Ill- 120 



For the limiting ray f the transmission loss (in db per bounce) due to scatter- 

 ing is given by 



a^ = 10 log -^ (III -170) 



•* o 



Using the above value of y . we have* 



a = -10 log ^1 - 0.00143 b^/^H^/^^L^ /^J (III-171) 



The factor H"^''"'^ varies only a little over a large range of possible sea states. 

 The term \}' '^ is also relatively insensitive, compared to the factor \?''^ . Using 

 typical values of L = 200 ft and H = 3 ft, we have 



r n 



a --10 log 1 -0 . 0226 b^ /^ I (III-172) 



Considering the extreme values of H = 6 ft, L = 300 ft at one end, and H = 2 ft, 

 L = 100 ft at the other, we obtain 



s 

 and 



a = -10 log 1 - 0.0297 b=^/^ i (III-173a) 



a = -10 log 1 - 0.0153 b^^^ I (III- 173b) 



respectively. 



Recapitulating the basis of the last part of this development, we 

 assumed that: 



(1) Sound is traveling in an isothermal layer for which the velocity 

 gradient (due to increasing pressure) is 0.018 sec "^ . 



(2) Only the sound in the limiting ray is considered. 



(3) For (III -172), which is used in most of the later material, 

 the depth, L, of the layer is taken as 200 ft and the average 

 trough to crest wave height, H, as 3 ft. The sensitivity of this 

 is shown by (III-173a) and (III-173b), which give analogous 

 expressions for H = 6 ft, L = 300 ft. for one extreme and H = 2 ft, 

 L = 100 ft. for the other. 



*This differs from as = -10 log [} - 0.0013 b^^^H^ /i°L^/!j as reported by 

 Marsh because of the different coefficient (0.528 instead of 0.485) in the expres- 

 sion for Q spec . 



artbur 2l.1LUtle.Ilnir. 



S-7001-0307 



