On the uniqueness of solution for all wavenumbers in acoustic radiation

The integral relations equivalent to Helmholtz’s equation with closed-boundary conditions possess nonunique exterior solutions at eigenwavenumbers of the corresponding interior problems. If the Green’s function for Helmholtz’s equation can be expanded into a series of orthogonal functions, then an infinite set of integral equations at the boundary results. These ‘‘null-field’’ equations are shown to possess unique solutions for all wavenumbers. Furthermore, these solutions can be used to represent the solutions in the exterior domain as algebraic series.