ACOUSTIC SCATTERING BY A SPHERICAL BODY NEAR A PLANE BOUNDARY

Acoustic scattering is studied by considering spherical bodies near pl ane boundaries when they are insonified by plane waves at arbitrary in cidence angles. Using the method of images, there is an image sphere o n the side of the boundary opposite to the side containing the real sp here, and both the sphere and its image contribute to the resulting so und field. The plane boundary is introduced and the scattering problem is solved. The resulting sound field consists of four parts: the inci dent field, its reflection from the boundary, the scattered field from the sphere, and that scattered by its image. The whole solution is re ferred to the center of the real sphere, and any depth below the bound ary is possible. The treatment is analytic and exact, and it uses the addition theorems for spherical wave functions and the whole (atomic-p hysics-like) machinery of the coupling of various angular momentum vec tors. The required coupling coefficients b(mn) emerge from the solutio n of an infinite linear system of algebraic equations, which is approp riately truncated to obtain numerical predictions for the ''form funct ions.'' Form functions that account for either one or two of the four components of the total acoustic field, as well as for the overall eff ect of all four contributions together, are considered. The two indivi dual components are shown so that the distortions they induce in the f ield can be separately assessed. All the form functions are displayed versus ka, for various values of the normalized sphere depth dla. Thes e plots also serve to predict quantitatively the critical depths beyon d which the effect of the boundary becomes negligible. They also provi de exact benchmark curves against which the accuracy of some approxima te techniques, based on the numerical evaluation of certain integral e quations can be assessed.