Transient Acoustic Scattering From a Finite Body

Transient acoustic scattering from a hard, finite body is considered from an integral equation point of view. It is shown that the operator inverse to the integral operator in the surface Helmholtz integral formulation is a meromorphic operator-valued function of the complex frequency. An explicit representation is given of the inverse operator in terms of its poles (the natural frequencies) and the nontrivial solutions of the homogeneous integral equation. Expressions for the scattered field in terms of exponentially damped sinusoidal oscillations are also deduced for the special case where the incident field is a delta-function plane wave and the inverse operator has only simple poles.