The Acoustic Wave Equation 



In view of the identity 



V (v-u) = v 2 v + v X (7Xu) (13) 



it follows that for irrotational motion (condition b), the 

 equation of motion (la) simplifies to 



Po It- (2^+^)v 3 v + Vp = (14) 



at 



Moreover, if (4) and (7) are employed then the latter rela- 

 tion is rendered in the form of a wave equation for the 

 displacement s: 



>ofrl=^o V 2 s + (2^ + X 1 )V=|| (15) 



The basic form of the wave equation remains unchanged 

 for a visco-elastic medium; the only modification is the 

 replacement of X by 2|_i + X . However, the boundary 

 conditions appropriate to the visco-elastic problem are 

 certainly more elaborate than those required in the viscous 

 fluid problem. 



In the special case of an inviscid fluid, (15) reduces 

 immediately to the canonical form for simple waves 



^-f- = a 2 V 2 s (15a) 



where a = y\ / p represents the wave speed. 



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