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2. 6 Sound intensity
• Let us consider a harmonic sound wave moving in a
pipe of cross-sectional area A at a wave speed v
and frequency f.
• The wave induces an excess pressure p in the pipe
and a particle displacement s.
• The power P supplied to the gas by the wave is
given by
P = Force * distance moved by particle/time
P = F*particle velocity
P = Fvp
2. 6 Sound intensity
• The force F acting on the element that is moved by
the wave is
• F = excess pressure * area
• F = pA
• Hence P = pAvp
• But
vp=ds/dt
• So P = pAds/dt
•The excess pressure p is given by
•So P = -BA(ds/dt)(ds/dx)
p  B
ds(x,t )
dx
2. 6 Sound intensity
• Now s = smaxsin(kx - wt)
ds/dx= ksmaxcos(kx-wt)
And
ds/dt = -wksmaxcos(kx-wt)
So P =ABwks2maxcos2(kx - wt)
With v2 = B/rand v = w/k we find
P =rAvw2s2maxcos2(kx - wt)
but the time averaged value of cos2 = 1/2
1
2
P  rAvw 2s max
2
2.6 Sound intensity
• We can measure the intensity I associated with the
sound wave.
• I = Power/Area.
1
2
I  rvw 2s max
2
An important sound source is a point source

2.7 Point sources and sound intensity
• An important source of sound is the point source.
• Here the sound waves are emitted over a spherical
surface.
• If the source emits a power P then the intensity a
distance r from the source is
I
P
4r 2
2. 8 Sound Intensity Level
• The sound intensity can be measured and this level
is often quoted against a reference level.
• The reference level is known as the “Threshold of
hearing” and has the value Io=1x10-12 Wm-2
• When measured against the reference level the
result is given the name Sound Intensity Level b
I 
b  10log10 
 

I
 o 