SECT. 4] SOUND SCATTERING BY MARINE ORGANISMS 513 



of the scattered sound as well. The details of how objects scatter sound can be 

 computed from theory only for simple shapes (see Morse and Feshbach, 1953). 

 Let us review some of the properties of single scatterers. 



A . The Properties of Single Scatterers 



The "strength" of a scatterer is a measure of its ability to scatter sound 

 from an impinging wave. It is expressed as the scattering cross-section of the 

 scatterer. The total scattering cross-section, a, is defined by the equation 



Is = aIl47Tr^ (1) 



where Ig is the intensity of the scattered wave at a distance r from the scatterer 

 and / is the intensity of an incident plane wave. This total scattering cross- 

 section depends usually on the orientation of the scatterer relative to source 

 and receiver. For the most common observation of backward scattering it is 

 usual to talk about a backward-scattering coefficient defined by cr/47r. In the 

 common experiment at sea, a small source is employed such that at distances 

 large compared with its size the wave fronts are spherical in water of uniform 

 velocity ; the intensity at a distance r is given by / = lojr^, neglecting dis- 

 sipative terms. Then we may write 



where Iq is the intensity of the incident sound wave measured at distance 

 r= I from the source. 



The shape and size of the scatterer are measured in relation to the wave- 

 length, A, of the sound. Given a scatterer of arbitrary shape and size, by varying 

 A we can describe qualitatively the relationship between the intensity of the 

 scattered sound and the ratio of size to wavelength. In the region where A is 

 much larger than any linear dimension of the scatterer, the intensity is in- 

 versely proportional to the fourth power of A, or directly to the fourth power 

 of frequency (Rayleigh, 1945). This is called Rayleigh scattering. As A decreases 

 one encounters the region where A and the object are comparable in size, and 

 then, finally, the region where the object is many wavelengths across. Where 

 A and size are comparable, the scattering intensity oscillates between maximum 

 and minimum as A decreases, the amplitude of the oscillation depending on 

 the shape and the acoustical contrast between medium and scatterer, A few 

 computations have been made, mostly of scattering by spheres of contrasting 

 material. Anderson (1950) computed scattering from a homogeneous fluid 

 sphere in water, using density and velocity ratios as independent variables. 

 His curves clearly show that back-scattering intensity oscillates more and more 

 widely as the scatterer becomes "softer" (more compressible than water), but 

 that scattering intensities remain low, more nearly constant, and oscillate 

 much less widely as the "hardness" increases. Machlup (1952) computed the 

 effect of a thin shell (carapace) over a fluid sphere. Anderson (1953) has measured 

 the scattering cross-section of hollow rubber spheres. 



