sound physics 202 professor lee carkner lecture 8
Post on 19-Dec-2015
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Sound
Physics 202Professor Lee
CarknerLecture 8
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Sound
More generally: sound = longitudinal wave
Unlike waves on a string, a sound wave propagates outward in all 3 dimensions Example:
String wave 1D, sound wave 3D
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Sound Speed For sound the velocity is:
v = (B/)½
Bulk modulus is like tension (how “springy” the fluid is) Density is like linear density
B = - p/(V/V)
Example: Water is more dense than air, so why does sound travel faster in water? It has a much larger B. Water is hard to compress
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Wave Equations
The displacement of any element of air will also be in the x direction and is represented by:
s(x,t) = sm cos (kx-t)
This is similar to the transverse wave equation but does not involve y
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Pressure Wave
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Pressure
p(x,t) = pm sin (kx - t) Where pm is the pressure amplitude
pm = (v) sm
This is not an absolute pressure but rather a pressure change
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Pressure Wave Equation
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Pressure and Displacement The pressure and the
displacement variations are /2 radians out of phase
When the displacement is zero the pressure is a maximum
and away from where pressure is low
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Interference
If an observer is an equal distance from each, the sound will be in phase
For a phase difference of 2 the path length difference is
LL
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Constructive and Destructive
L=m The sound will be at max amplitude (louder than an
individual source)
L = (m+½)
You can also have intermediate interference making the sound louder or softer
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Interference and You Why don’t we notice interference much?
Each with a different L
You hear a combination of many different L
Not all will have strong interference at your location
You don’t hold perfectly still at the spot with maximum interference
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Intensity of Sound
I = P/A The units of intensity are W/m2
I = ½v2sm
2
Compare to expression for power in a transverse wave
Depends on the square of the amplitude and the frequency (wave properties)
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Intensity and Distance
As you get further away from the source the intensity decreases because the area over which the power is distributed increases
I = P/A = Ps/(4r2) Sounds get fainter as you get further away
because the energy is spread out over a larger area I falls off as 1/r2 (inverse square law)
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Inverse Square Law
Source
r
2rA1=4r2
I1 = Ps/A1
A2=4(2r)2 = 16r2 = 4A1
I2 = Ps/A2 = ¼ I1
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Next Time
Read: 17.5-17.10