Following usual acoustical procedure, a mixed Lagrang- 

 ian-Eulerian system is employed in which the particle dis- 

 placement vector s is regarded as a field variable. Specifi- 

 cally r + s represents the position vector at time t of that 

 particle whose equilibrium position is r. In view of the 

 condition of small displacement implied by condition (a) it 

 follows that 



= v (4) 



zt 



Accordingly (2a) can be expressed as 



— (p+P o V.s) = 



(p-p ) = -p V-s = -p (5) 



where is a convenient notation for the dilation V • s. 

 Equation (3) implies that for small changes 



AP = ^Ap = ^ (6) 



dp ° p n 



where X Q is the second Lame parameter (or reciprocal 

 compressibility). Using (5) and taking AP as the acoustic 

 pressure anomaly (p) yields 



■K ® (71 



which is an adequate approximation for acoustic waves 

 whose intensity is not excessive. 



28 



