ACOUSTIC PRESSURE 259 



The air particle which possesses this small amplitude is about 4 X 10 -8 

 cm in diameter, so that the eardrum at threshold pressure executes dis- 

 placements which are about one hundred times smaller than the diameter 

 of a gas molecule. 



Acoustic Pressure 



In the previous section it was shown that the displacement in simple 

 harmonic motion is given by the expression y = A sin 2irt/T = 

 A sin (2wnt). The equation which describes the motion of all the 

 particles in the wave is 



y = A sin 2vr I - - - j = A sin 2-irn It - ^J 



where V = rih. The definition of elasticity is 



Stress 



Elasticity = 



Strain 



In a gas the stress or the force per unit area is the pressure, and the 

 strain is the rate at which an element of unit cross section but of length 

 dx changes with changes in values of the displacement dy. Hence 



_.. . . dy 



p = Elasticity — 



dx 



Since 



Thus 



y = A sin 2tu 1 1 — — j 



dy A2irn 



— = — — cos 2irn [ t - 



T-n ,- • 2wnA / a;\ 



p = =fc Elasticity X cos 2irn it — — J 



v 

 p = ± Elasticity — 



for a wave traveling with velocity V. Since 



y __ /Elasticity 



V 2 pv 



V = TT = P V * 



