III-38 



(f) 



^ 4TTnc^ 



= 1 + ^ 



4Trn c a 



= 1 + 



iiJ 



(5) 



•1 + 16 



■1-16 



K^)' 



= 1 + x + i y 



(III- 37) 



A little algebra leads readily to: 



mi 



mixture sound velocity 



'■^['■•i' 



(1 + x) = 



= 2 



[■■-(•)] 



Intensity attenuation 



■^ 



-1±A 1 + 



(1 + x)' 



(III- 38a) 



(III- 38b) 



We can compare these results with the limiting case of very low air bubble 

 densities. This means that x and y are both much less than 1, so that (III-38b) 

 yields: 



(jy 4TTn c^ a6/U) 



intensity attenuation ^ — Y ~ r" 



m 



+ 6' 



From Table III-2 we note that this is precisely nog (for either Model II or 

 Model III), as we would expect. 



Arthur B.littlcJnt. 



S-7001-0307 



