A unified approach to acoustic fields induced in inhomogeneous spheres by external sources

The evaluation of acoustic fields induced in inhomogeneous spheres by external sources, based on volume integral equations, is simplified considerably using Ivakinʹs integral equation and the use of the well-known expansion for the Green dyadic. The method presented here overcomes the difficulties of calculation arising from the possible step discontinuities in the density, allowing a quick and accurate evaluation of the fields. So the simple hybrid (analytical–numerical) scalar method, developed previously for spheres with variable, even discontinuous compressibility, is easily extended to the general case of inhomogeneous density in a manner requiring the least possible analytical and computational effort.