E. J. Skudrzyk 223 
Fig. 12.14. Path difference because of disalignment of patch, 
Where 2R has been substituted for the thickness dx of the disc. In reality, the 
scattering discs are not all arranged in a line above the axis of propagation but 
are randomly distributed. Because of the large diameter of the scatterers in 
comparison to the acoustic wavelength, the scattered pressure is highly colli- 
mated in the forward direction and practically all the scattered energy is con- 
tained within a cone of an apex angle [see Eq. (30)]: 
2.5, (52) 
eatin 
Ile 
where R is the patch radius. The patches that contribute to the intensity at the 
point of observation are therefore contained within a similar cone having its 
apex at the point of observation. Because of the misalignment of the patches, 
the scattered sound reaches the point of observation with different path differ- 
ences (Fig. 12.14), which, on the average, are not greater than 
' ae : ) 25 OP oe I 
ePors Li Srllil p84 so oo)|\lapeBees ees 53 
y ( 2 (“op ae Dee ee) 
where 6=1/ka has been assumed as the average value of the angle 6. The 
pressure scattered by the average patch is therefore out of phase by an angle 
heur: 
=k Fagz” ERE (54) 
with respect to the pressure scattered by a patch that is located on the axis of 
the beam of sound. The fluctuation of the transmitted signal is given by the com- 
ponent of the scattered pressure that is in phase with the incident sound. This 
component is 
se Sint =p,-, Sin—1_= 2kaRpy sin 4 55 
p p=p Te D9 (55) 
The deviations of the sound velocity in the various patches are statistically dis- 
tributed. Therefore, the squares of the contributions of the various patches add, 
and the average fluctuation of the signal becomes proportional to the square root 
of the number of patches n = yr/2R: 
o Tt 
Ap = Viipse = V2ka Rr sina) (56) 
At low frequencies, or for long ranges or small patches, the argument of 
