Axisymmetric scattering of spherical waves by a prolate spheroid

Theoretical analyses are performed, and numerical results obtained for the axisymmetric scattering of a spherical wave by a rigid prolate spheroid. In the numerical calculations, the complex farfield reflection factor (ratio of scattered-to-incident pressure) is computed as a function of frequency and observation angle for a 7-to-1 fineness ratio prolate spheroid. Different source locations are considered, all of which lie on the axis of symmetry. In addition, the superposition of the incident and scattered fields is investigated for a variety of two-source configurations. In one instance, these two sources are assumed to have equal strengths and to vibrate in phase, while in a second instance they are assumed to be incoherent. The computations are for relatively low frequencies, where the exact tabulated forms of the spheroidal wave functions may be used. The results for the directivity functions indicate that the reflection factor depends only slightly on aspect angle for a single source, but when two in-phase sources are considered, the scattering is very dependent on angle. If the two sources are incoherent, then the patterns approach the shape of the corresponding pattern for the single source closest to the pole, particularly when the second source is relatively far from the first.