The primary effect of the viscous parameter B enters 

 in the evaluation of a^. By separating relation (75) into its 

 real and imaginary parts and neglecting terms involving 

 B 3 , a f 3 and a. 2 the following approximate relations are 

 obtained: 



(a) uu 2 = c 2 £ h i 



(b) a^^a^+i^ 



where h^ and a^ (£ = 1, 2, 3) are given by relations of type 

 (70) and (72) with appropriate changes in subscripts. 

 Specifically, the allowable values of h^ depend only on the 

 cavity geometry and the equivalent thickness of the walls. 

 The values of a^ depend upon the cavity geometry and the 

 real part of the boundary impedance. 



Relations (76) differ from (65) only in the addition of 

 the viscous attenuation term to ct£. It will be noted that 

 the resonant frequency is not influenced by viscosity in the 

 present approximation. Moreover, relation (76b) shows 

 that the effects of internal (viscous) losses are additive in 

 respect to the attenuation coefficient a^. In other words 

 there is no first order coupling of the internal and external 

 (radiational) attenuation phenomena. This is an important 

 result, since it allows the possibility of evaluating the 

 internal losses in a fluid sample by measuring the total 

 loss and subtracting the radiational loss. The latter is 

 determined experimentally by the calibration tests with a 

 virtually inviscid fluid (air-free, pure water). 



It will be noted that relation (76b) is consistent with 

 the result anticipated in the considerations of the acoustic 

 energy decay (page 36 ). It was shown by a somewhat 

 heuristic chain of reasoning that the exponential decay 

 factor (per unit time) for energy could be expressed in 



(76) 



56 



