E. J. Skudrzyk 
Relative deviation 
of 
sound velocity, 
a 
ao, RKA 
ao, rSR 
aoe 
ao(1— r/R)°; rSR 
0; r>R 
TABLE 12:1 
Scattered pressure 
referred to classical 
scatterer of sames, 
D(8o) 
sin! R-TRcosTR 
(FR)* 
1 
a+T?R?) 
Remarks 
Classical scatterer 
Spherical scatterer 
of constant sound 
velocity 
Exponential increase 
of sound velocity 
Parabolic velocity 
increase 
215 
ao 
[1 + (r/R)?]? 
eT (r/R)? Gaussian increase 
a 
° of sound velocity 
is large compared to the wavelength of the radiation, the scattered pressure 
decreases at least as ([R)~” (see Table 12.1). It fluctuates above and below this 
value for a sphere of constant sound velocity and approaches this value asymp- 
totically if the change in sound velocity is exponential. The pressure scattered 
backwards by a large scatterer decreases at least inversely proportional to the 
square of the frequency and the square of the radius of the scatterer. Sharper 
transitions than the exponential, such as those of cases 4 and 5 in Table 12.1, 
lead to considerably less backscattering. Scatterers that exhibit a Gaussian ve- 
locity distribution produce a particularly small amount of backscattering. 
Forward and backward scattering, then, are almost completely independent 
phenomena. Forward scattering, as will be shown later, essentially describes 
the phase change of the wave caused by the scatterer. This phase change is pro- 
portional to the average change of the sound velocity over the scatterer, and 
consequently it does not depend upon whether the change is abrupt or continuous. 
Thus, all scatterers that exhibit the same average change of sound velocity over 
their volume (i.e., they have the same scattering strength) generate the same 
amount of forward scattering. The scattered pressure reaches a maximum in 
the forward direction and decreases with increasing scattering angle. Backward 
scattering, on the other hand, is essentially a reflection phenomenon; therefore, 
it depends greatly on the details of the variation of the sound velocity across 
the scattering patch. 
The results given above can be generalized to fit the case of a fluid contain- 
ing a large number of scatterers. Because of the small deviation of the sound 
velocity from the average value, there is equal probability that this deviation 
may be either plus or minus; therefore, the energies add, and the intensity 
scattered becomes directly proportional to the average ofthe intensity scattered 
