which represents the adiabatic compressibility. For liquids, 

 the value of K is much greater than the second term in (2 8) 

 and hence it makes little difference, in respect to the sound 

 speed, whether one uses the adiabatic or isothermal com- 

 pressibility (except in problems involving refraction of 

 sound rays). 



The physical justification of the assumption of adiabatic 

 changes of state lies largely in the notion that acoustically 

 induced heat conduction, like viscous generation of heat, 

 will be of second order compared with the change in intrin- 

 sic energy which occurs in an acoustic vibration. When 

 one neglects both viscosity and heat conduction, the resulting 

 acoustic theory predicts reasonably accurate propagational 

 speeds. However, no information is obtained regarding 

 the attenuation which is associated with irreversible proc- 

 esses. 



A good approximation of the viscous damping is achieved 

 for acoustic waves by ignoring vorticity, in spite of the fact 

 that viscosity introduces a flux of vorticity inwards from the 

 boundaries, if shearing motion occurs at the boundaries. 

 The approximation is justifiable for acoustic disturbances 

 since the rate of dilatation is much larger than the vorticity. 

 A similar sort of approximation can be made in considering 

 the effect of heat conduction. Although the latter causes a 

 change in entropy of the medium, the process can be con- 

 sidered nearly isentropic. 



If there exists a small departure of the specific entropy 

 (ergs/gm °K) from its mean value, then relation (7) should 

 be replaced by 





r\ - \ ® (29) 



where T is the mean temperature, r\ the anomaly of specific 

 entropy and \ has the meaning implied by (28). For isen- 

 tropic conditions this obviously reduces to (7) as a special 

 case. Let the flux of heat be given by -K V T where K is 



39 



