Diffraction of a sound wave on an open end of a half-infinite waveguide with impedance walls and impedance flanges

Abstract

Diffraction of a plane sound wave on an open end of a waveguide with impedance walls, connected with impedance flanges, is considered. A plane wave is incident upon the waveguide from open space. As a result of diffraction, part of the sound energy is scattered in the half-space and the other part of the energy penetrates into the waveguide. Results of the solution of this problem can be used for calculation of the amplitude of a sound wave, scattered by a hole, in particular, in the backward direction. Besides, one can calculate the sound energy penetrating into the waveguide. Absorption of the energy in the waveguide can be taken into account by introducing impedances with nonzero real parts. The distortion of the directivity pattern of a system of receivers located in the waveguide can also be obtained. The solution of the problem has been carried out by the integral equation method using Green’s function of the half-space with an impedance boundary. The equation was solved by expanding an unknown function in the eigenfunctions of the waveguide. It reduces to an infinite set of linear algebraic equations. Results of computation of bistatic diagrams of scattering on the hole and diagrams of backward scattering are presented.