Acoustic scattering by fluid spheres

Abstract

The problem of scattering of acoustic waves and pulses by an elastic sphere embedded in an infinite elastic medium is investigated for the case where the two media are very similar acoustically. This physical situation allows functions with arguments involving the acoustic parameters inside the sphere to be expanded in a Taylor series involving the acoustic parameters outside the sphere. Using only the first order terms in this expansion, the solution for plane wave conditions in the back-scattered direction is much simpler than the exact solution. This allows the solutions for the scattering of acoustic pulses to be calculated. The steady state solutions are compared with those obtained using the Born approximation, and are found to differ only in the algebraic sign of the difference in density of the two media; although they agree with the results obtained by Rayleigh in the proper limit. It is also found that the Born approximation differs from the results obtained by Rayleigh again only in the algebraic sign of the difference in density of the two media.