where 



2u + X 

 B=— ^ (21) 



The latter parameter has the dimensions of time and can 

 be regarded as a characteristic relaxation time associated 

 with the damping action of viscosity on acoustic oscillations. 



In order to appreciate the full significance of relation 

 (2 0), it is instructive to consider the integral of this rela- 

 tion for a finite fluid volume V bounded by the closed sur- 

 face S. By employing the divergence theorem, the integral 

 relation takes the form 



V s 



where E is the total acoustic energy in the volume V. If the 

 surface S is not simply connected, then one can regard the 

 surface integral as a sum of integrals over the pertinent 

 exterior and interior surfaces. The normal component of 

 velocity v n in every case is taken positive if the flow is 

 towards the surface from the fluid volume concerned. 



For an inviscid fluid, (22) reduces immediately to 



M 



v n p do (22a) 



which stipulates simply that the change in acoustic energy 

 in the volume V equals the net rate of influx of energy 

 across the closed surface S which delineates this volume. 

 For free vibrations, the acoustic energy level can be 

 maintained only if there is total reflection of energy at 



35 



