ ] ^ f ^d 9^2% ] (%<% "* ^&' "6f f+ ;% ^ " #% h ] D%#^&' ` " ' ] " '.k f '.^&% b b *- ^ ]. L= >@ N -.!f #- C E ^ #- "6j ;'1_ "# ^2' f+ ;% &g ^1^ ] 8" < - ^d7' ' #- 6" b h f ^&c 7L g&_)%K ) J " ' ] + + ) o 8U*- b *- ^ ]. %( C_ %(S3J^2' ] (% " / f 03J^ b h)_ #"6* ^&' " ' ] " %KS'.^ 3J^2' $ ;' ;' cH^&% " f! (%/ " ] ^2' _)/ Bh " % "6b ;% fF k fF` ^ 3 -)" '.g 'R%( "&f *Fb & 4E].] !* ^&' "&f!fF`&8X ' j# '.g d - (%K _./"Sh " % "6b ;% " %( *Fb $" % `C '.g 8*- DbO"` h.%#^ ] _)357%( "&f h^ f cH^&% ^ b 5h " % "6b ;% $"&f _, " ' ] 3;^ b h f ShU^ f cH^2%D^ #- ;% 8 bO" k '.g + ] 3J_ f!7 ^ b ^1^ *-)f!`O % " ' +# ^2' /" dB(' d "6fFf4f ^ * f+ ;% L^ 3 %,3J_ bS$ ;' h.%*^2/ f b d !*- ," ' ] " % ] b ^ ] fF '.g P3 - ' 2_) 8 3J^2' ] (% " 3 " 3 " ] ^&c b ' Fb _ b h -)" )% ^&% ] ;% - f )c f+ ;% #= H1@ + 8 = H1@ H F 8 = H = @ = 2 @*@ =H) J @ > * > * Wall Attenuation Magnitudes for a 0.2cm Diameter Tube with Different Lengths 0 −1 L=5 −2 −3 L = 10 Gain (dB) −4 −5 L = 15 −6 −7 L = 20 −8 −9 −10 L = 25 −1 10 0 10 Frequency (kHz) 1 10 g2_.%(S!o 5 8 "6fFf f ^ * f! (% b " g&' ! _ ] L= >@ 8 - ^d '.g " f ^d 9h " * 3 -)" % " 3 (% * 3 *-)"6m b ^&%(Sh)%*^I '.^2_.')35 ] d !*- " ' ')3;%K " '.g )_ / f ;'.g *- = f ;')g *- $ "6f _, 8$:8 g F$ ;' ' @ 7 ? d !*- " 3 - - f c f+ ;% -"$C .' g " g &" ' ^&c5^2', 8 " / " ' ] ] gg "6 ' = @ 8 " ' ] " g "6 ' = @0"0! % " ' !* ^&'OcH%( C_,(')3 ` 2 = @ :4 5 - ^d7' ' 4 h.h";' ] @ 18 #- - f c, f+ ;%<3;^ 3 ;' " %(e " !fF` 3J^ b h._ ] ' %( "&f *Fb & 4 f ^ 8 ')3 #- - f c f! (% " %K )% 9^2% ] (% 8 #- `Z-)"$ %K "6f hU^ f " ' ] D(%*^ 8>" ' ] " %( 5 %( f "*F$ f!` cH%(^&c " % # c " 3 d - ;' bO" ] *Fb $" % `C '.g 7 % 9^2% ] ;% - f c f+ ;% -)"$ % " ' c;%ScH_.')3 * ^&' d -) 3 - f ^d f!` % " ' +# ^2'Q/ dd;' *- % " ' ] / " ' ] ] g $"6f _, *- ;%(JcH^&%( b %( " ^&' " / f *-)"6" 3 " 3 " ] ^6c - f cC f+ ;% d !*- _ ] 3 ^2_ f!` 3 - ^ (' % " ' !* ^&' cH%KLC_,;')3 " ' ] g "6 ' 3J^&_ f ] " h)h.%*^ FbO" *- ] %( ] d "6fFf4f ^ * % " ' c(%5cH_.')3 # ^2' 4:< (' ' 7 g&_.(% !o " ' ] )Fo 5 81*- ] %( ] d "&f!fMf ^ * f! (% " " cH_.')3 * ^&' ^&c _./ f ('.g #- 8 % " ] F 8 " ' ] "&b h f! '.g% " " (% % k '.g f!` f c FbBFf " %:_)' ] ;% *- " h.h.%#^&h)% " %K 3 -. '.g^&c #- f ^&g bO" g&' ! _ ] ^&%?cHK% L2)_ ;')3 ` " 2 ' +#F"&f!fF`&8#- ] " d " ^ ] g&' $1F" /.%*_ 9cH^&%,35^2h *Fb D "* ^&' " f ^d ^&% ] ;% - f c f! (%?3 " 3 " ] d -. 3 - bO" 3 - ] #- ] K% ] % " ' c (%AcH_.')3 # ^2' "?" h " % * 3J_ fF" % "&b h f! '.g % "6 " ' ] _./ 5 " > Computed and Modeled Attenuation, [a, L, fs] = [0.1, 40, 44.1] 0 Computed Modeled Gain (dB) −5 −10 −15 −20 −1 0 10 1 10 10 Frequency (kHz) Computed and Modeled Phase, [a, L, fs] = [0.1, 40, 44.1] Phase (degrees) 0 −5 −10 −15 −20 −25 −30 −1 10 0 10 Frequency (kHz) 1 10 g2_.%(m) J 8 " %*"h ] T %*^2' ` .c *- ^&% ] (% b ^ ] fL" ' ] 3J^ b h)_ ] d "&f!fLf ^ * f+ ;% % " ' c(%7cH_.')3 * ^&' !fFf _ % "# ')g " ' .35 fFf ;' :"<"&f!f cH%( C_,(')3 7 g(^ b % ` -. h.%#^ ^ a` h f! (%?3J^2_ f ] *- ;'/ %( 3 - ] '%( h^2' ^ "6b h fF ')g % " " ' ] 3J^&' ] _ ! g(^ b % ` ' ] g2' '.g #- h.%#^ ^ a` h f! (% cH^2% ] ;%(;' ^&% ] (% - ^dB $ ;% 8D" h "j ;%#'C b ;%#g ] " ' ] ! d " ] 3;^ $ (%K ] #-)"*- e3 " 3 " ] D^6c - f c f! (% d !*- / " ' ] \ ] gTg "6 ' = 'S_.' ! ^6c "&b h f!! _ ] @" ' ] % " ' !* ^&' cH(% C,_ ;'3 = ' % " ] " ' @ @ g F$ ('/ ` + 8 Kh F 8 ; ; + f ' L= 6@ @ = @ %-H 8 o =H) 1o @ = @ -; 2 -)" " % " ' c;%EcH_.')3 * ^&'d -) 3 - 84" Ff!f _ % " ] ' 7 g&_.%( ) C) 8. " '&.3 fFf (' " h.h)%*^ Fb"6* ^&' ^ > * > * Computed and Modeled Attenuation, [a, L, fs] = [0.1, 40, 44.1] 0 Computed Modeled Gain (dB) −5 −10 −15 −20 −1 0 10 1 10 10 Frequency (kHz) Computed and Modeled Phase, [a, L, fs] = [0.1, 40, 44.1] Phase (degrees) 0 −5 −10 −15 −20 −25 −30 −1 0 10 10 Frequency (kHz) 1 10 g2_.%(B o 8 " '.k f .' ^2% b .c *- ^&% ] (% b ^ ] fT" ' ] 3J^ b h._ ] d "6fFfDf ^ # f+ ;% % " ' c;%cH_.')3 * ^&' !fFf _ % "# ')g " ' .35 fFf ;' :":"&f!f cH%( C_,(')3 7 K8 _./ f ;')g *- <81 _./ m% " ] ! B 8)" ' ] "6b h fF '.g% "6 ' *- Oh.%( ;'35B^6c " 3 -" '.g '.g _)/ Og;^ b % `&84!? %((3;^ bb ;' ] ] #-)"m#- f! (% L = HC@ /" !b h f b ;' ] " " 3 " 3 " ] B^6c$)% ^&% ] (% (3 * ^&' 8 d !*- 3J^X O3 (' fF ', " % f!` ^&%MKhU^&',(' #F"&f!fF`R ' ;%#hU^ f " ] /" dB;' 3J^ b h._ ] $"&f _) 6 ' *-. d "`286*- ] ` ' "&b 37% " ')g <^&c *- f! ;%53J^X O3 (' b ' Fb D ] 8K" ' ] f! (% -)"$1 '.g ' ;%#h^ fF"6 ] 3;^ 3 ;' " K% g2_ " % " ' ] ^ "/ ," / f Od +#- % " ' c;%cH_)')3 # ^2' %#^&_.g -.f!` bO" 3 -. ')g *- ^ " # ^K3 " ] d !*-R ' ;% b ] " $"6f ,_ ^6c g (^ b % 3mh " % "&b (% B<^ #-)" .c *- ^&% ] (% f! (% " %( _ O3 (' T ^0g F$ % " ' c (%DcH_.'3 * ^&' " 3;3J_)% "6 ^Sd +#-. '.g " cH% " 3 * ^&'O^&c " ] @ " 3;%*^ * #- " _ ] ^ / " ' ] cH^2% a` h 3 "6f " _ ] ^ "6b h fF '.g% "6 "&f!fL"j ;'1_ "6* ^&' f! ;% " K% " ' Fb h^2% ," ' h " % ^6c " 3;^&_ * 3 _."/ b ^ ] f = _ ] / `"fF" %*g E/U^ ] ` ^6c b _ 3 "&f) ' %*_ b (' @D" ' ]O - ^2_ f ] '.^ / E,' ;g f P3 ] cH^&% *- " k 7^&c Fb h fF 3 +a` - ^&_.g -*- % " _ ] / FfF+a` bO"` / f! g -C cH^&%<3 ;% #"6 ' _."/ Ag ;^ b % 8C#- ` 3 " ' 3J^2' % /._ g&' 3 " ' *fF` ^ *- (% ] _3 * ^&' ^6c -. g L= >@ cH^&% " d ] m% " '.gE^&c) f! (%7^&% ] ;% ; 0 " > Computed and Modeled Attenuation, [a, L, fs] = [0.1, 40, 44.1] 0 Computed Modeled Gain (dB) −5 −10 −15 −20 −1 10 0 1 10 10 Frequency (kHz) Computed and Modeled Phase, [a, L, fs] = [0.1, 40, 44.1] Phase (degrees) 0 −5 −10 −15 −20 −25 −30 −1 10 0 10 Frequency (kHz) g2_.%() I 8 ^ b h._ ] " ' ] b ^ ] f ] d "&f!fDf ^ # +f ;% F fFf _ % "# ')g " 'E K3 fFf (' _ ')g " 3 " 3 " ] A^&c,)% ^&% ] ;% f! ( % ^Oh.%*^ ] _35 " .c *- &^ % ] (%? f! ; %P 7 1 10 B"6B"&f!f cH%KL2_);')3 cH%( C_,;'3 ` 3J^ b h^2',;' *-"5f " ] ^ "&f! " '.g " ' ] 3 " ' "&f ^ f!Fb ' "6 ^ b ^&_.%,35 ^&c ' ," / Ff!!a` ' *- b ^ ] f A - ^&_.g - " h.h.%#^ FbO"# ^2' d Ff!f ^6c ;' / "6* c " 3 ^&% `&8C+5 de^&% *- d -.Ff ^ "6Fb cH^2% "Sb ^&%(:%#^&/._ P8 3 ;' * 3 "&f!fF` ^&_.' ] " ' ] $ ;% "*Ff ^ f _ * ^&'M 4: 2 b h fF ) ] / ` 7L g&_)%K ) C) 8M" 3 " 3 " ] B^&c )% ^&% ] (% - f c f+ ;% h.%#^ $1 ] " 'G K3 fFf (' " h)h.%*^ FbO"* ^&' ^ #- 53 `1f! ' ] % 3 "6f2 _)/ 5d "6fFf2f ^ # % " ' c;%LcH_.')3 # ^2' L= >@ cH^&% " d ] e% " '.gT^6c0 f+ ;% ^&% ] (% 8 _) / f ;'.g *- 81 _."/ % " ] F 8K" ' ] "6b h fF '.gB% " 5 "&f ^ 3 ;' > ^O3J^ b h._ EcH^&%73J^2' # '1_ "&f!fF` 3 -)" ')g '.g h " % "&b (% 81b" k '.g !:" ' ] "6f 3 - ^ 53 AcH^&% b ^ ] fF '.gOd "&f!f4f ^ # ' " 3J^&_ # 3 _)/ > * > * Wall Attenuation Magnitudes, [N, L] = [5, 20cm] 0 −1 −2 a = 0.4 a = 0.3 Gain (dB) −3 a = 0.2 −4 −5 −6 −7 a = 0.1 −8 −1 10 0 10 Frequency (kHz) 1 10 g2_.%(T) 8 ^ b h._ ] " ' ]0 - f c f! (%D3 " 3 " ] Td "6fFf1f ^ * f! (% bO" g&' ! _ ] "6$" % ^&_ _)/ 5% " ] F = $"6f _, g F$ (' ' @ d ! *-#- !f ;%:^&% ] ;% 8; 8)" ' ] #- _./" f ;'.g *- 84:8 3J^2' ," ' 7 ? " > Wall Attenuation Magnitudes, [N, a] = [5, 0.1cm] 0 −1 L=5 −2 Gain (dB) −3 L = 10 −4 −5 L = 15 −6 −7 −8 −1 10 0 10 Frequency (kHz) 1 L = 20 10 g2_.%(O) 8 ^ b .h _ ] " ' ] - f c f+ ;%S3 " 3 " ] Od "&f!f>f ^ * f+ ;% b" B g&' ! _ ] "S$" % ^&_ _./" f ;'.g *- = $"&f _, g F$ (' ' @ d ! *-#- f! ;%:^&% ] ;% 8; 8." ' ] #- _./"m% " ] _ 8 8 3J^&' ," ' 7 ? > * > * 5 Wall Attenuation Magnitudes, [a, L] = [1.0cm, 20cm] 0 -0.1 -0.2 Gain (dB) -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -1 10 0 10 Frequency (kHz) 1 10 g2_.%(e 8 ^ b h._ ] " ' ] - f c% f+ ;%D3 " 3 " ] 5d "6fFfKf ^ * f+ ;% bO" g2' + _ ] 7_ '.g / / / o J )% 9 ^2% ] (% - f c) f+ ;% 7 " > J 2 # & x (mm) 4 2 0 −2 256 258 260 262 264 266 268 270 272 274 276 256 258 260 262 264 266 268 270 272 274 276 256 258 260 262 264 266 268 270 272 274 276 256 258 260 262 270 272 274 276 p0 (Pa) 400 300 200 100 U (ml/s) 200 100 0 −100 p1 (kPa) 2 0 −2 264 266 268 time − milliseconds g2_.%(O) 0 8 "$ ;cH^& % b " (% 3;^ b h " % " / f ^ *- ^ Oh._)/ f! - ] / ` 7f 3 - ;% 8 ./ _ _ Od "$ ;g&_ ] d +#f _ b h ] f ^ * " ' ] " ' ] 9^2% ] ;%' (%*%#^&% "6f g&^2% !*-.b cH^&%D'1_ b ;% 3 "6f) ' (g&% "# ^2' ^ " 3 -. $ ," / f ] 3;%K * D " * ^&' "67" _ ] ^ "&b h f! '.g% "6 7 N!*- "6fFfX*- b ^ ] f f b ( ' ' h f " 3 8 7 g&_.%(E 10 - ^d *- #!b + $ ^ f _ # 2^ '^6c *- AcH^2_.% $" % " / f 'Z%( h^2' ^ " ' "6b h f " h)h f! ] h.%( # _.%( 7 N - ;' *- $"6fF$ ^&h";' 8D*- h.%( # _.%( ] ;(% ;')3 " 3;%*^ * #- $"6fF$ O3 -)" '.', f>" ' ] *- $ ^ f _ b i)^d *- %#^&_.g -*- $"6fF$ ] % F$ *- $ ^ f _ b Bi)^d ] ;% F$"6*F$ 8 " ' ] ' _.%#' '.i)_,;'35 #- $"&f!$ ^0/ -)"$1 ^2_.% " %(RKh.%( # ] $ (% ` 3 ` 3 f " *- $"6fF$ <^2h (' " ' ] 3 f ^ 'K% hU^&' ^ " ' '.h._ h)%K * _.%( " ' ] *- +(',;%#g ` %(Ji)P3 ] cH%*^ b *- % " 3 - " ^2h (' ')g) - h)K% * _.(% S;' (% '.g *- $"6fF$ ] h fF"` " h._ f "6* ^&' *-" 3 f " % f!` 3J^ ')3 ] d !*- #- cH%( C_,(')3 ` ^6c #- ?^ 3 FfFfF"6* '.g b b /.% " )' & N- ;' #- b b /.% " ,' ?3 f ^ *- 03;^&' % 3 * ^&' 3;^ b h f f!` =Hd - (' J @ *- "6b h fF! _ ] 0^6c 798A -) g -R" ' ] ! cHK% LC,_ ;')3 ` 3 f ^ ^ *- ?K% ^2' " '53 m^6c " _."/ S3 f ^ ] "6 ^&,' ;' ] ' , - & / . + *) ( % 3 Port Parallel Junction Trachea ! #$" Upper bronchi o Valves lung pressure lung pressure Lower bronchi Beak " > h.%( # _.%K "6b h fF+ _ ] ] ( 3;%K " " ' ] #- 0 cH%( C_,(')3 ` ')3J%( " ^ * N- ( ' *- b b /.% " ', ^&h";' 8X#- 0 %( ^&' " ')35S^6c " _./"^&h";' " /^ *- ;' ]. -) h.%#^ $1 ] : "# c " 3 ^2% ` $1 ] ;'35 *-)"6A#- b ^ ] f /" -)"$1 '.g " ! - ^2_ f ] 8C*- ^2_.g - ' *- EcH^ fFf ^d '.g -)" h ;%m= -)" h ;% @>" ' !b h.%#^ $ b (' T ^ $ ^ f _ b Ei)^d = :?@e 7] 3J_ # ] 7 g2_.(% - ^d " g&' "6f i)^d ] F" g&% "6b ^6c "6fFf5*- b ^ ] f f b ;' ] 3J_ * ] ' *-) 3 -" h ;%P 4 %h.(% # _.(% cH%*^ b *- f _.'.g (' ;% *- f ^dd(%S/.%#^&'3 -. = b ^ ] f ] " -)"$1 ')g " $ ^ f _ b " ' ] " 3;^&_ * 3 * ,' * @ 82*- <'.^&' f! ,' " % $1 /.% "# ')g $"&f!$ ?= b ^ ] f ] _ '.g )' ! ] ;%(;'35 b #- ^ ]. @J8&#- <_.h)h (%T/.%#^&')3 -) = b ^ ] f ] _ '.g " ] g !#"6f d "$ (g&_ ] @ 8*- *- (% 5hU^&% _.')3 # ^2' " ' ] )' "&f!fF`m#- % " 3 - " = "6f ^ b ^ ] f ] " " ] g !#"&f d "$ ;g&_ ] @ ^ bBb _ ] "7*- md "$ ;g&_ ] ;' ] h^ ' " (% ] g !#"6f f+ ;% b ^ ] fF '.gOd "6fFf4f ^ # " ' ] (% J)i P3 # ^2' % " ' b * ^&' f+ ;% ' #- % " 3 - " 0 + # . - E ^&_ h._ ^&c *- b ^ ] fU *- $ ^ 3 ] ^2_.' ] h)%*^ ] _)3 ] / `B*- $1 /.% "# ')g b b /)% " ', ' #- ` % ' 46 $ (% ` % 3 - ' -" % b ^2' 3 " ' ] '.^ 7*- i)_ fF k ^&')A^&c (' " * ^K3 " ] d +#- #- ^&'.g2/ % ] A - "&!b ^6c *-) %K " %,3 - ^3;%K " " 3;^ b h._ ;% b _ 3 "&f ' %*_ b (' ^2', *-"< / " ] ^2' " h -C` 3 "6f4b ^ ] f d !*- h -1` 3 "6f h " % "6b ;% *-)"6 3 " ' /" bO" ' h._ fF"6 ] " ' ] " ^&_)' ] *-" 3 -" '.g " 3;3J^2% ] '.g f!` - ^&_)g !: :] % " / f ^Ok(h *- b ^ ] fL" 3 f ^ " hU^ # / f ^ 3 ;' * 3m%( "&f!!a`&8)+:bO"` /"?_ JcH_ f ^N (' ] !7 .^ ;' _.(% *- mh.%#^ ] _)3 * ^&' ^6c *- ^&'.g2/ % ]4n 3 -)" % " 3 (% # 3Eh._.%( ^2',& !" #$% &'()* 4:>] 3;_ * ] ' #- : h.%( $1 ^&_ 3 -)" h ; % 8 h)%K * _.%(:3J^2' %*^ f!f ] $"6fF$ T ' b P 3 -)" ' 3 "6fFf!` ] % !$ ; ' b _ 3 "6f ' %*_ b (' 5 _3 -" /)% " * " ' ] de^C^ ] d ' ]. " ' ] " %K "6f ^0cH^2_.' ] ' bO" ' ` / ^ f ^&g 3 "6f ^2_.' ] h)%*^ ] _)3 ')g b (3 -)" ' b 4 _)3 -m" #- $ ^K3 "6f cH^ f ]. ' *- - _ bO" ' fF" % ` ' " ' ] #- $1 /)% "6* '.g b b /.% " ') ' *- ^2'.g&/ % ]4n $ ^K3 "6f ^&%#g " ' 8C*- ` % ' 4 4 fFF" '.g " 3;^ bb ^&' h.%#^&/ f b ' h -1` 3 "&feb ^ ] f! '.g ` ' *- " ' ] ' h " % * 3J_ fF" % ' b ^ ] f ^6c h.(% # _)K% 3J^&' %*^ f!f ] $"&f!$ d - (%K *- $"&f!$ 8 _ _ "6fFf!`Q"b b /.% " ',^&%O%( ] 8T-)" #- " / !fF+a`Q ^ 3 f ^ 3J^ b h f f!` ;"h ;' ] '.gB^&' - ^d #-. $ ;' T -" ' ] f ] 8C" ' " /.%#_.h > ;% b ' "* ^&'O^&c "6 %Di)^d " " %( _ f+ ^6c " 3 f ^ ] $"6fF$ ?3 " 'R3;K% " _.' ] % " / f ] 3J^2' # '1_ !* "6b ^&'.g^ *- (% " % * c " 3 ' *- #!b P $ ^ f _ * ^&' ^6c b ^ ] f $" % " / f f "#!$ fF`f ^d " _ ] ^ "6b h fF '.g % " 3 " ' 3J(% "6 + _ "# ^2' d - (K% 8L ' *- d>^2% 3 " 8 #- b ^ ] f /"(3J^ b 3;^ b h f fF` _.' ," / f ?d - (' ] 3J(% # D ] _ '.g " ' "&f g2^&% +#-.b d - ^ " 3(3J_.% " 3 ` E] ;h";' ] ;' ^2' *- "&b h f! '.g"h ;% ^ ] ' ^ b ' #" ')53 *-) (% b ] ] / `Bb ^ $1 '.g ^ "-. g - ;'% ^&% ] ;'% (%*%#^&% "6f g&^2% !*-.b _)3 -" *- % " h D;^ ] %*_ f AcH^&%7'1_ b (% 3 ' (g&% "# ^2' " 7] 3J% "/ ] ' -" h ;%7 " ' ] o 8 o 8 o 5 + _)3 - ^6c *- -. g - cHK% L2)_ ;')3 ` 3J^2' ;' 3 %#3;_ fF"6* '.g ' " ` b ' $ ^ f!$1 '.g "E$"6fF$ " ' ] " ' " 3J^2_ * 3 _. / d Ff!f "/ mK% b ^ $ ] *- %#^&_)g - *- _ m^6cK% ;)i (3 * ^&' " ' ] d "&f!f "6j ;'1_ "# ^2' f+ ;% d -. 3 -M8Kf ^d7h " * / ` ' "6 _.(% 8 (' ] ^(% ] _)3 ^ b e^&c #- R (3 ^&c bFf ] "6fF " '.g= " ] 3;_ * ] ' -" h ;%D, ' ^ b 53 " - ^Bd $ ;% 8 "Sb ^ ] f4bO"` b "# c " 3 ^&% Ff!` #" / f ` 5*- (K% d Ff!f *Ff!f "/ + $1 ] ;'53 A^6c "&f! " '.gB3;^ b hU^&,' (' ' *- ^&_ h._ h P3 %#_ b *-" 3 " '^&' fF` / AK% b ^ $ ] "6>#- ^&_.%,53 26 -) 3 -)" h (%Th.(% ;' bO" ;% F"&f h.(% $1 ^&_ f!` h._./ f! - ] / ` b0`C*-M8 4 "/ f5" ' ] bB!*-Z ' o + #-)" cH^13;_ ^2'Q(% ] _)3 ')g *- ^2_.%,53 O^6c "&f! " '.g ' " h.(% # _)K% 9 3;^&' %#^ fFf ] $"&f!$ !b _ f "* ^&'/ , ` + c "#- ;% '..g - *- 3J^ f!fF ^&'"/ Bd (' " ' ^&"h ;' " ' ] 3 f ^ ] $"6fF$ & 4 ' Fb h.%#^ $ ] ^ f _ * ^&' ^ *- *Fb b $ ^ f _ * ^&' ^&c $ ^ f _ b i)^d g F$ (' ' -" h ;%< 8 h.%#^ $1 ] " b ^C^ *- 8 ,' " % f!`"&f! " cH(% % " ' !* ^&' / dd ;' *- de^ ," 5 >> * < * 2 # *$ # > 0 *$ *$ < !6*$ 01 ' )- " h (% 8 cH^2_.% $" % " / f ^6c #- ` % ' b ^ ] f =H^2',f "&b h f E^6c " h)%K * _.%(<3J^&' %*^ f!f ] $"6fF$ b ^ ] f @ dB;(% Ag !$ ;' " 7 : 78 h.%( # _.%K^2' #- m/.%#^&')3 -. 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" ] 3J^ b hU^&');' d -. 3 " h) h " % " "h " k " '.^&' -)" % b ^&' 3EcHK% L2)_ ;')3 Magnified Volume Flow (U) 120 100 mL/s 80 60 40 20 0 258.1 258.2 258.3 258.4 time − milliseconds 258.5 258.6 g2_.%( K 108 4 b" g&' ) ] C$ ;d ^&c $ ^ f _ b i)^d 8 :B8 #" k;'cH%#^ b 7 g&_.%() 0 Ej ' fF` " 'n K3;%#h cH%#^ b 7 g2_.%( B - ^d7' ^ 3 f " % fF`!fFf _ % "6 *- #% _.')3 "# ^2'Z^&' " 6" b h f /^2_.' ] " % ` = ' *-. 3 " *- "6b h f EcH^ f!f ^d '.g 0 b @ 7 - _ 8&" 7 g&_.%(7) 0 cH%#^ b -)" h ; %D ' ] 3 "6 82"&f! 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C 76b h f A+ hf+4) ' ^ ] C4- +(d) ' 2 '=? g ` *-!o 3c>g '=8 +LC ` c ` p-Fo 0 c :/` c N ` c / B<^32A+/2 0 7 2 '=? 2 0 ' C:cH^3) b 2 0 + @B+>) ? ^2_ fFf@' 2A+4) b ' CNC '!bl'Ff=7 )M2*^I2 0 7 2E^&c ` p-FoLcQFd ' 2 0 7J8D76f=8 + 0 7o8:'=? g '=?;5 )A+ 7 CA+ ] 7 ),+ 7 !- ? ^32 0 +>A) de^3) ] C>F ' 2 0 7 C < + 5 ^ b + 7 f + 7 k `U8D7&f@8 +0d 0 ^:CG+ f + 7 k 7 gE+ '=?;5 ),+ 7 CG+LC:d ' 2 0 '=?;5 ),+ 7 C '=? g 8 ^ f _ b + i)^d\ ?7 ].] ' 2 ' ^ ? *2 ^ 5 ),+ 7 2 '=? gX2 0 + ] +>C ' )A+ ] + + 5 2 ^&c 7 gE+ ? 2 f +4)WC f ^&hf+3FB2 0 ' C ? +;d cH^3) b cH^E)J2 0 + @B+4) ? ^&_ fFf=' 2A+>) b ` pF- o 0 cBjC ^ f@8 +>CV2 0 + ? _ b +>) '654&7 ff'=? CG2 73<*!' f=' 2 `I'=?X` pF- oLc 1< `I7 ])] '@? g 7q? ^ ? D4+4)#^T2A+4) b 0 2#^T2 0 +0 ] + ? ^ bl'=?;7 2#^30 )LF 67 fFf ^d '@? g /`b cN*2 ^]2 7 kEB+ ^ ? 7 D>+4#) ^ 8D&7 f _*+EE- 2 ' C ? ^ f ^ ? g3+>) ? + 5 +>C,C 7 ) ` #2 ^ bl73? _ 76fFf!` 76f 2n2 + 73' )i^d 2 + b ^ b + ? 2r2 0 + 8o&7 f@8 + ' C ;5 f ^:CG+ ] - M7 2 0 +4)LF 7 C 5>7K?< +jCA+4+ ?W'=? 7a' g&_;)A+ p- 0 F:2 0 + 7K' 5) i)^d ' C ? ^d < + '@? g < )#^&_)g 0 2 2*^D>+4#) ^ 67 f ^ ? g S7 b ^3),+ 7E545 _;) 7 2A+ 730 ? ] C b ^1^K2 0 2A) 7 + 5 #2 ^3) ` F 7K? ] F 7 C !' fFf _ Ch2,) 7 2A+ ] '=? 7(' g&_*),+ *- F:2 0 +h*),+>CA+ ?;5 + ^6c 67 f='67 C '@? g ' 5C g3),+ 7 2 f!` )A+ ] _ 5 + ] d + ?U5 ^ b h 7 ),+ ] #2 ^ 7(' g2_*)A+ *- p 0 A + ?;67 f c+ 7+ 2 0 +>)A+ ] _.h ] 7 2,D+ cH^3) 8 ^ f _ b T+ i)^dd 0 + ? ] ' C 5 ),+Q2 ' D>+ ] _;C '@? gM2 0 +_2A) 7 hf9+ D(^ ' ] *) _ f T+ cH^3) ? _ b +>) '654&7 f '=? 2,;+ gE) 7 2 ' ^ ? o ' 67 f ^E)*g 7K? FS2 0 +/C ` ) '=? OF 7K' )C,C*_*)A+Ac)#^ b 2 0 + f _ ? g:C 5 ^ ? 2A)#^ f CB2 0 +0^EC 5Q'Ff!f67 2 ' ^ ? ^&c 7b + b < ) 7K? + 0 `<1`q5 0 0 7K? g 0 '@? gn0 2 0 :+ h;)A+LCAC*_*),+ 735 )#^EC,Ce2 0 0 + b + bT0 < ) 7K? +ocdF ' 2,C ] ' Cjh 0f=7E5 + b + ? 2 547 _ 0 C '=? g 7\8D7 ) '67K<.f + 5 ^ ? CG2A) '=5 2 ' ^ ? 2 0 )#^&_.g d0 '=5 73' ?) i)^dMC < +JcH^E)A+ ),+ 7E5 '=? g0 2 + _.h.hf+4) < )*^ ?;5 _;C 7K? ] 2A) 735 + 7 - '!bl'Ff=7 ) fF` 0 F <.f ^d '=? g '=? 2#^/2 + b ^&_p20 h ' + 5 + ^&c 7qJ5 f67 ) '@? +4e2 d F' fFf^547 _ CG+R2 +n),+4+ ] *2 ^ 8S'@< ) 7 2A+3F ?;7 )A)#^d '=? g 73? ] d ' ] + ?;'@? gq2 + 7K' )ji)^d 7 hf+4)A2*_;)A+N*2 ^q2 + < ^E)A+ER' g ' 2 67 f C !' b _ f67 2 ' ^ ? C ^6c bl731? ` de^C^ ] d '=? ] 7K? ] < ) 7 CAC b _;C '654&7 0 fZ'@? Ch2,*) _ b 0 + ? 2HC `b'@? CG2A)#_ b + ? 2HCn2 0 7 2?_;CA0 + 7 h*),+>C,jC _;)A+ 5 ^ ? 2,*) ^ f!f + ] 8D&7 f@8 +LcRjC _ +4) c#) ^ b 7 h*#) ^ .< f + b C F' bqF' f67 )R*2 ^2 7 A2 ^&c92 +^3) ' g '@?;7&f C ` ) '=? b ^ ] + f d + ? 2 0 +j)A+>+ ] < + 7 2HC 7 g 7K'=? CG22 0 0 + f=7 ` ^6ce2 0 + 0 b ^2_p2 0 h ' + 5 ?+ ^E)>F b ^E)Am+ gE+ ? +>) &7 f!fF` )F d 0 + ? 2 0 + 8D67 f=8 0 + 0 7 Cr2 0 + 7K<*F' f=' 2 ` 2*^ ;5 f ^:CG+ 5 ^ b h f +42A+ f!` A- 0 ? 2 ' CMCG+ 5 2 ' ^ ? FS2 +jC ` ) '=? 8D&7 f@8 + F' b h*#) ^ 8 + b + ? 2H0C 7 ),+ 7 h.h f=' + ] #2 ^q2 + ;5 0 f=7 ) '=? +Q20 ),+4+ ] _;Ch2 7 C 7K' T) c#) ^ b 2 + ' ) f _ ? g:C ] _;) '=? g <;' ) ] *C ^ ? g 5>7 _;CA+>C b ^K2 ' ^ ? ^6cO2 +NC ` ) '=? 8D67 f=8 + 73? ] 2 _ C 7T5 7K? gE+ '=? 2 0 + 0 + ' g 0 2 ^6cn2 0 + 8D&7 f@8 + 5 0 7K?*? + f Fr*C ^ ] ^S+>0C )< f ^d '=? g '=? #2 ^X2 0 + b ^2_p20 0 h ' + 5 + ^&c 7 0 ;5 f=7 0 ) '=? +Q2 5>7 _;CA+]2 0 + ),+4+ ] *2 ^ 8S'@< ) 7 2,+3F ? 7 ),*) ^d '=0 ? g 730 ? ] 0 d ' ] + ?*'@? g[2 + 7K' j) i)^d0 7 h +>)G#2 _*),+I#2 ^[0 2 + < 0 ^E)A+ d ' 2 2 + h^:CAC '=<*!' f=' 2 ` ^6c J5 f ^EC '=? g ' 2 5 ^ b h f +Q2,+ fF` C- ^2_.g 2 + 5473? +/),+4+ ] ' C b _ 5 b ^3),+/) ' g ' ] 2 7K? 2 + <*' ) ]4n CnC ` ) '@? b + bT< ) 7K? +EF ' 2,ClC F' b _ f=7 2 ' ^ ? 5>7K? < + ? 9+ *2c*) ^ b 2 0 +]C &7 b + h*) '@? 5Q' h f +L0C ^&c) '=? g h 7 )G2 '=5 _ f67 ) f!` d 0 + ? b +>+Q2 '@? gP2 0 + ] + bl73? ] 5C ^&c(),+ f67 2 '@8 + fF`Of ^d 7 _ ] ' ^JC &7 b h f@'=? gl) 7 2A+LC4 * " , ' H U Bore x y Lip Reed (' g2_*),+ 0 p- H 8e. C 'Fb h f=' ;+ 0 ]] '67 gE) 7&b ^&c 7q0 5Jf67 ) '@? +42V),+4+ ] -A 0 + 8D7 ) 0 '67K<.f + )A+(h*)A+LCG+ ? 2,CZ2 0 0 + b ^&_p2 0 h*),+>C,Cj_;)A+EF R' CM2 +h*),+>C,Cj_*),+ '=? 2 + < ^3),+3Fg ' CY2 + 8 ^ f _ b +?i)^d\F ' CR2 + ] ' C*h f=7E5 + b + ? 2E^6c92 +q)A+>+ ] F '=? ] 6' 547 2A+>C 2 0 m+ h^:C ' 2 ' ^ ?]76f ^ ? gT2 0 +\)A+>+ ] 7K? ] ' Cr2 0 + f + ? gK2 0 ^&ca2 0 +m_ ?;5;f=7&b hf+ ] + ? ] ^6cg2 0 +\),+4+ ] 7 V ! W#"%$ $&' )( +*,-./$02134( 5 ^:Ch2 5 _;)A),+ ? 2 b ^ ] + f C ^6cf2 0 + 5;f=7 ) '=? +42_)A+>+ ] 7 ),+ 'Fb h f + b + ? 2A+ ] _;C '@? g 7f ^1^&k1_.hT2 7K<)f +7d 0 '65 0 bJ7 2 5 0 +>C 8D76f _*+>C cH^3) i^d d ' 2 0 2 0 +7*h ),+>C,Cj*_ ),+ ] )#^&h 735 )*^:CACa2 0 +M)A+>+ ] 8D76f=8 +E-) 0 ' C ' C k ? ^d ?l7 C 7 C_ 7 C ' CG2 7 2 '65eb ^ ] + f C '@?;5 +r2 0 + 8D76f _*+D^&cCi0 ^\d FDqF ' C^+LCh2 7K<.=f ' C 0 + ] + 7(' g2_*),+ p-Fo J cf) 7 0 2 0 +4)^02 0 73?\< + '@? g ] +Q2,+4) bl'@? + ] <1P` ' 2,C < + 0 7o8S' ^2*_ )0^ 8 +4)n2 '!b + 7 C '=? ] '6547 2A+ ] ) ` C 7 2 ' Cac S` '=? jg ),+>C*_ f 2,C 7 )A+7^0 < 2 73'@? 0 + ] d ' 2 ),+ 6f 7 2 '@8 + fF`0f ^d 5 0 ^ b h.*_ 2 7 2 ' ^ ?;0 76ff 5 :^ Ch2L-60 +R)A+LCj_ f 2HC 0^Bd + 8 +4)LF 7 ),+ ? 3^ 2#2_ ' 2,+WC*^ '!b *h ),+>C,0 C '=8 +d + ? 2 +I0 )A+>+ ] < + 7 2HC 7 g 7K'=? CG2\2 + 6f 7` ^&rc 2 + b 0 ^2p_ 2 h ' + 5 +IC '@? 5 +J2 +hU^ '=? 2S^6c 5 ^ f!=f ' C ' ^ ? C < +Q2aBd +4+ ? 2 + ),+4+ ] 73? ] 2 + 6f 7` ' Cm^6c 2,+ ? 2*^1^ 7K< )*_.*h 2>F 5>7 ;_ C '=? g 2 + C*^&_ ? ] 2#^ < + b +42 76fF=f '=5J73? ] 7 )A2 ' . 54'=7&f ? + 5 + fFf + ? 2 ] +L+ C 5 ) ' ph 2 ' ^ ? ^&:c 2 0 +$C_ 7 C 0 ' Ch2 7 2 '65Z5J6f 7 ) '=? +Q2^),+4+ ] b ^ ]0 + f d 7 C4h)_ <.=f ' C 0 0 + ] F '!=f < +>)G2 7K? 7] 6 0 fF@f '=8S' +>) 0 '@? < p_ 2 ' C_Cj_ bBJb 7 ) ' D4+ ] +>)A+B2#^mg '=8 + 5 ^ ? 2,+S 2Z2*N^ 2 + ] ' C 5 _ CAC ' ^ ? 2 7 2 cH^ f!f ^Md C>-6 +CG2A+ 7 ] ` i)^i d 2 )*^2_.g 7T8D76=f 8 + ' C ] +Q2,+4) lb '@? + ] <;7 CG+ ] ^ ?W7K? '=? h.p_ 2 ` 3^ ) <)f ^d '=? :g cD*h ),+>C,Cj*_ ),+:;h )A+LCAC**_ ),+ 7K? ] 7 ),+>C*_ f 2 '@? g ^&*_ 2*h.p_ 2 ` 3^ ) b ^&*_ 2 0 h ' + 5 +Lce*h ),+>C,C**_ )A+E-6 0 + ] ' +4),+ ? 5 + < +Q2aBd +4+ ? 2 0 +>CA+n2ad>^*h ),+>C,Cj;_ )A+ ] g '=8 +LC8 BM+(g f + 5 2 '@? g '@? +>)G2 '=7 F>d 0 '=5 0 '=? 2,)*^ ] _ 5 +>C 7 ] + 6f 7` '=? 73? ] 0 + ?;5 +]2 0 +<@B+>) ? ^2_ fF@f ' ; h )A+LCAC**_ ),+ .o + FB2 0 + CG2 7 2 ' ^ ?;7 ) ` + C_ 7 2 ' ^ ? cH3^ ) 8 ^ f _ b +Ei^d ' C5g '=8 + ?<1` :9 8 ` p-Fo c d 0 +>)A+;8 ' Cn2 0 +h*)A+LCAC*_*),+ ] ' +4),+ ? 5 + 735 )*^:CACR2 0 + ),+4+ ] F ' Cn2 0 + 5 )#^EC,C\CG+ 5 2 ' ^ ?X7 )A+ 7 ^&cr2 0 + 37 ' ) 5 ^ f _ bl? b` 73? ] 2 0 + +42Hc 7K? ] ' CB2 0 + ] + ? C ' 2 ` ^6c 73' )L-A 0 ' Cr+ C_ 7 2 ' ^ ? cH^E) b CV2 0 n+ 2 7K<)f +AcH^&_ ? ] '@? 7(' g2_*)A+ p-Fo J 7K? ] ' C H10 !"#%$&'$( )&* (! Volume Flow as a Function of Pressure Difference 400 threshold of oscillation 350 300 U (cm3 / s) 250 200 150 100 reed closed 50 0 0 10 20 30 40 50 60 p0 − p1 (hPa) 70 80 90 100 (' g2_*)A+ * -!o J 8 0 +\)A+(g ' ^ ? ^6c ^EC 5Q'Ff!f67 2 ' ^ ?I' C7_;C*_ 76fFf!`I< +42adV+>+ ? 2 0 n+ 2ade^ ] ^K2A2A+ ] =f '@? +>C>7 5 ^ b h 7 ) 7K<.f +R2*^ ` *-!ooced ' 2 0 2 0 + ] +>) '=8D7 2 '=8 +EF F*CG+422*^ED4+>)*^ ] 2 0 + 0 + 'g 0 2 0 +?gE+;^ b +42A) ` ^&cZ2 0 + 5Jf67 ) '@? +Q2 8D76f=8 + ' CEg '=8 + ?U) ? 7 2 '=8 + f!` Fg2 0 + ] ' CG2 73?;5 + < +Q2adB+4+ ? 2 0 + )A+>+ ] 73? ] 2 0 + f=7` cQF -< 0 + 7 )A+ 7 F F ' C 2 0 +4),+JcH^3),+g '=8 + ?I<1` / ` p-Fo H c 0 + b ^K2 ' ^ ? ^&cg2 0 +\)A+>+ ] F f=' k3+N2 0 7 < 2 ^6c(2 0 +jC ` ) '=? 8D&7 f@8 +31F cH^ fFf ^dMC92 0 +c 76bl'Ff@'67 )+LC_ 7 2 ' ^ ? ` c9 8 p- J c ` N N 0d +>)A+ ' C 7 ] 67 b h '=? g 5 ^S+ 54' + ? 2>F ' Cn2 0 +J+ + 5 2 '=8 + bJ7 C,C ^6cB2 0 +J),+4+ ] 73? ] ' Cn2 0 +J),+4+ ]4n Cn)A+LjC ^ ?;7K? 2 * " , ' H '=?;5 + ' C)A+ f=7 2A+ ] 2#^T2 0 +jCG2 ' f? +LCAC 7K? ] 2 0 + bJ7 CAC <1` ` p- ooc d 0 +>)A+ ' Cr2 0 +\),+4+ ] CG2 ' ? +>C,C `'=? 7 b cQFS + C_ 7 2 ' ^ ? ` p- J c 5>7K?< +\),+;d) ' 2G2A+ ? cH^E) 5 ^ ?S8 + ?;' + ?;5 + 7 C ` p- I c N N W 8 d 0 +>)A+ ' C bJ7 C,0C hf+4) 7K? ] g ' C 7[8S' C 5 ^2_;C ] &7 b h '@? g 5 ^S+ 5Q' + ? 2 `'=? c + - ? 2 0 + C_ 7 C ' CG2 7 2 '65 b ^ ] + f FO2 0 + ] +4) '@8D7 2 '@8 +>C '=? ` p- I c 7 ),+lCG+42N#2 ^ D>+4#) ^W),+ ? ] +4) '@? gI2 0 + b + 5 0 7K?;'=5>76f )A+>+ ] + + 5 2 '@8 + fF`RbJ7 C,C f +>C,C>F d ' 2 0 2 0 +TCG2 ' f? +>C,C < + '=? g 2 0 0+ ^ .? fF` ),+ 7E5 2 '@8 +\+ f + b + ? 2>- 0 +/L+ C_ 7 2 ' ^ ? cH^3)M2 0 +2_ 7 C ' Ch2 7 2 '=5 ),+4+ ] 2 0 +>)A+;cH^3),+ < + 5 ^ b +>C W 8 / ` p- :c c ' CI2 0 + + C_ F' f='@< ) ' _ b ^&hf+ ?*'=? g F2 0 7 2 ' C>FM2 0 + ^2h + ?*'@? gZ^6c\2 0 + 8o&7 f@8 + '=? 2 0 + 73< CA+ ?;5 + ^6cmi^d\F2 0 + ] ' Cjh f=7E5 + b + ? 27^&ca2 0 +\)A+>+ ]] +Q2,+4) bl'@? +LCB2 0 + 8D7&f@8 +A^2h + ?*'=? g;F F C*h^ ? ] '=? gP2*^ 7X5Jf ^ECA+ ] )A+>+ ] ' C ] +Q2,+4) bq'=? + ] 1< ` CA+Q2G2 '@? gT2 0 +m^&hf+ ?;'@? gl2#^D4+4)#^^3)LF 76f 2A+4) ?;7 2 '=8 + fF` FS2 0 + ] ' Cjh f=7E5 + b + ? 2r2#^ ' 2,C bl7 '!b _ b F W - 0 7 2 ' C4F 8 ` p- Ec p- 0 c 8 ` 'c J 8 p- 3c ` 0d +>)A+ ),+;h*),+>CA+ ? 2HC92 0 + bJ7 'Fb _ b h;)A+LCAC*_*),+ ] ' +4),+ ?;5 + 7K< ^ 8 +Ad 0 '=5 0 2 0 + 8D76f=8 + ' C ;5 f ^:CG+ ] @ `W7 h)h f!`S'=? g ` *- c 7K? ] ` *- 3cQFS2 0 + 7 )A+ 7 ^&cg2 0 +\)A+>+ ] ^&hf+ ?*'=? gc)#^ bm` p-Fo H c < + 5 ^ b +>C 8 ` p- c d 0 '65 0 5>7K?< +cH_;)G2 0 +4)M),+ ] _ 5 + ] #2 ^ o 8 8 ` p- ;H c 0 0 <1`I7 h)h f!`S'=? g ` *- KcdA- +jCG2 7 2 ' ^ ?;7 ) `J8 ^ f _ b A+ i)^d c#) ^ bm` pF- o c 5>7K? 2 +>)A;+ cH^3),+ < m+ d) ' 2A2A+ ?]7 C / o 8 8 9 8 / ` p- J c H E_ !"#%$&'$( )&* 7K? 2 ' 2 ` _7&f _*+ Y 7K? gE+ `1bT< ^ f C_ 'Ff@'=< ) ' _ b )A+>+ ] ^&hf+ ?*'=? g +4+ ] Ch2 ' ? +>C,C 0 KA + 5 2 '=8 +d ' ] 2 ^6c +Q2 5 7 'Fb _ b 8 ^ f _ b +Ai)^d 7f ^d ^ ? 2 0 +\),+4+ ] ^ + 5Q' + ? 2HC R7&b h '@? g 5 S + ? C ' 2 ` ^6c 73' ) Y'=< ) 7 2 ' ^ ? c 0 ),+ C*_ + ? 5J` ^&c(),+4+ ] ` b ^ ] O+ ooc +4+ ] f + ? Kg 2 K # o # o ;- J5Jb J J JIJIJJ J D ' 7K<.f + p -Fo 8 K 67 + b h f + 8D76f _*+J) 37 ? g3+LCAcH^3) 8o7 ) 6' 7K<)f +LC^6cr2 0 + 2_ 7 C ' Ch2 7 2 '=5l5Jf67 ) '=? +Q2 2 7 k3+ ? c)#^ b Qc < CG2 ' 2*_p2 '@? g 8 8 d 0 '65 0 ' CN2 0 + 8D7&f _*+^&c 8 _ Ch2 < + f ^d 2 0 +T2 0 ),+>C 0 ^ f ] ^&c>^:C 54!' fFf=7 2 ' ^ ? F ' C,Cj_;)A+ ] ' +4),+ ?;5 + ' C:gE)A+ 7 2,+4)2 0 7K? F ' 2 ' C 7 CAC*_ b + ] 2 0 +4),+ ' C ? ^i)^d 2 0 )*^2_.g 0 2 0 + 8o&7 f@8 + 5 0 73?*? + fV` CA+4+ 7(' g2_*),+ *-!o J 0 c 7K? ] ' CMCA+Q2M2#^ED4+4)#0 ^;-$ 0 ' C 0 7K? ] f@'=? gO^6c(2 0 +mi)^d < +42adV+>+ ? ^&hf+ ? 73? ] 0 J5 f ^ECA+ ] 8D0 76f=8 +LC ' C9),+ bl'=?*' C 5 + ? 2>^6cO02 + ),CG2 ' 2A+>) 7 2 ' ^ ? ^&cO2 +NC ` ) '@? b ^ ] + f - 2 5>7K?I7&f C*^ < + 'Fb h;)*^ 8 + ] <1` c+ 7 2 +4) '=? g 2 + 5 ^ fFf=' C ' ^ ? C < +42adV+>+ ? 2 +m^&hf+ ?U7K? ] 5Jf ^ECA+ ] CG2 7 2,+>C> .*&1- $& 0213( " ( - $ . $& *&43) $ - 3 B+JcH^E)A+ 7 h)h f!`S'=? g2 0 + - A;> -/. - : < + 7 2 '=? gU0 ),+40 + ] F^2 0 +J+ C_ 7 2 ' ^ ? CAcH^3)?i)^d 73? ]] ' C*h f6735 + b + ? 2 '@? 2 0 + C_ 7 0C ' CG2 7 2 '=55b ^ ] + f.b _;CG2;)HCG2 < +M),+;h f6735 + 0 ] d ' 2 2 + ' ) 5 ^3),),+>C*h^ ? ] '=? g ] ' +4),+ ? 2 '676f + C_ 7 2 ' ^ ? C>F '@? 5 ^3)#hU^3) 7 2 '=? gN2 + 7 h)h**) ^2h*) '=7 2A+ 8o7&f@8 +g3+;^ b +Q2A) ` cH^3)r2 + 5Jf67 ) '=? +Q2L@ 0 +NCh2,) 7 2A+;g ` cH^E) ] +Q2A+>) bl'=?*'=? g\2 0 + 8 ^ f _ b +7i)^d ] +>) '=8D7 2 '=8 + '@? 2 0 + 5Jf67 ) '@? +42V),+4+ ] b ^ ] + f ' CBC 'Fbl'!f67 )V2*^/2 0 7 2 cH^3)r2 0 +jC ` ) '=? OF ] ' C 5 _ CACA+ ] '@? S+ 5 2 ' ^ ?W - - FKd 0 +4),+!@V+>) ? ^&_ fFf@' n Cr+ C_ 7 2 ' ^ ? `b - Ec ' C 7 g 73'@? + b h f ^ ` + ] 0 +\C 0 7 hf + ^6c(2 0 + ;5 f=7 ) '=? +Q2),+4+ ] ' CC_ ' 2,+ ] ' +>)A+ ? 27c)#^ b 2 0 +jC ` ) '=? b + bT< ) 7K? + 7K? ] ^ ?.f!`W7 2 0 '=? C f='=5 + * " , ' HIH 76f ^ ? g/2 0 + 7 ' C ` CA+4+ 7a' g&_;)A+ p- H cT0 d 0 '65 0 ' C '@?]05 ^ ? 2 735 2>d ' 2 0 0 2 0 +Ai)^d `b< +;cH^3),+N2 0 +Ei)^d CA+;h 7 ) 7 2A+LC 73? ] cH^3) b C 7 +Q2Hc ? +4+ ] < + 5 ^ ? C ' ] +>)A+ ] -A +cH^3) 5 +^ ? 2 ' C7h 7 )A25^&cg2 +\)A+>+ ] ' C)A+ /` fc ' CV2 0 + 7 )A+ 7 ^&c^2 0 + 8D67 f=8 + 5 0 7K?*? + fO7 2B2 0 ' eC h^:C ' 2 ' ^ ?7K? ] 8 (` *c ' C92 0 +Ah;)A+LCAC*_*),+ ] )#^&h 7E5 )#^EC,C 2 0 ' CMCA+ 5 2 ' ^ ? ^6ca2 0 +\),+4+ ] - 0 ' eC cH^3) 5 + ' C 7 h.h f=' + ] *2 ^ B7 bJ7 C,5C ^6c T` c ` p- c d 0 +>)A+ ' Cr2 0 + 7K' ) ] + ? C ' 2 `W7K? ] T` c ' Cr2 0 + 8 ^ f _ b +n*2 ^d 0 '65 0 2 0 + cH^E) 5 + ' C 7 h.h f=' + ] - '=?;5 m+ h*)A+LCA*C _*),+ ' 5C h**) ^2h^E)G2 ' ^ ?;67 f #2 ^cH^3) 5 +3F BY;+ dr*2 ^ ? n CMCG+ 5 ^ ? ] f67 d\F fF 547K?< + 7 h.h f=' + ] *2 ^ ` *- Ec9*2 ^O^ < 2 73'@? ` p- Ec /` fc 8 a` *c9 /` fc d 0 +>)A+ 7E545 + f +>) 7 2 ' ^ ?]' ) '=8D7 2 '=8 m+ ^&ce2 0 S+ h 7 )A2 '6J5 f + 8 + f ^ 5Q' 2 ` F F 7 C,jC _ b + ] 5 ^ ? Ch2 7K? 2 ^ 8 +>)B2 0 ' CCG+ 5 2 ' ^ ? ^&cg2 0 +\)A+>+ ] '=?;5 + 8 ^ f _ b + i)^d ' CI+L2_ 76f 2#^Zh 7 )G2 '=5;f + 8 + f ^ 54' 2 ` C 5476f + ] <1`i7 ),+ 7 FV2 0 + + 1h;)A+LCAC ' ^ ? cH^3) ] ' +4),+ ? 2 '676f h*),+>C,jC _;)A+ 7 C 7 cH_ ?;5 2 ' ^ ? ^6c hU^EC ' 2 ' ^ ? 67 f ^ ? gT2 0 +\),+4+ ] 5 0 7K?*? + fO' )A+ J ' Cl2 0 + 5 0 73?*? + f + ? 2,) 73?;5 + 7K? ] ' C 2 0 +RhU^ '=? 2 7 2d 0 '=5 0 2 0 + i)^d CG+(h 7 ) 7 2,+>CBc)#^ b 2 0 +q*C _**) c 735 S+ ^6c_2 0 +q)A+>+ ] 73? ] cH^E) b C 7 +42>C- 0 B+ h*),+>C,jC _*),+ 7 2R2 0 + 5 0 7K?*? + f + ? 2A) 7K?;5 + ' C ] +Q2,+4) bq'=? + ] _;C '@? g @B+4) ? ^&_ f!f=' n CB + C_ 7 2 ' ^ ? F `b - EcdF 7K? ] ' < C g '=8 + ?1< ` a` J c_ T` J fc ` p- c d 0 +>)A+ ' CY2 0 + b ^&_*2 0 h;)A+LCA*C _*),+3- '=?;5 +/2 0 + h*),+>C,jC _;)A+ 7 2R2 0 B+ h^ '@? 2 ^6c i)^dvCA;+ h 7 ) 7 2 ' ^ ? F (` cdF ' CR+ C_ 76f *2 ^q2 0 + < ^E)A+ h*),+>C,*C _*)A+ F ` p- Kc < + 5 ^ b +>C K H T` c / ` p- H c H T` J fc M^^ < o JJ !"#%$&'$( )&* (! 0 + ] ' +4),+ ? 2 '676f +L2_ 7 2 ' ^ ? g&^ 8 +4) ?*'=? g 8 ^ f _ b +Ei^d ' Cr2 0 + ? g '=8 + ?W<1` ` c /` fc ` p- J c /` c d 0 +>)A+2 0 +Ei)^d ' C 7 C,Cj_ b + ] 2*^ < + '@?I5 ^ ? 2 7E5 2Td ' 2 0 2 0 +N)A+>+ ] cH^E) 7 ] ' CG2 73?;5 +<^&c 7 2 7j5 ^ ? Ch2 7K? 2 7 )A+ 7 + C_ 7&f 2*^ /` fc9 /` J fc9 ` fc ` p- ooc d 0 +>)A+ ' CB2 0 m+ d ' ] 2 0 ^&ca2 0 +\),+4+ ] ` ^E) +Q2dc 7K? ] \' C2 0 m+ ^2h + ?*'@? gO^6cg2 0 + 8D67 f=8 + 5 0 73?*? + fg'@? 2 0 + 7K< CA+ ?;5 + ^6ci)^d\ J l 0 +\+L2_ 7 2 ' ^ ? cH^E) ] ' Cjh f6735 + b + ? 2 ' C ] +Q2,+4) bl'@? + ] b _ 5 0 7 C ] +>C 5 ) '@< + ] '=? S+ 5 2 ' ^ ?] - - <1`W5 ^ ? C ' ] +>) '=? gq2 0 + cH^3) 5 + 735 2 '=? g^ ? 2 0 + 5Jf67 ) '=? +Q2N)A+>+ ] - c_2 0 +q),+4+ ] ' CR) ' g ' ] 73? ] 0 '=? gE+ ] d ' 2 0 Cjh*) '=? g 5 ^ ? CG2 7K? 2 7 2 7 hU^ '=? 2 c 7 )Ac)#^ b 2 0 + b ^2p_ 2 0 C ' ] +B^6cV2 0 + f=' hgF f +42 < +T2 0 + f + ? g32 0 ^6cV2 0 +q)A+>+ ] )*^2_.g 0 fF` 76f ^ ? g 2 0 + ` 7 ' CAd 0 '65 0 CA+4+>CB2 0 + b ^&p_ 2 0 *h )A+LCAC*_*),+3F1d 0 +>)A+ ' C ] +9 ? + ] 7 C < +;cH^3),+3F 73? ] 7 cH^E) 5 +^6c ` p- c d 0 '65 0 cH^3) 5 +LCr2 0 +T)A+>+ ] 5Jf ^ECA+ ] H + - ? 5 ^ ? 2A) 7 CG2>Fp2 0 +?cH^E) 5 +m^ ? 2 0 + < ^E)A+TC ' ] +?^&c(2 0 +j),+4+ ] 7 d 7` c)#^ b 2 0 + +Q2LF.g '=8 + ?W<1` ` c ` p- :c cH^3) 5 +LCR2 0 +l),+4+ ] ^&hf+ ? - 0 +BcH^E) 5 + 7 h.h f=' + ] <1` 2 0 +Bi)^d ` d 0 '=5 0 76f Cj^ cH^3) 5 +LCR2 0 +J),+4+ ] ^&hf+ ? c ' CAcH^&_ ? ] 1< ` '=? 2,+;gE) 7 2 '=? g/2 0 +mh*),+>C,Cj_;)A+ 76f ^ ? gq2 0 +i)^d 73? ] ' C7g '@8 + ?1< ` H ` p- 3 c KH T` c / 0 +E^ 8 +4) 76fFf cH^3) 5 + 735 2 '@? g?^6cO2 0 +Y),+4+ ] ' CT^ < 2 7K'=? + ] <1` Cj_ bBbl'=? g ` p- cdF ` p- :c 7K? ] ` p- 3 c 7K? ] ' C>g '=8 + ?q<1` ` c ` c / ` fc / ` p- Ec 6 ?;5 +I2 0 +cH^3) 5 + ' Ck ? ^d ? F_2 0 + ] ' Cjh f=7E5 + b + ? 2^6cR2 0 +]),+4+ ] ' C^ < 2 7K'=? + ] _;C '=? gP2 0 +c 7&bq'Ff='=7 ) ] ' +4),+ ? 2 '676f + C_ 7 2 ' ^ ? ` c9 p- 0 c ` N N d 0 +>)A+ ' C ] 9+ ? + ] 1< `[` p- Ecd@ ` c+ 7 2 0 +4) '=? g/2 0 + 5 ^ fFf=' C ' ^ ? > C ^6c^2 0 + < + 7 2 '=? gq)A+>+ ] '=? 2 0 + J5 f67 ) '@? +Q2BC F' b _ f67 2 ' ^ ? F:2 0 +\*C ^&_ ? ] ' C F' b h;*) ^ 8 + ] 7K? ] F '=? h 7 )G2 '=5 _ f67 )LF*2 0 + 67 f='67 C '@? g 7 CA*C ^ 5Q'67 2,+ ] d ' 2 0 2 0 ' CR+ 8 + ? 2 ' CM),+ ] _ 5 + ] 7 CYC 0 ^d ?U'=? 7(' g2_*),+ pF- o d 0 + ? I oJo ! 5 ^ b h 7 ),+ ] d ' 2 0 (7 ' g&_*),+ p -Fo&oEls 1u Mw eQu 0 + ] ' +>)A+ ? 2 '=7&f + C_ 7 2 ' ^ ? ` p-FoLc ] +LC 5 ) '=<*'=? g 2 0 + < + 0 7o8S' ^2_*)B^6c 8 ^ f _ b +i^d ` *-!ooc 5>7K? < + ? _ b +4) '=5>76fFf!` _ ? CG2 73<.f + < + 547 _ CG+7^&c 2 0 +MC '=? g2_ f=7 ) ' 2 `j'=? 2 0 + @B+>) ? ^2_ fFf@' 2,+4) b d 0 + ? 2 0 + 8D76f=8 + 5;f ^:CG+LC4- 5 ^3),+;^ 8 +4)LF 76f='=7 C '=? g ' C 547 _;CA+ ] 1< `T7K< *) _.h*2 fF`T5 _*2G2 '=? gm^ 0 i)^d d 0 + ? 2 0 + 5 ^ b h._p2A+ ] i)^d h 7 C,CG+LC(2 0 0 )#^&_)g 0 D4+>)*^ -)@e^K2 0 h;)*^ <.f + b C 7 ),+ 7 ])] )A+LCACA+ ] 1< 0 `]'@0 ? 5 ^3#) hU^3) 7 2 '=? gl2 + 0 ? (+ d C bJ7&f!f 7 )A+ 7 Cj^ f _p2 ' ^ ? cH^3)j ` cQ- + 8 ^ f _ b +mi)^d0 ' C ? ^dl_)h ] 7 2A+ ] '=?[7 d 7 ` d '=5 h**) ^ ] _ 5 +>CNC b ^1^32 +>)Y2,) 73? C ' 2 ' ^ ? 0 C < +Q2adB+4+ ? ^&hf+ ?[73? ] 5;f ^:CG+ 8o7&f@8 +>C>- ' C b ^3),+ 735>5 0_*) 7 2,+ 7K? ] 0 ? _ b +>) '654&7 f!fF` #) ^ < _;Ch2qjC ^ f _p2 ' ^ ? + f=!' bl'=?;7 2,+>Cj2 + ^3) ' g '@?;&7 f_'=? Ch2 7K<*F' f='0 2 `X7K? ] ),+ ] _ 5 +LC 76f='67 C '@? g F 7 C/C ^d ? '=? 2 +]C ` ) '=? b ^ ] + f *C hf+ 5 2,*) ^2g3) 0 67 b mC ^&c 7a0 ' g&_;)A+LC p- 73? ] *- 73? ] 2 + 5;f=7 ) '=? +42 b ^ ] + f Cjhf+0 5 2A)#^&gE) 7&b C?^6c - ? + 7E5 5>7 CA+3Ff2 + 5 ^ ? 2A#) ^ f h 7 ) &7 b +42A+>) b 0 ^ECG2n)A+LjC hU^ 0 ? C '=.< f S+ cH^30 ) h ' 2 5 ' C '=?;5 )A+ 7 CA+ ] 7(' g2_*),+>C pF- o&o 7K? ] pF- o ! 0 ^ 8 +>)N2 F' b + *C ^2 +>)A+ ' C 7 g3),+ 7 2A+>A) hU^K2,+ ? 2 '667 f cH^E) 67 f='67 C '@? g - ? < ^K2 547 CA+>C>FO2 + + c+ 7 2 +4),+ ] - 8D76f=8 +g '=8 +LC 7 b _ 5 0 ;5 f + 7K? +>7) ^&_p#2 h._p2> oJ !"#%$&'$( )&* (! Output of Quasi−Static Flow Clarinet Model 10000 Frequency (Hz) 8000 6000 4000 2000 0 0.4 0.5 0.6 0.7 0.8 0.9 Time (s) 1 1.1 1.2 1.3 1.4 (' g2_*),+ pF- o&o 8 6 _p2#h.0 _p2e^6cO2 0 + C_ 7 C ' CG2 7 2 '657b ^ 0 ] + f ^6cO2 0 + 5;f=7 ) '=0? +Q2L- 0 ^ ? 0 2A)#^ f h 7 ) 76b +Q2,+4) 8D76f _*+LCTdB+4),+ b ^&_p2 0 h*),+>C,Cj_;)A+EF J eo J 7 F 7K? ] c)A+L2_;+ ?;5;` F JIJ JIJ DE- 2^'=? +>C92 )#^&_)g 2 +RC*h + 5 2A)#_ b1'Ff!f _;CG2A) 7 2A+E_ ? ] +LC ' ) 7K<.f + 7 )A2 ' c 735 2,C>7 I oJ ! Output of Feathered Flow Clarinet Model 10000 Frequency (Hz) 8000 6000 4000 2000 0 0.4 0.5 0.6 0.7 0.8 0.9 Time (s) 1 1.1 1.2 1.3 1.4 (' g2_*),+ p-Fo 8 6 _p2#h._p2>^&c 0 2 0 + + c+ 7 2 0 +>)A+ ] - ] `S?;7&bl'=57b ^ ] + f ^&cf2 0 + 5;f=7 ) '=? +42Td ' 2 0 2 0 +RC 76b + 5 ^ ? 2A)#^ f h 7 ) 7&b +Q2,+4)HC 7 C 7(' g&_*),+ p-Fo&o3- +m^2_p2*h._*2 ' C 'Fb h*)*^ 8 + ] ^ 8 +>) 7&f!f 7K? ] 7&f!b ^ECG25c)A+>+^6c 7 )A2 ' c 735 2HC47 oJ !"#%$&'$( )&* (! % ( # * , % 0 ' C 5 0 7 hp2A+>) 7 ].] )A+LCACA+>C(2 0 + ?;7&f CG2 7 g3+ '@? ] + 8 + f ^2h '=? g 5 ^ b h)_p2A+>) b _;C '65r'@? CG2A)#_ b + ? 2HC 7 CD^&_p2 f@'=? + '=? V0 7 h 2A+>)o3- ? h*),+ 8S' 0^&_;C 0 5 0 7 hp2A+>),C92 0 + ] + 0 8 + f ^&h b + ? 2e^&caCj^2_ ? ] 0C `S? 2 0 +LC ' CV+ ? g '@? +LC `b7K? ] '=? 0h 7 )G2 '=5 _ f=7 0 )>FSC `:? 2 0 +>C ' C b ^ ] + f 0C ^&c < ^32 2 + 5Q'6547 ] 7 7K? ] 2 +]C*^ ? g <;' ) ] c 7K? ] 2 + ] + 8 + f ^&h b + ? 20^&c 7Rb + 5 7K?*'6547&f F 7 hp2 '655 ^ ? 2A#) ^ fFf +4) <;7 CA+ ] ^ ? 2 0 0 + 54'=5>7 ] 7 n C < _ 5 k 0 f='@? g b + 5 0 7K?*' C b dB+4),+ ] ' C 5 _;C,CG+ 0 ] -A 0 0 + 0 ?;76f CG2 7 g3+ ' C bJ7 h.0 h '=? g FCd 0 0 +4),+ '=? #2 _ ' 2 '=8 +q)A+ f=7 2 ' ^ ? C ' h;C < +Q02adB+4+ ? 2 +S_ CG+>) n C '=? h._*2 ` 7 CE^ < 2 7K'=? + ] 2 )#^&_)g 2 + 5 ^ ? 2,)*^ f!f +4)dcdF 2 +lC `:? 2 +>C ' C 5 ^ ? 2A#) ^ f h 7 ) 67 b +42A+4)HC 7K? ] 2 + '@? 2A+ ? ] + ] h;)*^ ] _ 5 + ] C*^&_ ? ] 7 ),+ ] +Q2,+4) bq'=? + ] _ Cj_ 7&f!fF`I<1` d 7` ^6cZC*^6c 2ad 7 ),+3? Z 7 b ^ ] + f\7 C 5 ^ b h f0 + 7 C 2 0 +PC ` ) '=? OF2 0 0 +4),+ 7 )A+ ? _ b +>)*^2_;Ch 7 ) 76b +Q2,+4)HCJ2 0 7 2 5>7K?z< 0 + b ^ ] 0 ' ;+ ] ] _*) '=? gRhf+4)*cH^3) bl73?;5 +EF d ' 2 C*^ b + 8D76f _*+LC?cH^E)j2 +>CA+ h 7 ) 7&b +Q2A+>),C?g '=8:'=? g c 7 ) < +Q2A2A+>)q),+>C*_ f 2,Cj2 73? ^K2 +4)HC>@ ` ),+>CG2A) '=5 2 '=? g 7K? ] C 5>67 f='@? gW2 0 + 5 ^ ? 2A#) ^ f h 7 ) &7 b +42A+>),A C ^6cV2 0 + b ^ ] + f *2 ^ *C ^ b +Q2 0 '=? g2 0 7 2?d>^2_ f ] f=' kE+ fF` < + _;CA+ ] <1`X7 )A+ 76f_<;' ) ] F ' 2 ' C 0 ^&hf+ ] 2 0 7 2 7 b ^3),+ bJ7K?;7 g3+ 73<.f +J) 73? g3+O^&c f=' k3+ fF` h 7 ) 76b +Q2,+4) 8D7&f _*+LC 5473? < + ' jC ^ f=7 2A+ ] 7K? ] bl7 ] + 7o8D7KF' f=73.< f +R#2 ^J2 0 ?+ _;CA+4)LF !' b 0 h*#) ^ 8S'@? g 0 ' C 0 +>) 7K<;!' f=' 2 ` *2 ^ '=? 2A+4) 735 <2 d ' 2 0 2 0 + b ^ ] + f d 0 F' f + CG2 'Ff!f 0 ^ < 2 7K'=?*'=? glC 7 2 ' Cac 7E5 2*^E) ` ),+>C*_ f 2,C>- 6 ? 5 +M2 ' Cr) 73? g3+E0 ^6c 8D76f _*+LC ' C>cH_ fFf!` + Kh f ^E)A+ ] 73? ] bJ7 CG2A+>)A+ ] F ' 2 ' C>_)h 2*^q2 + 5 _*) ' ^&_;C 73? ] 7 ] 8 + ? *2 _*#) ^&_;eC h f67 ` +>)B*2 ^J+ S2,+ ? ] 2 m+ hU^EC,C '@<*F' f=' 2 ' +LC4 ? 2 0 ' C 5 0 7 hp2A+>)>F B 7 b +Q2 0 ^ ] ' C,Cj_;)A+ 7K? ] b + b/< ) 7K? +B2,+ ? C ' ^ ? Fc)#^ b )A+ 5 ^3) ] + ] <*' ) ] Cj^ ? g;- 5 _ 5 ^6cf2 + bJ7 2A+4) '676fp'=?;5Jf _ ] + ] 0 +>)A+ 0 7 C < +>+ ? h*),+ 8S' ^&_;C f!` h._ .< f=' C 0 + ] 1< ` b0` 2 0 F . < + fR73? ] bl' 2 0 '@? J + - 0 + b +42 0 ^ ] + b h f ^ ` C 7 A I8 4 698 I-/6 8 2 2 : 7 h.h*)#^ 7E5 0 'FfFf _;CG2A) 7 2,+ ] '=?<7a' g&_;)A+ 0 -!oN2*^I+S2A) 735 2C> 0 +M),+ 5 ^3) ] '=? g ' : C ;)0 HCh2rCG(+ g b + ? 2,+ ] *2 ^0h**) ^ ] _ 5 + 7 CGL+ 2_;+ ?;5 <+ ^6c hU^dV+>)9*C0 h + 5 2A) 7 c) 67 b +>TC ^ 8 +>)Z2 F' b E+ d 0 '65 0 5473? < + 5 ^ b h 0 7 )A+ ] 2*^T2 +N2 7K< _ f67 2,+ ] b ^ ] + f 0 h^dB+4)rC*h + 5 2A) 7 _;C '=0 ? g 70f=' k3+ f=' ^10 ^ ] cH_ ?;5 2 ' ^ ? 2*0 ^ '@? ] '=5>7 2A+g2^C^ ] ? +>C,C ^6c *2L- ^ECA+ 5 ^ ? 2A#) ^ f h 7 ) 67 b +Q2,+4)MCA+Q2,C 7o8S'@? g f=7 *) gE+ f@' k3+ f@' ^1^ ] 7 2Y+ 735 c) 67 b + 7 ),+\2 + ? 67 f=' g ? + ] *2 ^OcH^E) b 2A) 7 + 5 2#^3) ' +LC7^ 8 +>)2 'Fb +3- 7a0 '=?;7&f!fF` F ' c b _ f 20 ' h f +0h 7 ) 7&b 0 +42A+>)RCA+Q2,C bJ7 2 5 0 2 0 + ] 7 2 7 dB+ fFf F 2 0 +T2A) 7 + 5 2#^3) ' +LC 7 ),+ 7 ] _;Ch2,+ ] *2 ^ 7E545 ^&_ ? 2 cH^3)Z2 + 7K<;!' f=' 2 ` ^6cf2 + <*' ) ] *2 ^ 5 73? g35+ h*),+>C,*C _*)A+ 73? ] 2A+ ? C ' ^ ? _;C '@? g 870F8 4 A!>@8B2;0 oJ oJ0 " I (* ( * , T P time Tension (0 ' g2_*),+ 0 0 -Fo 8 _76f _*+LOC cH^3) 0 h*),+>C,Cj_;)A+ 73? ] 2A+ ? C ' ^ ? 7 ),+ ] 4+ 2A+4) bl'@? + ] ^ 8 +4)J2 '!b + <1` 2 0 A) + 7 ] '=? g 2,) 7 + 5 2#^3) ' +LC 2 )*^2_.g 7 Ch2 735 k^&c f=' kE+ f=' ^1^ ] '!bJ7 gE+>C>Pressure 7 # 0 ^:CG+ 7 Cjhf+ 5 2,CD^&c 2 0 + 7o8:'67K? C ` ) '=? b ^ ] + f(` ;),CG2 '=? 2A)#^ ] _ 5 + ] '@? V0 7 hp2,+4) c 'Fb hU^3)A2 73? 2_2*^\2 0 +CG2 'FbJ7 2 ' ^ ? 0 7&f g2^3) ' 2 0 b d '!fFf ),CG2 < +T),+ 8S' +;dB+ ] 2*^ g 0 '=8 + 5 ^0 ? 2A+ :2Y2*^ 2 0 + ] ' C 5 _;C,C 0 ' ^ ? 2 0 7 2:0 cH^ fFf ^dMC4- 0 + bJ7 F' b _ b f@' k3+ f@' ^1^ ] 7K? ] bl'=?*'!b _ b 735 2 ' ^ ? 7 h.h;)*^ 735 ' Cn2 + ? ] +>C 5 ) '@< + ] 73? ] 2 + f@' k3+ f@' ^1^ ] cH_ ?;5 2 ' ^ ? ] +42 7KF' f + ] - 7('=?;67 fFfF` F*2 0 +/),+>C*_ f 2,C:^ < 2 7K'=? + ] <1`U7 h.h f!`S'=? gl2 0 + b +Q2 0 ^ ] 2*^ 7 ;+ f ] )A+ 5 ^E) ] '=? gO^&c 7 D4+ < ) 7 ?;5 0 7 ),+ !' fFf _;Ch2,) 7 2A+ ] Js 1}]x e}]x e u UxYw x e (x + 5476fFf 2 0 7 2Y2 0 + <*' ) ] n C 7K' )*d 7`W5 ^ ? C ' Ch2HC<^6c 7 2A) 735 0 + 7J7K? ] 7f +Jc 2 73? ] ) ' g 0 2 < )#^ ?;5 0 _;C>- 0 ^2_.g 0 2 0 + <;' ) ] ' C 7K.< f +/2#^ 5 ^ ? 2A)#^ f 2 0 +h*)A+LCAC*_*),+ 0 73? ] 2,+ ? C ' ^ ? ^&c_2 0 + f +Jc 2 73? ] ) ' g 0 2nC ' ] +JCG+(h 7 ) 7 2,+ fF` FUcH0 ^3)N2 0 +Bh)_*)*hU^ECA+B^6c C !' b h f=' 547 2 ' ^ ?P73? ] 2#^W),+ ] _ 5 +j2 +l)A+LC_ ' ),+ ] 76b ^&_ ?0 2A^6cVCG2*^E)A+ ]] 7 2 7 FX^ ?.f!` ^ ? + < )*^ ?;5 _;C 73? ] ^ ? + 8o7&f@8 + ' C 5 ^ ? C ' ] +>)A+ ] cH^3 ) h 7 ) 67 b +Q2,+4) +LCh2 0'!bJ7 2 ' ^ 0 ? - 7 ^3) 2 ' C ),+ 7 C*^ ? F f +>C,CIC*_ 5>5 +>C,Cj0 cH_ f ),+>C*_ f 2,C 7 )A+ 0 ^ < 2 73'@? + ] cH0 ^E) +S2,)A+ b + f!`P8S' )A*2 _.^:C '65q<*' ) ] *C ^ ? g;0 MF d 0 +4),+T2 + <*' ) ] ' C f=' kE+ fF`bJ7 k '=? g _;CA+O^6cB2 + f +;c 2 7K? ] ) ' g 2\C ' ] +O^6cr2 + C ` 0 ) +'=? j*2 ^\) 7 h ' ] fF` _ b hc#) ^ b ' g *2 ^ f ^d ),;+ g ' CG2A+>),C 7K? ] '=? Cj^ b + 547 CA+>C(2#^mh f67` 2ad>^ ? ^32A+LC_C 'Fb _ f 2 7K? +(^&_;C f!` 0 +[C ` ) '=? iC 0 ^dMCJ2A),+ b + ? ] ^&_;C 8o7 ) '67 2 ' ^ ?i'@? CG2A#) _ 5 #2 _*),+ < +4a2 dV+>+ ? ] ' +4),+ ? 2 <*' ) ] C*hf+ 5Q' +>C + 76b h f + 8D0 67 f _*+>?C ^6cjC ^ b + 73?;7 #2 ^ bl'65467 f h 7 ) 67 b +Q2,+4)HEC _ CG+ ] '=? 2 0 + b ^ ] + f cH^E) 8o7 ) ' ^&_ C <*' ) ] C ' D>+>C 7 ),+g '=8 + ? '=? 73<.f + F- o3 0 + b ^ ] + f ^6cf2 0 +MC ` ) '=? 8D&7 f@8 + 0 7 Ce2 0 5 + cH^ fFf ^d '=? gAcH^&_;) 8D7 ) '=73.< f +LC d 0 '65 0 + 8 ^ f@8 + ] _;) '=? gj*C ^&_ ? ] h*#) ^ ] _ 5 2 '0 ^ ?U` 67 f jC ^g 0 '=8 + ?T'=? ` !- ooc 8 2 0 7+ h*),+>C,*C _*)A5+ ^ ? 2 0 0 + < #) ^ ?;5 0 '=&7 f C ' ] 7+ ^6cf2 0 + 0 8o&7 f@8 + ` cdF 7K' ) 8 ^ 0 f _ b e+ i)0^d 2 0 #) ^&_)g 0 2 + 8D67 f=8 + 5 7K?;? + fr` \cQF ] ' jC h f6735 + b + ? A2 ^6c_2 + b + b/< ) 7K? + ` c 73? ] 2 S+ h;)A+LCA*C _*),0+ ^ ? 2 +T2A) 735 + 67 f C ' ] S+ ^6c ) * " $( ! I E_ 73? 2 ' 2 ` oJ M?*' 2 bl7&f!f k1g b bb b bb bb bb bb bb bb o JIJIH J Eo o JIJ + b/< ) 7K? + ] + ? C 0' 2 ` 5 + b/< ) 7K? +Ad ' ] 2 5 + b/< ) 7K? +R2 0 '65 k ? +>C,C 2 +Jc 2 0 < #) ^ ? 5 0 _ 0 C f + ? gK2 0 0 ' g 2 < #) ^ ? 5 _ C f + ? gK2 2,) 7E5 0 + 7Bf + ? 0 g32 0 2 J+ c 2 0 < #) ^ ? 5 _ 0 CV) 7 ] ' _;C ' g 0 2 < #) ^ ? 5 _ CV) 7 ] ' _;C a) 7E5 + 7 ) 7 ] ' _;C 5 5 + ] '_ b o JIJIJ ;- o JIJ o o o p-!o o3- o3- H Eo - - - ;- g7 )*gE+ 2 o JIJJ -Fo o JJ J J p- 0 * - * - -Fo 0 8 0 0 0 0 +>7K)A<.+Ef F + ' 2 -!' o C ? K ^K2 76? b + 5 h +Lf CA+>C EC 7 )^6` c:2 0 p7 + 2] 2 730 ?;+ 7 f 2#+;^ c bl2 7K'654? 76] f h) ' 7 g ) 0 762 b < +4)#2A^ +4?;)H5C70 cH_;^EC ) < ] +/' C +4`C),b+ ? b 2 +Q<*2,' ) ) '6] 547&C f ' - D4+LC4-! ^2_.g ' 2 ' CY2 + 5>7 CA+ 2 0 + 8D76f=8 + ` cd- _7&f _;+>C>cH^3)V2 0 +LCG+ 8D7 ) '=73 V<.f 0 +>C 7 ),+ ] +Q2,+4) bl0 '@? + ] ^ 8 +4)92 'Fb + 735>5 ^E) ] '=? g\2#^/2 0 + ' ) 5 ^E)A),+>C*h^ ? ] '=? g ] ' +>)A+ ? 2 '676f + C_ 7 2 ' ^ ? C 7 CE^&_p2 f@'=? + ] '@? 7 h*2A+4) -! +LCG+ 8D7 ) '=73<.f +LC 7 )A+ '!fFf _ Ch2,) 7 2A+ ] ^ ?[7 C 'Fb h f=' ;+ ]] '67 g3) 67 b ^&cg2 0 + 8D7&f@8 + '=? 7(' g&_*),+ - q73? ] 7 C ' g ?;76f i)^d ] '=7 g3) 76b ^6ca2 0 + 5 ^ b h f +42A+ b ^ ] + fO' CrC 0 ^d ?W'@? 7(' g2_*),+ - p 0 + b ^ ] + f ^6c 2 0 + 8D76f=8 + ] ' Cjh f=7E5 + b + ? 2 7K? ] 2 0 +Y),+>C*_ f 2 '@? gmh*)A+LCAC*_*),+B2 0 )#^&_.g 0 2 0 + 5 ^ ? Ch2,) '65 2 ' ^ ?q' C <;7 CG+ ] ^ ? 2 0 + b + 5 0 73?*'=5>67 f h**) ^2h +>)G2 ' +LMC ^&cp2 0 + b + bT< ) 73? + 73? ] 2 0 +@B+>) ? ^2_ fFf@' + C_ 7 2 ' ^ ? cH^3)a2 0 + 73' )Li)^d `'=? 2A)#^ ] _ 5 + ] '=? V0 7 hp2A+>) J7K? ] f=7 0 2A+>) ] + 8 + f ^2h + ] 0 '=? V0 7 h*2A+4)Ecd-0 0 +h*) '!bJ7 ) ` 5 ^ 0 ? 2A)#^ f h 7 ) 7&b +42A0 +>),C0 7 ),0 +R2 0 +>)A+;cH^3),+3F:2 0 + 7K' <) h*),+>C,*C _*)A?+ c*) ^ b 0 2 + f _ ? g:C 7K? ] 2 +/2A+ ? C ' ^ ?U'=? 2 + b 0 + bT< ) 73? +3F;2 + f=7 0 2G2,+4:) ^&cDd '65 2 + <*' ) ] 5 ^ ? 2A0 )#^ f 0 C <1` 5 ^ ? 2,) 7E0 5 2 '@? g/2 +\C ` ) '=? g3+ 76fUb _;C 5Jf +>C 73? ] <1` ) 7K' C '=? g/2 +h*),+>C,Cj_;)A+ '@? 2 + '=? 2A+>) 5;f=7o8S'65 _ f67 ) 7K' )rC 735 d '65 + ? 547 CA+>CV2 +jC ` ) '@? 0 +4),+ ' C 7 ] + ?;' 2,+I),+ f67 2 ' ^ ? C 0 ' h < +4a2 dV+>+ ? 2 0 + h ' 2 5 0 ^6cr2 0 +W*C ^&_ ? ] h;*) ^ ] _ 5 + ] 1< ` 2 0 + <*' ) ] 73? ] 2 0 + 2A+ ? C ' ^ ? ^&ce2 0 +/C ` ) '=? gE+ 76f4b + b/< ) 7K? +E- 0 + + 547&f!f 2 0 7 2Y2 0 + ] ' C*h f6735 + b + ? 2<^6ce2 0 + b + b/< ) 73? + 7 C 7 cH_ ?;5 2 ' ^ ? ^6c 2 F' b + `b >c cH^3) b ^ ] + ' 5C g '=8 + ?W1< ` ` 0 !- ooc N N ` c d 0 +>)A+N2 0 + c)AL+ 2_;+ ?;;5 ` ^6ca2 0 + ;)HCG2 b ^ ] + ' 7C g '@8 + ?WC< ` ` 0 - c d ' 2 0 < + '@? g 2A+ ? C ' ^ ? F 2 0 + b + b/< ) 7K? + ] + ? C ' 2 ` FeU2 0 + ) 7 ] ' _;mC ^6cB2 0 + < #) ^ ?;5 0 _;C>F 2 0 + b + b/< ) 73? + d ' ] 2 0 7K? ] 2 0 + b + b/< ) 7K? +2 0 '=5 k ? +LCAC ` d ' 2 0 + &7 b h f + 8D67 f _*+>C g '=8 + ? '=? 7K)< f + 0 !- oocd- 2 5>7K?i< + CA+4+ ? # ' # ' ' # o JI " I (* ( * , 2 0 +4),+JcH^3),+3F*2 0 0 7 2:d 0 0 + 0 ? 2 0 + 0 <*' ) ] '@?;0 5 )A+ 7 CA+>CB2 0 +\0 2A+ ? C ' ^ ? ^6c(2 0 + b + b/< ) 7K? +n2 0 +?h ' 2 5 0 ^6c(2 0 +qCj^ ? gd '!fFfa7&f C*^ '=?;5 ),+ 7 CG0 + ` 2 ^&_)g ` - cnC ^dMCN2 ' C\)A+ f=7 2 ' ^ ? C ' h ' 0C ? ^32 f='@? + 7 )dcd- 2g' kE0 +;d ' CG+EF 7K?X'=?;5 ),+ 7 CG+ '=? 7K' )mh*)A+LCAC*_*),+ c#) ^ b 2 + f _ ? gEC5d 'Ff!fa547 _ CG+ 7 g3+ ? +4) 76fO'=?;5 ),+ 7 CG+ '=? 2 + 76b h f=' 2*_ ] +m^&cg2 +mh*)#^ ] _ 5 + ] C*^&_ ? ] 0 + bJ7 h.h '=? g^6ceh*)A+LCAC*_*),+ 73? ] 2,+ ? C ' ^ ? 2#^ f ^&_ ] ? +>C,C 7K? ] h ' 2 5 0 )A+LCjhf+ 5 2 '=8 + fF`]' C ? ^K2\Ch2,) 73' g 0 2*cH^3)#d 7 ) ] 0 ^dB+ 8 +4)LF3C '=?;5 + ? ^ )? f@'=? + 7 ) ' 2 ' +>C '@? 2,) '=? C '=5 2#^\2 0 + ] `S?;7&bq'65 CT^6cO2 0 +RC ` ) '=? 5>7 _;CA+ f +>C,CDh*),+ ] '=5 2 7K<)f + < + 0 7o8:' ^&_;) + - . C f=' g 0 2 5 0 7K? gE+ '=? ^ ? + h 7 ) 67 b +42A+4)L F cH^E) '@? CG0 2 73?;5 +EF 5>7K0 ?i547 _;CG++ + 5 2,C C*_ 5 0 7 Chf+4) ' ^ ] ] ^&_ <)f@'=? g;F b ^ ] + f ^ 5 k '=? g 7K? ] 2A) 7K? C ' 2 ' ^ ? :C c#) ^ b h +>) ' ^ ] '65 #2 ^ 5 7 ^K2 '65j< + 7o8:' ^&_;) bJ7 k '=? g ' 2\+S2A),+ b + fF` ] ' 5 _ f 2 73? ] _ ?*'=? *2 _ ' 2 '=8 +M*2 ^ 5 ^ ? 2,*) ^ f^` 2 0 ^&_.g 0 ^6c 5 ^&_;),CA+3F 7n<;' ) ] h^:CACA+>C,C '=? gN2 0 ' C '=? CG2A#) _ b + ? 29C '@?;5 + 0 7 2 5 0 '=? gmd>^2_ f ] 0 7o8 + O7 b _ 5 0 < +42G2,+4)M2 !' b S+ ^6c ' 2dcd- :2 de^&_ f ] &7 f *C ^ < +TjC ^ b (+ d 0 7 E2 _ ? ),+ 7 *C ^ ? 7K.< f +N*2 ^ 7 jC k 7 h f67 ` +47) ^&ce2 0 + b ^ ] + f 67 f ),+ 7 ] ` c 7354'@? gn2 0 +LCG+ '=? 0 +>)A+ ? 2 ] ' 5 _ f 2 ' +>C #2 ^ 5 ^ ? 2A#) ^ f 2 0 <+ h 7 ) &7 b +42A+>), C d ' 2 0 2 0 +R*C hf+4+ ] 73? ] 8S' )A*2 _)^EC ' 2 ` ^6c 7 0 jC ^ ? g <*' ) ] 0 _ .? f +>C,CeC 0 + ' CeL+ 2_ ' h.hf+ ] d ' 2 0 7 *C h + 5Q'667 f*5 ^ ? 2A#) ^ fFf +>) bJ7 0 k '=? gR2 0 ' C h^:CAC '=.< f +E)- 2 ' C J5 f + 7 )(2 0 +4),J+ cH^E)A+EF 2 7 2 7K? ^K2 +4) bJ7 h.h '@? gJCG2A) 7 2,;+ g `J< +>C ' ] +>C 7 ^ ? + k*2 ^I 9^ ? +R),+ f67 2 ' ^ ? C ' h ' C ? + 5 +>C,C 7 ) ` signal spectrogram, 12−msec. frames. 5 frequency − kHz 4 3 2 1 0 200 300 400 500 600 700 800 50 60 time − milliseconds 10 20 30 40 (' g&_*),+ 0 - 8 ^dV+>)BC*hf+ 5 2,) 7 cH^E) ;+ f ] )A+ 5 ^3) ] '=? gB^6c 7 >D + < ) 7 ?;5 0 7 power − dB I * * Js * ~ ' oJH * " /xRw44}]uIu u UxYw (' )HCG2>FK2 0 + p+ ] 73?;7 2#^ bl'=5>76f h 7 ) 7&b 0+Q2A+>0 ),C^&0 c 2 0 + b ^ ] + f;7 )A+C*h + 5Q' ;+ ] 0 7E545 ^E) ] '@? gR0 2*^n2 0 0 + <*' ) ] C*hf+ 5Q' +>C d 0 ^ECA+ C*^ ? g ' CR2*^ < +qC '!b _ f67 2A+ ] 73? ] ^&cTd '65 2 +4),+ ' C 07 ),+ 0 5 ^E) ] '@? g - ? 2 ' C 547 CG+T0 2 0+/2,+ 5 0 ?*' C_*+ ' C 'Ff!f _;CG2A) 7 0 2A+ ] bJ7 k '=? gT),+Jc+>)A+ ?;5 +R2*^ 7 ),+ 5 ^E) ] '@? gS^6c 7 D>+ < ) 7 ?;5 ` 2 +jCjhf+ 5 2A)#^&g3) 76b cH^E)ed '=5 ' CC ^d ?'@? 7(' g2_*),+ - c 7K? ] bJ7 kE+>5C _;CA+ ^6c(2 0 +jC bJ76fFfO<*' ) ] 7K?;7 2*^ bq'6547&f h 7 ) 76b +42A+4)HC>c)*^ b 7K<.f + 0 -Fo3. f ^1^&k _.h 2 7K<.f + ' CBg3+ ? +4) 7 2,+ ] <1` h 7K' ) '@? g 5 ^ b/<*'=?;7 2 ' ^ ? CS^6cM2 0 + 5 ^ ? 2A)#^ f h 7 ) 7&b +42A+>),C0h*)A+LCAC*_*),+ 73? ] 2A+ ? C ' ^ ? d ' 2 0 2 0 + b ^ ] + f n C 5 ^E)A),+>*C hU^ ? ] '=? g^2_p*2 h)_pm2 h^dB0 +4)njC hf+ 5 2A) 7 - 7(' g&_*),+ 0 - C 0 ^dM0C 73? + 5 +4)#hp2E^&c_02 0 + C*h + 5 2A)#_ b 2 73<.f +0cH^3)Y2A+ ? C ' ^ ? ) 7K? g '@? gc)*^ b D>+4)#^l2*^ + ' g 2 7 2 8 +?h*),+>C,C*_*)A0 + 8D7&f _*+LC4- + 735 2*_ 7&f 2 73<.f + 7 C bJ7K1? `b ^3),+N+ ? 2A) ' +LC 7K? ] C '@?;5 + ' <2 ^ .? f!`I? +4+ ] < + 5 ^ b h._p2A+ ] ^ ?;5 + ` cH^3)M+ 735 <;' ) ] jC hf+ 54' +LC,cQF ' 2 5>7K?< + bJ7 ] + 7 C f67 #) g3+ 7K? ] ] + ? CA+ 7 C ' 5C h +>) bl' 2G2A+ ] C< `5 ^ b h)_p2A+>) b + b ^3) ` 7 T 0 200 ... Tabulated Spectra P 650 ... 8 0 1100 ... 8 0 1550 ... 8 0 2000 ... 8 0 8 0 0.5 1 10 1.5 2 2.5 3 Frequency (kHz) 20 30 power − dB 40 3.5 4 50 4.5 60 5 (' g2_*),+ 0 - 8 . ? + 5 +>*) h*2^&c 7Z0 f ^1^&k _.hz2 7K<.f +[2 0 7 2 h 73' )HC 5 ^ bT<*'=?;7 2 ' ^ ? C^&c/2 0 +[0 2ade^ h*) 'FbJ7 ) `5 ^ ? 2,)*^ f h 7 ) 7&b +42A+>),C>F>h;)A+LCAC*0_*),+ 0 c)*^ b 2 + f _ ? g:C n n `b'@? h 7 C 5476f C ` 7 cGc 7K? ] 2,+ ? C ' ^ ?'@? 2 + b + b/< ) 7K? + n n `'=? ? (+ dr2*^ ? C ` BRcAcdFd ' 2 2 + b ^ ] + f n C 5 ^3),),+>C*h^ ? ] '=? g0^2_p2*h._*2de^&_ f ] 5 ^ ? 2,) '=< _p2,+:_ ?*? + 5 +LCAC 7 ) `J5 ^ b h 0f + ' 2 ` cH^3)B2 00 + h._*)#hU^ECA+<^6c 'Ff!f _;CG2A) 7 2 '@? gj2 + bl7 '!b _ b f@' k3+ f@' ^1^ ] b ^ ] + f(` 7K? ] F2^&c 5 ^&_;),CA+3F2d>^2_ f ] '=?;5 )A+ 7 CA+2 +NC ' D4+:^6cO2 + 2 73.< f +jjC _ < Ch2 7K? 2 '667 fFf!` cB*C ^ScH^E) ? ^d\FS2 0 ' C ' C f +Jc 22*^cH_*2*_*),+md>^E)*k ' 2 0 2 0 +\2 73< _ f67 2,+ ] b ^ ] + f Cjhf+ 5 2A) 7J'=? h f=7E5 +EF*2 0 +/),+ 5 ^E) ] + ] <*' ) ] C*^ ? g ' C:h*)*^ 5 +>C,CG+ ] 8S'67 7 C 0 ^3)A2? k2 'Fb + + + ^&c hU^dB+4)R*C hf+ 5 2,) 7 ^ 8 +4)M2 'Fb +E- . ? + 76b h f +/C*h + 5 2A)#^&gE) 7&b '=? 7 ^2_*) ' +>)M2A) 7K? aC cH^E) b 0 #2 ^OcH^3) b 7 CA + C_*+ ? 5 ? 7(' g2_*),+ 0 - Fp2 7 k3+ ? c)#^ b 7 ;+ f ] ),+ 5 ^E) ] '@? g F*C 0 ^dMC 7 CG+LC_*+ ?;5 +^6c g3+LCh2#_*)A+LCecH^3)2 0 +/C*^ ? g^&c 7 D>+ < ) 7 ?;5 0 . C ' CM2 ` h '654&7 f ^&cA;+ f ] ),+ 5 ^3) ] '@? gEC>F ' 2 5 ^ ? 2 73'@? C 7 C ' g ?*' 5473? 2 67 b ^&_ ? A2 ^6c <;7E5 kCgE*) ^2_ ? ] ? ^ ' CA+ 5 ^ ?;5 + ? 2A) 7 2,+ ] '=? 2 0 + f ^d c),+ C_*+ ? 5Q' +>C>Pressure−Tension Likelihood Matrix 200 400 Pressure (Pa) 600 800 1000 1200 1400 1600 1800 2000 0 1 2 3 4 5 6 7 8 9 10 Tension (N) 10 20 30 40 50 60 (' g2_*),+ 0 - 8 . h*),+>C,jC _*), + k2A+ ? C ' ^ ?ZbJ7 2,) ' QcH^3)^ ? +2 'Fb + 0c) 76b +3- 0 + f=' g 0 2A+>)Oh ' p0 + f C '=? 0 ] '6547 2A+ h*),+>C,C*_*)A+9 2A+ ? C ' ^ ? CA+Q2G2 '@? gECh*)#^ ] _ 5Q'=? g C*hf+ 5 2,) 7 8 +>) ` C '!bl'Ff=7 )I2#^ 2 + b + 7 C*_*),+ ] c) 76b +EF:0 d 'Ff +P2 + 0 ] 7 )#k3+40 ) h ' S+ f C '=? ] '6547 2,+Rh*),+>C,Cj_;)A+9 2,+ ? C ' ^ ? CG+42G2 '=? g:Ch*)#^ ] _ 5Q'=? g 8 +4) ` ] ' +>)A+ ? 2C*h + 5 2A) 7 - ? 2 + 5>7 CA+ d +4),+U2 +4),+ 7 ),+ 2ade^I),;+ g ' ^ ? CRC 0 ^d '=? gWCG2A#) ^ ? g f@' k3+ f@' 0 ^1^ ] F 2 0 + 8D7&f _*+LCEcH^3)R2 0 +h 7 ) 7&b +42A+>),C 7 ),+TCA+ f + 5 2A+ ] <1`U'@?;5 ^3)#h^E) 7 2 '=? g bl'@?;!' b _ b 7E5 2 ' ^ ? 7 Log Likelihood I * * * ' o&o2o * " . 2/+ 7E5 0 2 '!b +Oc) 76b +EF 7]? ^E) bJ7&f@' D4+ ]6 2 p 698 I-/698 2 2 : 4&0 !>G8B250 + ' Cm_ CG+ ] 2#^ '=? ] '6547 2,+l2 0 +WC 'Fbl'!f67 ) ' 2 ` < +Q2adB+4+ ? 2 0 + <*' ) ] C*^ ? gC '=? 0 2 0 +rC*h + 5 2A)#_ b 2 73<.f +3F 0 fFf@'=? g 7 h*),+>C,Cj_;)A+9 2A+ ? C 0 ' ^ m? bl7 2A) ' \0 C '!bl'Ff=7 )O2*^2 +T^ ? +9C ^d ?\'=?C7a' g&_;)A+ - -, + 0 f@' k3+ f@' 0 ^1^ ] cH_ ?;5 2 ' ^ ? _;CA+ ] +>0 )A+ ' C ? ^3) bJ76f=' D>+ ] C*^R2 7 2V+ ? 2A) ' +LC 7o8S'=? g 7n8o7&f _;+ 5Jf ^ECA+B2*^?^ ? + '@? ] '=5>7 2,+ ] <1` 2 + f@' g 0 2,+4)Dh ' p+ f C '=?7(' g&_*),+ - 5 ^E)A),+>C*hU0 ^ ? ] 2*^Bh*),+>C,jC _;)A9+ 2,+ ? C ' ^ ? CA+Q2G2 '@? gEeC h*#) ^ ] _ 5Q'=? gljC hf+ 5 2A) 7/0 8 +4) ` C 'Fbl'!f67 )V2*^q2 0+ b + 7 C*_*)A+ ] c) 76b +nCjhf+ 5 2A)#_ b - ^E0 CA+ h*#) ^ ] _ 5Q'=? gn+ ? 2,) ' +>C ;5 f ^:CG+r#2 ^!D4+>*) ^ '=? ] '6547 2A+ ] <1` 2 + ] 7 )*kE+4) h ' p+ f C 7o8 + 8 +4) ` ] ' +>)A+ ? 2BCjhf+ 5 2A) 7 c)#^ b 2 + b + 7 jC _*),+ ] c) &7 b B+ _ ? ] +4) 5 ^ ? C ' ] +>) 7 2 ' ^ ? - 6 545>7 C ' ^ ?;67 fFfF` 2 0 +4),S+ d F' fFfZ< + dB+ fFf CA;+ h 7 ) 7 2A+ ] f=' kE+ f=' 0 ^1^ ] bJ7 'FbJ7 5 ^E)A),+>*C hU^ ? ] '=? gq*2 ^ ] ' +4),+ ? 0 2N)A(+ g ' Ch2,0 +4)H7C ^3) 0 b ^ ] +L^ ` 2 0 ' C ' C 8 +>) ` 7 h.h 0 7 )A+ ? 2 '=? 7(' g&_*),+ - cQ- ' C ' C 73? ] f + ] C< `I'@?;5 ^3#) h^E) 7 2 '=? g 870?8 4 A!>@8B2;0 ] ' C 5 _;C,CG+ ] < + f ^d '=? S+ 5 2 ' ^ ? - * 0 + f=' kE+ f=' 0 ^1^ ] cH_ ?;5 2 ' ^ ? d 7 C 5 0 ^ECA+ ? cH^E) ' 2HCCh2 7 2 ' CG2 '654&7 f h**) ^2h +>)G2 ' +LC 8 ? 2 0 + f=F' bq' < 2 ^6ceC bJ0 &7 f!f +LCh2 !' bJ7 2 ' ^0 ? + 0 +4),#) ^3)H0 C4F ' 2,EC h + 7 k f ^ 5>7 2 ' ^ ?U' :) de^30 ) ] C>Fp2 + f=' kE+ f=' ^1^ ] cH_ ?;5 2 ' ^ ? d F' fFf eF ^ ? 7o8 +4) 7 gE+3 F hf+ 7 k 7 2q2 + 5 ^3),)A+ 5 2 5 ^ ? 2,*) ^ f h 7 ) 67 b +Q2,+4) 8D67 f _*+>C>F 73? ] 2 + h + 7 k f ^ 5>7 2 ' ^ ? d F' f!fO< + 7 C '=? CA+ ? C ' 2 '=8 + 7 5C hU^EC,C '@.< f +N*2 ^ b + 7 jC _*),+ b + ? 2 ? ^ ' CA+3 2 ' C 7 C,jC _ b + ] 2 0 7 2B2 0 +n),+ 5 ^E) ] + ] C ' g ?;67 f :` c 5 ^ ? C ' Ch2HT C ^&c^2 0 + b ^ ] + f ^2_p*2 h._*2 ` Tc d ' 2 0 b + 7 *C _*)A+ b + ? 2 7K? ] ^E) b ^ ] + f@'=? gl+4),*) ^E) ` ec d 0 '65 0 ' C 7 ].] ' 2 '=8 + 73? ] 7 _;C,C '67K? ] ' Ch2,) '=< _p2,+ ] FS2 0 7 2 ' C>F 0 - :c :`b c9 `b c N ` c ` 0d +>)A+ ' C 73? _ ? k ? ^d ? C 54&7 f@'=? gBc 735 *2 ^E) 7K? ] + ' Cr2 0 ?+ h 7 ) 67 b +42A+4) 8 + 5 #2 ^3) 5 ^ ? 2 73'@?*'=? gh*),+>C,jC _;)A+ 7K? ] . 2,+ ? C ' ^ ? - 0 C,jC _ bq'=? g]0 2 + b + 7 *C _*),+ ] C ' g ? 67 fZ' C\Ch2 7 2 ' ^ ? 7 ) ` ^ 8 +4)N2 0 + ] _*) 7 2 ' ^ ? ^&c 73?X73?;67 fF` C ' EC c) &7 b +3F^2 0 O+ hU^dV+>) *C h + 5 2A#) _ b ^&ca2 + b + 7 jC _*),+ ] C ' g ?;67 f ' 7C g '=8 + ?W1< ` 0 - c ` c_ ` c ; ` c ` N 0d +>)A+ ),;+ h*),+>CA+ ? 2HC2 0 + b ^ ] + f ^2_p*2 h._*A2 hU^dV+>)R*C h + 5 2,*) _ b cH^EE) h 7 ) &7 b +Q2A+>),C 73? ] ; ` c),;+ h*),+>CA+ ? 2,CM2 0 + ? 0 ^ ' CAm+ h^dB+4)M*C0 hf+ 5 2,*) _ b 7 72 c)AL+ 2_;+ ?;;5 ` - ? 2 0 + 5>7 CA+N2 0 7 2M2 0 + ? ^ ' CGm+ hU^dB+4) ; ` c ' C b _ 5 0 C bJ67 fFf +>)2 0 73? 2 +]C ' g ?;&7 f F92 + h*#) ^ < 7K<*F' f@' 2 ` ^&cE^ < CG+>) 8S'=? g 7 hU^dV+>)JjC hf+ 5 2A#) _ b g '@8 + ? 5 ^ ? 2A#) ^ f h 7 ) &7 b +Q2A+>),C bJ7 ` < + 7 h)h**) ^ F' bJ7 2A+ ] 1< ` c ` c ` + Kh ` ] +Q 2 ` c c ` c ` 0 - Ec d 0 +>)A+ P' CB2 0 +jCG2 735 k 5 ^ ? 2 73'@?;'@? g b + 7 jC _*),+ ] h^dB+4)r*C h + 5 2A#) _ b <*'@? C ` c 7K? ] C !' blF' f=7 ) fF` ' CB2 0 +jCG2 735 k ^6c b ^ ] + f hU^dV+>)jC hf+ 5 2A#) _ b <*'=? C>M? ] +4)Z2 0 + 7 C,jC _ b h*2 ' ^ ? 2 0 7 2Z2 0 + 7 ].] ' 2 '=8 +M*C h + 5 2,) &7 fp? ^ ' CG+ ' C '=? ] ;+ hf+ ? ] + ? 2 73? ] ' ] + ? 2 '65467 fFfF` ] ' Ch2,) '=< _p2,+ ] F ! ! # # ' % ' o&o " I (* ( * , unnormalized, quantized spectrogram estimate, 12−msec. frames. 5 time − milliseconds 4 3 2 1 0 200 300 400 500 600 700 800 (' g2_*),+ 0 - 8a. CA+ C_*+ ?;5 +>^6c)hU^dV+>)(C*hf+ 5 2,) 7 c)*^ b 2 0 + f ^C^2k 9_.hj2 7K<)f + <;7 CA+ ] ^ ??bJ7 'Fb _ bf=' k3+ f=' 0 ^1^ ] 5 ^ ? 2,)*^ f +>CG2 'FbJ7 2,+>C>2 0 + f ^2g f=' k3+ f=' 0 ^1^ ] cH^3) 7 h 7 ) 7&b +Q2A+>)CG+42 g @' 8 + ?b + 7 C*_*),+ b + ? 2HC X' C ` c_ o ` c ` c / ` 0 -0 c 7 ^E) 5 ^ ?:8 + ?*' + ? 5 +3F_2 0 + f=' kE+ f=' 0 ^C^ ] ' C ? ^E) bJ&7 f@' D4+ ] C*^[2 0 7 2 ' 2J) 73? g3+LCSc)*^ b D4+>)*^ F '@? ] '=5>7 2 '@? g 73? _ ?)f@' k3+ f!` bJ7 2 5 0 FS*2 ^O^ ? +3F '=? ] '6547 2 '=? g 7 g&^1^ ] *2 8 ` c9 o `` cc `` cc / ` 0 -3c 0 +CA+ 5 ^ ? ] 2A+4) b c#) ^ b ` 0 - Kc bJ7 `j< + '@? 2A+>*) h;)A+42A+ ] N 7 C(2 0 +MC 2_ 7 ),+ N ]0] ' CG2 73?;5 + < +Qa2 dB+4+ ? 2 0 +MC 5>67 f + ] b + 7 *C _*),+ ] ] 7 2 7l7K? ] 2 0 +R2 7K.< f +\+ ? 2,) ` F ? ^3) bJ67 f=' D>+ ] 1< ` 2 0 +\'C C_ 7 )A+ ] f + ? g32 0 ^6ca2 0 + ' )M*C _ b - 0 + ? 2 0 m+ h 7 ) &7 b +42A+>),C 7 ),+ *C _ 5 0 2 0 7 2l2 0 + b + 7 *C _*)A+ ] 7K? ] b ^ ] + f *C h + 5 2,) 7 5 ^ '@?;54' ] +3F_2 0 + ? _ b +4) 7 *2 ^E) 73< ^ 8 + d F' f!fr< +UC bJ67 fFf7K? ] 2 0 + 7 frequency − kHz I & * * * o&o (! f=' kE+ f=' 0 ^1^ ] 5Jf E^ CA+N2*^O^ ? +3- 0 + ? 2 0 + b + 7 C*_*),+ ] 7K? ] b ^ ] + f C*hf+ 5 2,) 7J7 )A+ 8 +4) ` ] ' +>)A+ ? 2LF*2 0 + ? _ b +4) 7 2*^E) ' C f67 )#3g + ' 2 5473? ? + 8 +4) < + f67 )#g3+4)92 0 73? 2 0 + ] + ? ^ bl'=?;7 2#^3) 7 C < ^32 0 Cjhf+ 5 2A) 7/7 ),+76fFf!` 2 0 +>)AS + d '!fFfa< + 7 ) 73? g3+m^&c f@' k3+ f@' 0 ^1^ ] ) 7 2 ' ^ECr2 0 7 2 bl7 2 5 0 2 0 + ] 7 2 7 dB+ fFf - 0 +0h;)A+LCAC*_*),+ k2A+ ? C ' ^ ? f=' kE+ f=' 0 ^1^ ] cH_ ?;5 2 ' ^ ? Cq2A+ ? ] 2*^ 0 7o8 + bJ7 'FbJ7 2 0 7 2 7 )A+d ' ] + '@? h*),+>C,Cj_;)A+ 7K? ] ?;7 )A)#^d '=? 2,+ ? C ' ^ ? - 6 ? ^ 545>7 C ' ^ ? 2 0 +>)A5+ d 'Ff!f;< +5dB+ fFf CG+(h 7 ) 7 2,+ ] f=' k3+ f=' 0 ^1^ ] bJ7 'Fbl7N5 ^E)A),+>C*hU^ ? ] '=? gY2*^ ] ' +>)A+ ? 2Z),+;g ' CG2A+>),C^3) b ^ ] +>C ^6cU^EC 5Q'Ff!f67 2 ' ^ ? d ' 2 0 7 ] '@8S' C ' ^ ?T< +4a2 dV+>+ ? 2 0 +r2ade^ ` 2 0 ' C ' C 8 +>) `j7 h.h 7 ),+ ? 2 '@?7(' g2_*),+ 0 - cd-6 2 ' C 7 C,C*_ b + ] 2 0 7 2 2 0 + <*' ) ] d F' f!f^? ^K<2 _;CA+ 0 7K1? ` _ ?*? + 5 +>C,C 70 ) ` + ? +>)*g ` ] _*) '@? g 0 Cj^ ? gh +>)jcH^E) bJ7K? 5 + 0 7K? ] '=? 2 0 +\0 + 8 + ? 2<^&c b _0 f 2 ' h f + dB+ fFf CA;+ h 7 ) 7 2A+ ] bJ7 2 5 '@? g bJ7 F' bJ7 2 A+ ^ ? +N)AL+ 2_ ' ) '@? gj2 + f + 7 Ch2r+ ^3)A25^ ? 2 +Ah 7 )A2e^&c^2 + <;' ) ] ' C 5 ^ECA+ ? 5U'=?*!' b _ b 735 2 ' ^ ?U' C '=? 2A#) ^ ] _ 5 + ] '=? #2 ^J2 0 + f=' kE+ f=' 0 ^C^ ] cH_ ? 5 2 ' ^ ?P'@? 2ad>^d 7` C 8 ^ ? +j2 7 k3+LC '=? 2#^ 7E545 ^2_ ? 2 2 0 +T+ ^E)G2 '@?S8 ^ 0 f@8 + ] #2 ^ b ^ 8 ?+ c*) ^ b ^ ? S+ h 70 ) 67 b +Q0 2,+4)0 8o&7 f _;+/#2 ^ 7K? ^K2 0 +4A) ^ 8 +4)Y2 F' b S+ d 0 F' f +/2 0 S+ ^32 0 +>)NC 'Fb h f!` '=?;5 ^E*) hU^3) 7 2,+>CV2 + '@? CG2 73? 2 7K? ;+ ^&_ C+ ^3)A<2 d +4),+ ' g +>) 8D67 f _*+>C,jC _*),+ 7 ),+ 5 ^ ? C ' ] +4),+ ] 2#^ ), + C_ ' )A+ b 0 ^3),+N+ ^E)G2L0 0 0 7 ^E)I2 + '=? CG2 73? 2 7K? (+ ^&_;CI+ ^3)A2 ' 2 ' C 7 C,jC _ b + ] 2 7 2 ' 2 ' C b ^E)A+ ] ' 5 _ f 2*2 ^ h*#) ^ ] _ 5 + ' g +>) 8D67 f _*+>C ^6c),C>FL2 0 +CA + C_*+ ? 5 e+ ^6c f=' kE+ f=' 0 ^C^ ] cH_ ?;5 2 ' ^ S? bJ7 F' bl' D>+4)HC 7 ),+ b + ] '67K? f 2A+4),+ ] *2 ^N+ f=F' bq'=?;7 2A+jC hU^3) 7 ] '=5 F C 0 ^3)A2 f='@8 + ] F 0 _ b h C 0'=? 2 0 +W2A) 7 0 + 5 *2 ^E) ' +>C>- . cH_*)A2 0 +>)qC f ;+ d f=!' bl' 2 '=? g f 2,+4) ' C 7 h.h f=' + ] *2 ^P+ ? *C _*),+I) 7 2,+>SC ^6c h 7 ) &7 b +42A+>) 5 7K? gE+Y2 7 2 7 )A+ h ` C '654&7 f!fF` h f67 _;C '=.< f +E Js 1u Mw eQu K CG2 'FbJ7 2 '@? g/2 0 +N2ade^0h*) 'Fbl7 ) `J5 ^ ? 2A)#^ f h 7 ) 76b +42A+4)HC>^6c^2 0 +\C ` ) '@? OF f _ ? gSh;)A+LCAC*_*),+ 7K? ] b + bT< ) 73? +R2A+ ? C ' ^ ? F CA+4) 8 +>Cj2ad>^ h._*)#h^:CG+LC 8 oLcj2*^ _ ] g3+W2 0 + b ^ ] + f n C 7K<*'Ff@' 2 ` 2*0 ^h*)#^ ] _ 5 +W)A+ 76f=' CG2 '65 <;' ) ] C*^ ? g 76f='@< ) 7 2 '=? g ' 2J*2 ^ ),+ 5 ^3) 0 ] + ] <*' ) ] C*^ ? g 73? ] cT2#^ )A+LCh2,) '65 2 0 73? 0 ] C 5>76f +]2 + 5 ^ ? 2A)#^ f h 7 ) 76b +Q2,0 +4) C*h 735 + '=?z7K? + ^E)G2J0 2#^ 'Fb h;*) ^ 8 +U2 + _;CA+4) n C 7K<*'Ff=' 2 ` 2*^ '@? 2,+4) 730 5 2d '0 2 0 2 + b ^ ] + fR<1` F:cH^3) '@? CG2 73?;5 +EF 7o8S'=? g 7 5 ^ ? 2,)*^ f!f +4)I2 7 2 cH^ fFf ^dM>C h;)A+ ] +Q2,+4) bq'=? + ] 2,) 7 + 5 2*^3) ' +>C92 )#^&_.g 2 + bJ7 2,) ' WCG2 735 k 0 < + h 7 ) &7 b +Q2A+>)e+>CG2 F' bl7 2 ' ^ ? b +Q2 0 ^ ] d 7 C 7 h.h f=' + ] 2*^n2 0 +D4+ < ) 7 ?;5 0 Cj^ ? g ` 2 0 +YC*h + 5 2A)#^&gE) 7&b ^6cXd 0 '65 0 ' CBC 0 ^d ? '=? 7a' g&_;)A+ 0 - cQ- 0 7K< _ f=7 2A+ ] hU^dV+>)BC*h + 5 2,) 7 c)*^ b 2 0 + f ^C^2k 9_.hI0 2 73<.f + 5 ^E)A),+>C*hU^ ? ] 0 '=? g\2#^/2 0 + b ^ECG2 f=' kE+ fF` h 7 ) &7 b +Q2A+>),C 7 2/+ 7E5 2 F' b + c) 67 b + 7 ),+ CA + C_*+ ? 5 + ] 2#^Rh*)#^ ] _ 5 + 2 +Cjhf+ 5 2A)#^&g3) 76b C ^d ? '=? 7(' g2_*),+ 0 - p! - 0 +qC F' bl!' f67 ) ' 2 0 `< +Qa20 dB+4+ ? 2 0 S+ ^E) ' g '=?;&7 f D>+ < ) 7 ? 5 0 0 C*h + 5 2A)#^&gE) 7&b ` 7(' g2_*)A+ 0 - c 7K? ] 2 0 + 5 ^ ? Ch2,)*_ 5 2A+ ] CA + C_*+ ? 5 + ` 7a' g&_;)A+ - C ^dMC 8 +>) ` g&^1^ ] h^32A+ ? 2 '=&7 fg'=? 2 + b ^ ] + f n C 7K<;!' f=' 2 ` #2 ^ +>CG2 F' bJ7 2A+ f@' k3+ f!` h 7 ) &7 b +42A+>) 8D67 f _*+>0C 73? ] _ f 2 !' bJ7 2A+ fF` #2 ^Oh*#) ^ ] _ 5 + 735>5 _*) 7 2,+ <;' ) ] f@' k30 +\*C ^ ? g - 0 C + ?;67 fe5 ^ ? 2,*) ^ f 2,) 7 + 5 #2 ^3) ' +LC+ S2,) 7E5 2A+ ] c*) ^ b 2 + D4+ < ) 7 ?;5 ),+ 5 ^E) ] '@? g 7 )A+TC 0 ^d ?U'=? 7(' g&_*),+ 0 - 0 o&o " I (* ( * , Estimated Tension Tension (N) 5 4 3 2 1 200 300 400 500 600 700 800 700 800 Time (ms) Estimated Pressure Pressure (Pa) 2000 1500 1000 500 0 200 300 400 500 600 (' g2_*),+ 0 - 008 + < ) 7 ?;5 0 5 ^ ? 2,)*^ f 2,) 7 + 5 2#^3) ' +LCmcH^E)Bh;)A+LCAC*_*),+ 7K? ] 2A+ ? C ' ^ ? ^ 8 +>)j2 '!b + 7 C0 ] 0 +42A+4) bl0 '@? + ] <1` 5 ^ ?*? + 5 2 0 '=? g b ^ECG2 f@' k3+ f!`[8o7&f _;+>Cc)#^ bm7 CG2 7E5 kR^6c5h*),+>C,Cj_*),+ k2A+ ? C ' ^ ?bJ7 2,) '65 +LC ` ^ ? +O^6c>d '=5 ' CjC ^d ?P'=? 7(' g2_*),+ - cd 0 +qCjhf+ 5 2A)#^&g3) 76b ^6cZ2 0 + 5 ^3),)A+LCjhU^ ? ] '@? g b ^ ] + f ^&_p2#h._p2 ' CNC 0 ^d ?U'@? 7a' g&_;)A+ 0 -p- 0 ^2_.g 0 ? ^K2 ' ] + ? 2 '65476f 2*^W+ ' 2 0 +>) 7(' g&_*),+ 00 - ^3) 7a' g&_;)A+ 0 - q2 0 +lC*^&_ ? ] ^&_p2#h._p2 ' CEh +>) 5 +;hp2#_ 760fFfF` C 'Fbq'Ff67 ) 7K? ] 2 0 +lCj^ ? gg3+LCh2#_*),+ ' C dB+ fFff5>7 hp2#_*)A+ ] -A +>CA+Y),+>C*_ f 2,C>d>^2_ f ] f@' k3+ f!`l< +EgE)A+ 7 2 f!`q'!b h*)#^ 8 + ] ' cg2 + f ^1^2k _.hJ2 7K<.f +:dB+4),+Y+ Kh 7K? ] + ] 2#^ '=?;J5 f _ ] + ] 7 2 0 7 c*) ^ b < ^K2 0 C ' ] +LC<^6cZ2 0 + C ` ) '=? 0 ' CDd 7 2>F '@?b ^:Ch2 547 CA+>C>F3+ ?;7K<)f +LCe2 + <*' ) ] 2#^/C '=0 ? g 8S' )G2#_.^EC '65 Cj^ ? gEC -A +M),+>C*_ f 2,CTd>^2_ f ] 7&f C*^ < + b _ 5 !' b h*#) ^ 8 + ] ' c b ^E)A+ 73545 _*) 7 2A+ b + 7 *C _*),+ b + ? 2,MC ^6c*2 +VC ` ) '=? 7K? 7 *2 ^ b0` dV+>)A+ 7o8o73!' f67K)< f + cH^E) ] ' +4),+ ? 2 <;' ) ] C*h + 5Q' +>C>-C ? 2 0 ' Cn)A+LCG+ 7 ) 5 0 F 0 73?;7 2#^ bl'65476f h 7 ) 7&b +42A+>) 8D76f _*+L0 CEdB+4),+B^ ?.fF` 7 h.h;)*^ 'Fbl7 2A+ ] cH^3)\C bJ7&f!f F b + ] ' _ b 7K? ] f67 #) g3+ <*' ) ] C4- '=8 + ? 2 + 8D7 ) ' +42 ` ^6c <*' ) ] 0 *C h + 5Q' +>C>F^2 ' C ' C J5 f + 7 ) fF`[73? ^ 8 +4)HC 0 F' b h f@' 5>7 2 ' ^ ? - 7('=?;67 fFf!` F ' c ^3) ' g '=?;76f_<;' ) ] ),+ 5 ^E) ] '@? g:CmdB+4),+ f +LCAC ? ^ ' C ` F(2 +h 7 ) 7&b +42A+>)/+>CG2 'FbJ7 2 ' ^ ? 76f g&^E) ' 2 b de^&_ f ] ? n 2 7 2G2A+ b hp2/2#^ 0 7o8 +\2 0 + b ^ ] + f h**) ^ ] _ 5 +\2 0 ' C ? ^ ' CA+ jC ^ b +Q2 0 '@? gd 0 '=5 0 ' C f@' k3+ f!`U547 _;C '@? gWjC ^ b +/+4),*) ^E) 7K? ] 2 0 S+ ^2_p*2 h._*2 ^6c(2 0 + b ^ ] + f d>^2_ f ] f=' kE+ fF`I< + 7l5Jf ^ECA+4) bJ7 2 5 0 2*^l2 0 +m^3) ' g '=?;76f ),+ 5 ^E) ] '@? g 7 Time (ms) I & o&o ! signal spectrogram, 12−msec. frames. 5 frequency − kHz 4 3 2 1 0 200 300 400 500 600 700 800 50 60 time − milliseconds 10 20 30 40 power − dB (' g2_*),+ 0 - 8 ^dV+>)B*C h + 5 2,) 7 ^6c b ^ ] + f ^2_p2*h)_p2<_;C '@? g 5 ^ ? 2A)#^ f 2A) 7 + 5 2#^3) ' +LCTc)#^ b 7a' g&_;)A+ 0 - 0 @ `ZbJ7 h.h '@? g 2 0 +Rh*),+>C,Cj_;)A+ 7K? ] 2,+ ? C ' ^ ? 2,) 7 + 5 2*^3) ' +>C^6c 7(' g2_*)A+ 0 - 0 2#^ 73?i'@? h)_p2 ] + 8:'65 + d ' 2 0 2ade^ '=? ] '=8:' ] _ &7 f(50 ^ ? 2 '=? _.^&_ C 5 ^ ? 2A)#^ f C4F;0 2 0 +Bh f67` +>):^6c92 0 0+ b ^ 0 ] + fe' C 0 7K<.f +T2*0 ^I),+;h;)*^ ] _ 5 + <*' ) ] f=' kE+TC*^ ? gd ' 2 0 ^&_p2 ),+ C_ ' ) '=? gU2 + <;' ) ]4n C/+ 1hf+4)A2q0 2A+ 5 ?*' C_*+E- 7(' g&_*),+ - C0 ^dMC ^d12. +I2,) 7 + 5 2*^3) ' +>C?dB+4),+ 7&f C*^_;CA+ ] '@? 7 ? ^ ? )A+ 67 f 2 !' b + 5 7 2 f=73< g3) 7 h '=5>67 f _ 0 CG+>) '=? 2A+>)jc 7E5 + 2#^ 2 + b ^ ] 0 + f - ] )*^2h ] ^0 d ? b + ? _ 76fFf ^dMC ] ' +>)A+ ? 2 2A) 7 + 50 #2 ^3) ' +LCB0 *2 ^ < +TCA+ f + 5 2,+ ] 7K? ] ^K2 +4) b + ? _ < ^ p+>C7hf+4) bl' 2R2 +?_ CG+>)2*^ICA+Q2Y2 + 73?;7 2#^ bl'65476f h 7 ) 76b +Q2,+4)HC 7 CC A+ d ' C +>C>7 o&o 0 " I (* ( * , (' g2_*),+ 0 - 8 N) 7 h 0 0 '65 _;CA+4) '@? 2,+4)*c 735 + . '@? 5[7 2 f67K< C 0 ^dMC 7K? + 7&b h f 0 +0_;CG+S^6ce2 0 0 +Sh*),+>C,0 C*_*)A+9 2,+ ? C ' ^ ?]5 ^ ? 2,)*^ f 2A) 7 + 5 2#^3) ' +LCcH^3)/2 + 0 5 _ 5 k2^C^ <;' ) ] - ] )*^2h ] ^d ? b + ? _ 760 fFf ^dMCn2 ' C 7K? ] ^32 +>)0^K2 +4)S0 h^:CAC '=<.f + 5 ^ ? 2,)*0 ^ f 2A) 7 + 5 2#^3) ' +LC ` cH^3)^K2 +4) <*' ) ] 0 C*hf+ 5Q' +>CHcT2*^ < + f ^ 7 ] + ] - 6 0 2 +>) b + ? _ < _p2A2*^ ? C 760 fFf ^d 2 + _;CG+>) 76f 2A+>)J2 + 7K? 7 *2 ^ bl'=5>67 f h 7 ) 67 b +Q2,+4)HC4-! + 6 n < _*2G2*^ ? 5 ^ b h._p2,+>CR2 +qC*h + 5 2,)*^2g3) 76b 7K? ] 2 + f67` < _p2A2*^ ?P76fFf ^dMC 2 0 m+ _;CG+>)r*2 ^ 0 + 7 )r2 0 + b ^ ] + f n C7h*)#^ ] _ 5 + ] Cj^2_ ? ] 7 * & && ls 1u Mw eQu +LCG+ 7 ) 5 0 +4)HC 7 ),+ '=?;5 ),+ 7 C '=? g f!`Bf ^1^2k '=? g 7 2 <*' ^ f ^&g '=5>76f Ch2,)*_ 5 2*_*),+>CDcH^3) ? +;d 7 h.h*)#^ 7E5 0 +>Ce2#^ ] +>C ' g ? h*)*^ <.f + b C4F 7K? ] bJ0 73?C`P0 7 ] 8D7K? 5 +>C '=? 2A+ 5 0 ? ^ f ^2g ` 7 ),+q0 2 0 +I)A+LCj_ f 2?^60 cB2 7 k '@? g 7U5;f ^:CG+>) f ^1^&k 7 2 ?;7 2*_*) 76f h*)#^ 5 +LCACA+>C>- 0 + CA+ 7 ) 5 +>),C 7o8 + cH^2_ ? ] FecH^E) '@? Ch2 7K?;5 +3FB2 7 2 ' )#^ ?i' Cl2 +Rk3+ ` '@? g3),+ ] ' + ? 2OcH^3) 7 4 F-/. p 694F- 76fFf ^d '=? gP2 + 5 ^ 0 bb ^ ?l.< f _;+ b _;C,CA+ f #2 ^ J5 f='@? 0 gn2#^j)#^ 5 kpC <1` cH^E) bl'=? g 7K? + :2,)A+ b + fF` CG2A)#^ ? g <*'=? ] '=? g 7 g3+ ? 2D_ ? ] +4)9CA+ 7 d 7 2,+4)L 'e C d !' fFf h*#) ^ 8:' ] + 7/? ;+ d 7 ] +>C '=8 +Ah 7 )A2 '65 _ f67 ) fF` C*_ ' 2A+ ] 2#^qC*_*)#g3+4) ` C '=?;5 + 0 ' 27d>^E)*kpC>dV+ f!f '=? dB+Q2 5 ^ ? ] ' 2 ' ^ ? C 0 +- 0 + 0 g3+ 5 k&^ F 7 f=0' D 7 ) ] CG+>+ bl'@? g fF0 ` 5>7 h 73.< f O+ ^&c ] J+ c0 `S'=? gRg3) 7o8S' 2 ` d ' 2 ' 2HC 73<*'!f=' 2 ` 0 2#^ 5Jf='@? g]2*^ 5 + 'Ff@'=? gEC 7K? ] hU^ f=' C + ] g f67 C,0 C>F 7 C '=? *C h ' ),+ ] 2 + 5 )A+ 7 2 ' ^ ? ^6cR2 + - H2 p + - 2 F 7 )#^ < ^K2d ' 2 CG2 '65 k ` c+4+42 7K? ] 7 20 73!' f cH^E) < 67 f67K?;5 +j2 7 2 0 547K? C 5 _p2G2 f + 7E5 #) ^EC,C 0 ] 73? g3+>*) ^2_;C2,+4),) 73'@? J - ^ b h._p2A+>) b ^ ] + f AC 0 ^&c '@? 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E ^$ : ) "X#c+' ; -B 7 sj > B"AoA 8 : =$A B0A ?> A ; ^g* 7 8=?@9A B 7 _p ;= > 0 ;@:W7 B 7 - 9J J - 66 ,- D b 2 D D . DED P . ' X ) 1a- +& 1 ' ) ( - B - a C !3 Z P ! +$L E IP# 'J 3 ) 0GQ Q! J 3 J) "&#h+' ; -+B 7 sj > B0AOA 8 :Y=$A B0A ?> AE; ^ Pj; * 7 8=?@ AB 7 _ p ;+= > 0 ;+@4:kA B h>W7 B 7 - J - 6 ,- b 6 A 2 b P DED D . A X )@1a- & 1 "E ) Z 4[3! E4 !Q" "!$3?/&! @ Q +$L E EX C "!5?P! Q + $ Q EQ&! !3 ^h* 7 8=?@ AB 7 _1p ;= > 0 ;+@4:kA B [>W7 B 7 - 9J - 6 1- AJA . P 2 AJA !PC DED D .E. (*5# 1a- " C " =?k: jC= 7 7 V h>W7 A 7 8 : > 1 $ V "EP!$ ) I2$!$!3 $# 8h C E ) D b D . ! 5 - - 3 3E a- C#P L O , g- IN!$EE,E I - I - 5 0$P Z #SQ J" E "03 3) I';! H$# ! ) $" "f#)J 3 " e $L E HI&! %" ^ A : 8=$; J - A D ! ,- D P 2 P DED b . D 8*C L" XSA- 3 "+P# Z 0 ! E 2 : E P0 E J!5$' ^a* 7 8=?@9AB 7 _ Pj; 7 =$;: > PAB [>W7 B 7 - J - A! ,-. !J! 2 . b D b b . P 8*C L" XSC - 3 0P#33 7 8 : > H+U- :<; 0 c> @ [>W7 B 7 - 6 E 7V "E3!$ ) I3!! 8h C E ) ( 8* C ) D D AJD I A R . b 8h3CL0 X&-3 "+PP#) ( - J'! ) ) ]Z$(aS J4!F"3!; J $#O6C' ` C3_$PE+3 ^* 7 8=?@9AB 7 _ :kj; 7 8 : > PAB + 7 > ;:.- 7 _ 10 ;+= > PA J J - 6 !C - 1- A! 2 . D *E ) DED D . D 8h3C L0 XST - 3 0P#33bZ$( S'E!! J )P#4 "`%0 3L"! ^ * 7 8=?@9A B 7 _`: j; 7 8 : > A B + 7 > ;+: - 7 _ 10 ;+= > PA 4J - 6 b - 1- b 2 b DG(; !5 66J6 ! 6 I - - 3 !5 X ) 1a- + 1 ' ) Z$(a! ) I+$ ) J a ) &%4hE+$L E !5$Q?Q$Z" +' ( !!$0% ")Q J"g"o$# 4?$L E0 HS 0 ! E ! ^ * 7 8=?@9A B 7 _1p ;= > 0 ;@:W7 B 7 - J - 6 ,- P P 2 P A 6 3 %Q E ) DED b ! I - #- 3 E!$33O 4 - 5 - X 3 Y Z6I#4E!$"gE+$L E5 N$#Q$4&! 9!S "2 '$!l$#&J "0 &! "Z"3 ! ^ * 7 8=?@9AB 7 _1p ;+= > 0 ;@:W7 B 7 - 4 J - DED ,- !A! 2 ! .E. 5 EP# D D D ! ' L BQE B /- 1 P#Y 5 - 5 E!S 4J 4 - _ ( EhE BQ %$" a- 5 " "01 Z CL 0 E !FQ 3! E[%0 ! E ! ^ j - ?> A B ;+ > ; S1;: :<;= J - b PG - 6 ,- 2 . 8 E &%9 66 !A 3 - B "]E 6 - 8 - 1E!$, Z 9 g @ + > :Y8 %L JI3P#E' 0 ;@:W7 B 7 - 9J J - 66 ,- D ! 2 PD DED P ! . 4/ G!5 IE ) L0'! [> = V + 7 8@ V A@ V Pj; > = < ;PA@ > @ 1 E V "E3!$0 ) I2$!$!3 #E33 8h C E ) D b .4 !J! ( - T - 5 0 17 = 0 A @ 7V 8@ +: >W7 @ > @ h> = V gP# $ 3 4?$L E4 Q(h J ) J Q$# ) $" ,6 ! 2 D 8* C E ) (* I' I3!! D b D !D 4/ 3$' ) ( - *#P! Z 1 EG$"% !)Q d%" &! ^Q J # "S jO # I!5 9 ! J h$#o" PE+ ! ) " ^ A : 8=$; J - A . P ,-. PA 2 . PJP 6 + E%9 DED 6 !P 4/ 3$' ) ( - *#P! Z$ "E% "Q ! ) I+ ) E $&! Q0G$#S6G' fJ J $PE+ ( !5$Q J % !5'$! E*0 0C L )0 '!5$"?* " e !3 ^g* 7 8=?@ AB 7 _ ;A7 0 A=$A : > ; j- ?>W7 B 7 - LJ - P! ,. ! P 2 . DJD DED . ! Ab a4 - 0 e Z # # ) !$'T ! 2! IJ < " Q 9 G!$ L'$L E> H$# C3 J !3 ^ * 7 8=?@9A B 7 _ k: j; 7 8 : > PAB + 7 > ;.: - 7 _ 10 ;+= > PA J J - b A -. ,- !AD 2 !J! ( D bEb ! D 4 - 0 e ET Z #hJ "l !2 !5'J "!F /3G J /3G %93$3+!%9+ C O O %L JL "3 3!$ !3 ^ " = 7 P;P; V> @ c7 _/+ 0 ;+@4:kA B h>W7 B 7 - 9J - ! ,-. 2 !JD D JD 6 D - J X ) 1a- & 1 "E ) Z #&Q J"9 H# ) % N"X+' ]! J Q +$L E, ^ Pj; * 7 8=?@ AB 7 _p ;= > 0 ;@:W7 B 7 - 9J - D b 1- 66 2 6 D DED . A A R D ' - - ,C0$", - 3( JI!32E 4 - - ( JO! Z 1 EG$Q J PI$P!2 9!$"3 04!FI3 P! ( $LE 0 E a C O 0 ^ !FQQ ]! J ^ l =.GA@ > ; V + 7 8@ V 9J - P - ,- P 2 b D 6J6 DJA 1 #E" 3! * 8 "P# " !3 Z #fC% C a L I3 < J g C0$JlGL J""i% C # $'o#*O 3<S $3 "G$W EE ^ 0 = 7 ;P; V> @ 7 _ 9s< p 8@A T %"01 ' ) 66 1 E3 ^3$3+ E 8* C !5$QI GP! E !$' " 3 $!$!$LE D . - CL0 F #P ", B0A- > @8 - ;P;B 9 @ 7 = 7 =$A: > @8! A 9: > ;P; V A > @: 7g;70 8:k;= A ; V < 8 ?> PAB 9 @ : =?8 0 ;@: CI# - - $#3!$"!3 1/1 4 (&GP 3 W V "E3!$0 ) 66J6 D! O P%* ) $#OE " L !" - *I0$#,TZ 1 $$" ! ) !5E0 E 3! C 0$#I$#h+' F !N %4 ) " " I 3P#4 '!&Z ^ 0 = 7 ;P; V> @ Z7 _ 9s< p 8 T %" ", $ " E ) 66 1 E ^ E B*8 C !5$QI GP! E !$' " 3 $!$!$LE DJD O PB* ) # 0 L !# - *I0$#, Z( 9 !$'g S " ]%E!$ $# +' F !cOR 03G %4 ) " " / P# "!Z ^ * 7 8=?@9A B 7 _ ; S < 8 ?> ; ;PA = j a3+ & %9 6J6 A D P - 4/ , - [R 3" ) - ; % E I - a L0 Z !F/ 3G 3!5 P3O 0 !F $ 0! !h 3 3!!$0C0 )0 $3I " G!a"dS $3T !$" 3& O 4+E ^ " = 7 P;P; V> @8 I7 _&:kj;%/$ A @ ; > Pj; P4; sjC@ 7 B 7 - 7 _p 0I7 : >W7 @ 7 = j 7 UBg3 J ) &g ?QE %9 D D P ' ) ( * + -,, ( D bA - g - ( L" E - 4 - 4hE%"CZ$( Q P#Q g!5# 5 I J03\E ) !5'!1E ! ) #3!$'! ^ = 7 /. 9 p,p p J - D! - ,- !J! b 2 !D . J8; E %43 D PP D D 1 E - 3 OE C$ ( - aP! e *V 6A @ P; Vd< A:kj; 0 A : > PAB < ;+:kj 7V _ 7 =W+ > ;@: > : A@ V p @ > @ ;P;+= Bg C X LY E D P b P 6 I 3! XS-0 1 0 ' ,14/E J [ - P# ^33hE 1 E ) ( - 33 + > = :2 < 8B : > 0 ; V> A 8 C P!5 ) D b 9= 7 A j IG$'+ X L V; 3T " 4[0 h P (* C 4hL ) #B 3 e J J0 G E!$#E!$#,1Z$(h4 ) "Q!$ 3 $LE 2 $ ![E ! ^ 9 p p,p P=A@ A +: >W7 @ Z7 @ + > @ AB = 7 P; ?> @8 2 J -N. H - , - A . 2 A . ! 8 %43 DED .4 P ' J'C ! - P#E& F +9:kA : > : > PAB+ > E@9A B = 7 P; ?> @8 ;+:<; +: >W7 @#Qp : > 0 A : >W7 @fQ\A @ V P > 0 ; +L;+= > ; @9ABG- P> ( '&! 3 [ 3! " ) I% ""!$#" 1 J ) - D D AA R ; C@ > 8; _ 7 = S> > : B :<;+= ; P> E@ A @ V +!- :k; 093V ;@: > K PA: >W7 @ S > : j 9B > PA: >W7 @ : 7 :kj;N >W7 B > @ I2# - - #3!$"!3GP 3 WV "E3!$0 ) GP 3 1 " $' D b A P . 0L! - *I #, Z( E!5EG& " 0J \3! E4 [ % ) ]!$0 0IS CRO03G3 ^ ;70 8:k;= < 8 ?> * 7 8=?@9AB J J - D -. ,- AD 2 . 6 D b P! 0L ! - *I0$#&E # - (h%9 Y= Z E ) " 4 % "03 ,$P &! EQ O! ^ 9 p,p,p P=$A@ A : >W7 @ 7 @ +;P; sj`A @ EV 8 V>WY7 = 7 ; ?> 8@ 8 &%9 DEDED P D 0L 1 ! - *I0$#, Z G$Q +$L E Q 0J 50$P!3 ^ C/C/C k3+Q O - !FP 3 L- CiM ( ! 0$3! C $ &%9 6J6 A "2J 0C" "0Q% * ) PJP 5 C$ "0 e &> > : @ AB = 7 ; ?> 8@ = > 0 ;+:= S > k: j B > PA: >W7 @ : 17 &> > :W7 A @ aV ;A7 0 98:<;= < 8 ?> ( "! E3 [ 3! 0 ) I"'!5#" 1 J E ) E HIH ) 1 " $' DED D P Ab V; J e 33 S> > :W7 + > @ AB = 7 P; P> @ E#a [ L 0 ) E * E!3 - 8* C E ) DED D P A 0L! *I0$#, P sj , * *` , ' , E $#E5 - (h%9Y,I0)S E3! 4+ -CV )B1 4 \(;0 -3 ) 4 \E (h $ C a-=5 # gZ 1 * P0 %L0cQ E% "3! (h3 $+ G!* 0 "$?$LE 4! ^ 8: 7 @ 7A0O7 8 h*7 7 : J -. - 1- P 2 A DED P X 3 )5a 1 - +& 1 ' ) &I2$"$)E $! E h8 3CL0 X&-#3 0 P#33,I2$"gE $! E 8 , Bg P #"E V&- - L#0 0$L E 0$L E, 2> ;+B V ml8 >WV ;c: 7 :kj; h> = V O7 _ 7 =?:kj 10 ;= > PA 9a DbP( " %9$JB0 "! )*) 4/ %435 PUj;+=; 0/> @&T p :kj;= < 8 P> QA @ V p >W7 @ A G; V "EP!$ ) J L" 0 "! I3!!3 g ? %43 6J66 1W X 3E$,TZ !5? !5'+' 4! ^O" p 7 : > A @ VQ ;:Y= 7 ; : > 6; 1 - A DA2 b 6 -AV "E3!$0 ) I3!!3 E #W[ ' !E U * , 1 % V (& 3b D b 'P# X f ) 0, Z * L ^ $#S!5 ^ A:Y8=$; * E ) 6J6 .44/ a 1 - 5 %4*E H X #4 Z 1 JL0 ?$"E[QE % "3! ^ ! +' "!$3+!HQS QE % !3 ^ aV A 9: > 6; ; jA >W7 8=sQ c E 4J J - - , - b D'2 b DED Z6I ^ #G$ E C/C/C - $ $ - 4 8 J0 aIN 3!$,:Z 3 JL C $# * G3 ^/# $ E C/C/C - G - I 0 6J6 6 @D " A - #EQ PD b6 b b ' bA b. b! bD bP bEb A bD A. R DJ6 3 L I C L :Z Bg ) ) $#S E ^ A : 8=$; ( !5 6J6 D g6 3 E%9Y mhAB > B0; 7 : A 8 j:k;= > : 7 = > PA B < ; 0O7> = 7 _ + > ;@ P; Q A > :kj8Q A @ V 7 ; 5Q03%E ) * ) ! *'!5$0%$ % ) aO ' *E ) 6J6J6 D ' " ! - 3/0$#1 I0 $)S $3! 3+ D A Z G ) ^ #G$ E C/C/C k3+Q I - !5E3 E L- ! j C !5 ) D . E#W [ #0& Z$(* P![!5#4 g Q F !l% !FhE$0 Y ^ A : 8=; ;( !5 66 5

Applications Of Bioacoustics To Musical Instrument Technology

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