for zero boundary impedance is small, the expansion of (66) 

 leads to the approximation 



K (0) , ,v 



(bX )l = x .„, (Z +Z ) 

 i o,n(o) \ i 1/ 



where AJ is the departure from K (0) = jn n I . This 

 relation can also be expressed as 



Mo) / / \ 

 ( ^ u = p^(bT(^ +z (67) 



where 7c (0) and uj(0) are the zero order estimates of the 

 wave number (for direction 1) and the frequency under the 

 condition of zero boundary impedance (hence no loss). 



The unit area acoustic impedances of the boundaries 

 can be estimated by assuming that the walls behave like a 

 flexible rectangular membrane with the edges rigidly 

 clamped. The tank employed in the experimental work 

 reported here employs stainless steel sheets of such 

 dimensions that the free resonance frequencies of the walls 

 are much less than the resonance frequencies correspond- 

 ing to the cavity modes. The load of the wall can there- 

 fore be considered as a combination of a resistive and 

 mass load such that 



Z = r + J uj m (68) 



where r is the loss resistance per unit area and m is the 

 mass per unit area. 



Setting f Z +Z J = r + j w m, in relation (67) and 

 separating the real and imaginary parts yields 



51 



