High-frequency scattering from rigid prolate spheroids

The scattering of an acoustic plane wave by a rigid, immovable prolate spheroid is investigated over a broad frequency range (0<kL/2≤300). An unexpectedly large, off-axis radiation lobe dominates the bistatic beam pattern for axial incidence and aspect ratios larger than unity, over the entire frequency range considered. This lobe is found to be due to an amplitude-modulated creeping wave. A new asymptotic expansion of the spheroidal radial functions is introduced that gives an improved estimate of the functions for moderate values of the azimuthal index at high frequency.