Transcript
Producing sound waves Displacement
1.4 Sound
Density Pressure
Producing sound waves Speed of sound Energy and Intensity Spherical and Plane waves. Interference of sound waves
•Produced by compression and rarefaction of media (air) •Sound waves are longitudinal resulting in displacement in the direction of propagation. • The displacements result in oscillations in density and pressure.
Frequencies of sound wave
Speed of sound Speed of sound in a fluid
infra-sonic
Audible Sound
10
20,000
v=
ultra- sonic
B=−
Bulk modulus
m ρ= V
Frequency (Hz) 30
∆P ∆V / V
B ρ
0.015 Wavelength (m) in air
Density
Similarity to speed of a transverse wave on a string
v=
elastic _ property int ertial _ property
Speed of sound in air v=
B ρ
v=
γP ρ
γ is a constant that depends on the nature of the gas γ =7/5 for air.
Why is the speed of sound higher in Helium than in air? Why is the speed of sound higher in water than in air?
P - Pressure ρ - Density Since P is proportional to the absolute temperature T by the ideal gas law. PV=nRT v is dependent on T
v = 331
T 273
(m/s)
1
Energy and Intensity of sound waves Find the speed of sound in air at 20o C. T 273
v = 331
273 + 20 = 343m / s 273
For calculations use v=340 m/s
Sound intensity level The decibel is a measure of the sound intensity level
⎛ I⎞ β = 10log ⎜ ⎟ ⎝ Io ⎠ 10-12
W/m2
decibels (dB)
the threshold of hearing
note - decibel is a logarithmic unit. It covers a wide range of intensities.
Spherical and plane waves A = 4πr 2
area of sphere
As sound spreads out uniformly from a point source The intensity decreases as 1/r2
P 4πr 2
I=
Intensity
power P = area A
(units W/m2)
The ear is capable of distinguishing a wide range of sound intensities. What is the intensity of sound at a rock concert? (W/m2) ⎛ I⎞ β = 10log ⎜ ⎟ = 120 ⎝ Io ⎠ ⎛ I ⎞ 120 = 12 log ⎜ ⎟ = ⎝ I0 ⎠ 10
I = 1012 I0 I = 1012 I0 = 1012 ⋅ 10 −12 = 1
I=
energy time area A
v = 331
Io =
P=
power
W/m2
Suppose you are standing near a loudspeaker that can is blasting away with 100 W of audio power. How far away from the speaker should you stand if you want to hear a sound level of 120 dB. ( assume that the sound is emitted uniformly in all directions.)
I=
r=
P P = A 4πr 2
P 4πI
=
100W = 2.8m 4π(1W / m2 )
2
Question 1 The sound intensity of an ipod earphone can be as much as 120 dB. How is this possible?
A) B) C) D)
The ipod is very powerful The area of the earphone is very small The ipod is a digital device Rock music can be very loud
The sound intensity of an ipod earphone can be as much as 120 dB. How is this possible? The earphone is placed directly in the ear. The intensity at the earphone is the power divided by a small area. Say the area is about 1cm2.
P = IA = 1w / m2 (10−4 m2 ) = 10−4 W A small amount of power produces a high intensity.
Question 2 The sound level in a truck is 20 dB greater than the sound level in a Strarbucks cafe. If the intensity in the cafe is 10-7 W/m2 the intensity in the truck is_______ W/m2.
Interference of sound waves Two sound waves superimposed Constructive Interference
A) 20 X10-7 B) 10-9 C)10-5 D) 20
Destructive Interference
Interference due to path difference
Noise canceling headphones
Wave 1
path difference =δ =r2 – r1
r1
Noise Wave 1
A r2
Wave 2 Anti-noise
Wave 2
Superposition of waves at A shows interference due to path differences
In phase at x=0
Condition for constructive interference Condition for destructive interference where m is any integer
δ = mλ 1 2
δ = (m + )λ m = 0 + 1, + 2,….
3
Interference δ=0
Constructive Interference
Interference λ δ= 2
Destructive Interference
Sum
λ
Interference δ=λ Constructive Interference
Interference
Interference δ=
3λ 2
Destructive Interference
Interference of sound waves Phase shift due to path differences
δ=2λ
Constructive interference
x
When
r2 –r1 =mλ
When r2 – r1 = (m+½) λ m is any integer
Constructive Interference Destructive Interference
4
Example 14.6 Path difference for two sources.
Determining the wavelength of a sound wave – determine the speed of sound
Find wavelength of the sound from interference.
r2-r1 =0.13 m
At position P the listener hears the first minimum in sound intensity. Find the frequency of the oscillation. vsound =340 m/s At position P the path difference is equal to λ/2. (first minimum) destructive interference. λ = r2 − r1 = 0.13m 2 λ = 2(0.13) = 0.26m v 340m / s f= = = 1.31x103 Hz λ 0.26m
5
