Low Frequency Scattering by Spheroids and Disks 2. Neumann Problem for a Prolate Spheroid

The problem of scattering of a scalar plane wave by a prolate spheroid is solved for Neumann boundary condition, arbitrary major to minor axis ratio, and arbitrary incident direction. The solution is obtained by using an iterative method applied to solutions of the corresponding potential problem and is expressed as a series of products of Legendre and trigonometric functions and ascending powers of wave number. A recursion relation for the coefficients in this series is derived. These results and the corresponding results for the Dirichlet case are employed to calculate scattering cross-sections for 2: 1, 5: 1 and 10: 1 prolate spheroids.