without frictional losses. An approximate solution can be 

 obtained, if it is assumed that the losses are low. The 

 cavity is, in other words, strongly resonant. The highest 

 attenuation that can be measured with the present equip- 

 ment corresponds to a cavity Q of 470, and the Q with clean 

 water in the cavity is of the order of 7500, so the losses 

 are actually quite small when compared with electrical 

 resonant circuits. 



The wave equation (15) for a viscous fluid is employed 

 in the present analysis. The solution for the components 

 of displacement as given by (45) is still pertinent; however, 

 the expressions for the complex wave numbers and fre- 

 quency will differ from the previous case. Substitution of 

 (45) in (15) yields 



|-§- = o 3 (1-Bfi) v 2 s (74) 



at 



where a = ^J \ / p and 6 = (2^ +X 1 )/X as employed pre- 

 viously. 



The evaluation of the characteristic equations is 

 formally the same as in the previous case except that a 2 

 is to be replaced by c 2 (1 - 6 Q) in relation (64). Thus the 

 counterpart of (64) is 



3 



[f = c 2 (1 - B n) V K t 3 (75) 



The auxiliary relations relating K^, Q and the boundary 

 impedances are formally the same as (66), except that the 

 Kj and Q are now dependent upon 6 as well as the boundary 

 impedances. However, the form of (66) demands that the 

 first order effect of attenuation on K^ is due to the boundary 

 impedance. Any effect of 8 will be of second order in 

 respect to K^. Consequently relations (69) and their 

 counterparts for coordinates x z and x a are still valid. 



55 



