III-114 



After some analysis, which requires that a> > 1, Marsh obtains* 



I = 3.38a2 - 1.86a (III- 156) 



Recall that a = ks^/2g, where s is the wind speed. With an incident frequency 



of f kilocycles and a wind speed of S, in knots, a is given by 



kc knots 



a = 0.05 f S^, (III- 157) 



kc knots 



For a typical condition of 2 kc sound and 10 knot winds, we have a = 10, which 

 satisfies the necessary condition that a > > 1 . 



With the value of I given in (III- 156), the expression for ^gpg^ , the intensity of 

 the scattered sound in the specular direction, becomes. 



n„_„ = 1 - -^^^1 (3.38 a^ - 1.86a) (III-158) 



2g (2a) 



This expression can be written in terms of the variables H and b, where H is 

 the average trough to crest wave height in feet, b = fH, (and f is the frequency 

 of the incident sound in kilocycles)- We require the following relations for the 

 sea's behavior: 



(h )2 = 2.42.10 "^ (S, f (III- 159) 



^ feet knots 



H = 1.77h 



Neglecting the term 1 .86a (a^ is large compared to a, since a > > 1) and sub- 

 stituting (III-159) in (III- 158), we have^^^ 



^spec = 1- 0.528 b^/^ H' ^° Y (III-160) 



*The expression for I given in (III- 156) is two times that reported by Marsh. 

 This results from the error mentioned in the preceding footnote . 

 (l)Marsh reports fispec = 1 - 0.485 b^ ^^ H^/^ ° Y • Part of the difference is ac- 

 counted for by the factor of 2 omitted in evaluating I : this is partly compen- 

 sated for by a second arithmetic error by Marsh. Though not stated explicitly, 

 Marsh presumably also drops the linear term in I, for otherwise another term, 

 with different exponents for the variables, would appear in the expression for 



n 



spec 



artbur m.littlcJnt. 



S-7001-0307 



