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 = Fv p

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 = pAv p Butv p =ds/dt So P = pAds/dt The excess pressure p is given by So P = -BA(ds/dt)(ds/dx)

2. 6 Sound intensity Now s = s max sin(kx -  t) ds/dx= ks max cos(kx-  t) And ds/dt = -  ks max cos(kx-  t) So P =AB  ks 2 max cos 2 (kx -  t) With v 2 = B/  and v = w/k we find P =  Av  2 s 2 max cos 2 (kx -  t) but the time averaged value of cos 2 = 1/2

2.6 Sound intensity We can measure the intensity I associated with the sound wave. I = Power/Area. 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

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 I o =1x Wm -2 When measured against the reference level the result is given the name Sound Intensity Level 