E. J. Skudrzyk and G. P. Haddle 261 
replaced by the width y(é) of the hydrophone. By properly shaping the hydrophone, 
the factor 1/l, of the preceding formulae can be changed into a factor (1/xl;)”, 
and the flow-noise sensitivity of the hydrophone can be made considerably 
smaller (as long as the nearfield pressure determines the received level). The 
flow-noise sensitivity of a hydrophone is thus a function of its shape, and the 
experiences acquired in shading hydrophone arrays can be used to reduce the 
received flow-noise level. 
For a circular hydrophone whose radius R is small in comparison to the 
transverse correlation length, the force on the hydrophone can be given by the 
following integral: 
1 
R = 2 
rar p(k) cos xé ER? = poor? f cos (kRy) dy fia hi OE (16) 
R aT TET @«R 
where IT is the gamma function, and J: is the Bessel function of the first order. 
At higher frequencies, when xR > 1, the Bessel function can be replaced by its 
asymptotic expression, and 
2 
F = constant LOE = constant - Fo se (17) 
Doubling the radius now decreases the narrow-band noise level by 9 db. If the 
transverse correlation length of the eddies were independent of their longitudinal 
wavelength, the effect of the finite diameter of the hydrophone would reduce the 
flow-noise output by 9 db per frequency octave. 
A hydrophone whose width increases as the sine of the distance from its end, 
y = sin (18) 
1 
would yield an output 
ty a 
: (K)lilot Fo 
PS I (k) cos (kx) sin 2 dx = 2 k) -~—cos xk = EN, S 19 
af p(k) cos (kx) T, x ace Tiare 1 ; elt 2 (19) 
The hydrophone shape shown in Fig. 14.1 is interesting from a practical 
point of view. Its flow-noise sensitivity is proportional to the integral 
a a+b 2a+b 
[rcosexae +f acosnxde + f (2a + b — x) cosKx dx 
0 a a+b 
~ Jy 2 sin? tina 28 +) a (20) 
K 2 2 K 
Fig. 14,1. Special hydrophone shape. 
