Assumptions 



The additional stipulations regarding the nature of the 

 disturbances are the following: 



(a) The changes in P, v, and p associated with the 

 acoustic disturbance are regarded as sufficiently small 

 that the usual linearizing approximation can be made. 

 Specifically, the anomalies of p and p are regarded as 

 small compared to their respective mean values within 

 the chamber. Also v is regarded as small compared with 

 the speed of sound for the fluid occupying the chamber. 



(b) The motion is regarded as irrotational, 



V x v = 



(c) It is presumed that there is no net translation of 

 the medium. 



(d) The body forces (including gravity) are considered 

 to have negligible influence on the acoustic disturbances. 



Linearized Relations 



In view of conditions (a), (c), and (d), relations (1) 

 and (2 ) can be approximated by 



~ - u x v 3 v - (\x 1 +\ ) v (vS) + Vp = (la) 



~+ P V-5 = (2a) 



where p is the mean density and p is the departure of the 

 pressure from hydrostatic. 



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