Sound propagation over convex impedance surfaces

Abstract

Theoretical calculations for the diffraction of sound by large spheres and cylinders with finite impedance surfaces are reported. The differences between existing two-dimensional and new three-dimensional results are made explicit and are shown to involve a simple correction factor in the case of a large sphere. The results for propagation over an infinitely long cylinder have a bearing on the widely used analogy between sound propagation over a curved surface and sound propagation in a refracting atmosphere above an impedance plane. Specifically, it is found that there is a rigorous analogy between sound propagation above a large circular cylinder and propagation in a medium where the sound speed varies exponentially with height. This differs from the bilinear profile that is often used when exploiting the analogy [see, for example, J. Acoust. Soc. Am. 83, 2047–2058 (1988)]. Predictions for both profiles are found to agree well with each other and with the published data in the shadow zone, but considerable discrepancies are found in the penumbra region.