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Acoustic scattering by a circular semi-transparent conical surface. (English) Zbl 1131.76047

Summary: We study the scattering of a plane acoustic wave by a circular semi-transparent conical surface with impedance-type boundary conditions. An analytic solution is constructed on the basis of incomplete separation of variables and the reduction of the problem to a functional-difference equation of the second order. Although the latter is equivalent to a Carleman boundary value problem for analytic vectors, the solution is studied by means of the direct reduction method, that is, converting the functional-difference equations to a Fredholm-type integral equation. Its unique solvability is then studied, and an expression for the scattering amplitude of spherical wave from the vertex is discussed. Some numerical results are also presented for axial incidence.

MSC:

76Q05 Hydro- and aero-acoustics
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