II- 4 



second or higher order scattering terms become negligible. Since single scatter- 

 ing is invariably adequate for the far field of any one of the small inhomogeneities 

 of interest to us, the question as to whether single scattering suffices for a col- 

 lection of scatterers depends primarily on the number of scatterers involved. 

 For very large scattering volumes, it may occasionally prove necessary to in- 

 clude multiple scattering effects. 



B. SCATTERING BY STRONG INHOMOGENEITIES 



Chapter III covers the scattering from air bubbles, marine organisms 

 and the ocean surface. The chapter commences with a study of the scattering 

 from a fluid sphere (different from water) immersed in an infinite ocean. The 

 purpose of this investigation is to give a feeling for the dependence of the scat- 

 tering properties of an object on the parameters of the scattering object. It is 

 found that the most important parameters are the relative size of the object and 

 its relative compressibility. More precisely, the qualitative features of the 

 scattering are determined by the size of the scatterer relative to the wavelength 

 of the sound and by the compressibility of the scatterer relative to that of the 

 surrounding water. We find that for scatterers small compared to a wavelength 

 the scattering consists basically of isotropic and dipole radiation. If the scat- 

 tering fluid is very compressible (e.g., a gas), the small fluid sphere pulsates 

 predominantly with a breathing motion which gives rise to isotropic radiation. 

 If, on the other hand, the sphere is very hard compared to the water, the prin- 

 cipal motion of the sphere is that of rigid body oscillation (a sloshing motion) 

 which causes the scattered radiation field to correspond to a dipole field. 



When the scattering fluid sphere is no longer small compared to a wave- 

 length the scattering becomes highly directional. No simple analytical results 

 describe the scattered field, and we must be content to examine some numerical 

 results. In general, however, the scattering from a medium or large object 

 (always comparing the size of the object to the wavelength of the incident sound) 

 becomes very much dependent on the shape of the object, and the idealization of 

 the object as a sphere is no longer appropriate. 



Next, in Section III-B we delve into a more detailed treatment of scat- 

 tering from air bubbles. Since air bubbles are very compressible, the scatter- 

 ing from a single air bubble is essentially isotropic. We may liken the pulsating 

 motion of the air bubble to the oscillation of a mass on a spring. Hence, we 

 would expect a resonant behavior to occur when the inertial and compressibility 

 effects are matched. This is indeed what happens, and the resonant frequency 

 of air bubbles can easily be predicted. 



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