Impedance theory of sound scattering: General relations

The problem of sound scattering by an elastic body of arbitrary geometry in an acoustic medium is solved by the impedance method. It is shown that, for a complete solution, three impedance matrices are necessary: one of them characterizes the scatterer and the other two, the medium. The scattering matrices and other characteristics of the solution are expressed through the incident field and these three impedance matrices. The necessary general relations are presented, and the most important particular cases are considered. Three new representations of the diffraction field are proposed in the form of a sum of two components obtained as solutions to two simpler boundary-value problems.