where c is the wave speed, A the surface area, V the volume 

 and y^ a transmission coefficient dependent upon the imped- 

 ance mismatch between the medium and its environment. 

 For small volumes, the second term (radiational loss) will 

 dominate, while for sufficiently large volumes the viscous 

 term will ultimately dominate. 



The above deductions, which have been obtained in a 

 somewhat heuristic manner, will be derived more rigorously 

 in the development which follows. 



Effect of Temperature Fluctuations* 



The question of temperature fluctuations associated 

 with acoustic disturbances was avoided at the outset by 

 adopting relation (3). Actually the equation of state for 

 any pure substance should involve a third thermodynamic 

 variable, the absolute temperature T being a possible 

 choice. 



Thus formally one should stipulate that for the particu- 

 lar medium 



f(P,T) (24) 



The differential counterpart of this is 



-dp = K dP-b dT (25] 



P 



where K is the isothermal compressibility and b the(volu- 

 metric) coefficient of thermal expansion. Relation (3) 

 and its differential counterpart (6) can be consistent with 



v The following section as well as that on energy considera- 

 tions was suggested by R. O. Reid. 



37 



