are quite adequate. Making use of these in (64) leads to 

 the approximate relations 



(a) uu 3 = c 3 \ h^ 



(65) 



c 3 v 1 



(b) at= ~L hi(li 



It will be noted that the temporal decay factor a^ in the 

 present case is related entirely to energy leakage through 

 the walls of the tank. It will be shown that this loss is 

 about tenfold greater than the viscous losses when the 

 cavity is filled with pure, gas-free water. However, it is 

 much less than the attenuation as measured with most of 

 the sea water samples. 



It remains to consider the transcendental relations of 

 the type (6 3). The limiting situations for which Z->0 and 

 Z~ x ^0 both lead to 



tanh K.l =0 



which corresponds to the special case of total reflection at 

 the walls and zero attenuation. Actually Z = corresponds 

 to the extreme soft wall condition and Z' 1 = to the extreme 

 hard wall discussed in the previous sections. 



For the case of compliant walls for which \Z\ is small 

 compared with the characteristic impedance of the fluid 

 p c, the quadratic term in Z can be neglected in (es^iving 



tanh/T I =-^-(z+z') (66) 



ii p n\ i i/ 



Moreover, since the departure of K from the value K (0) 



50 



