Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

Abstract

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.

Sound Radiation from Non-Uniformly Lined Duct with Partial Rigidity

“…, which satisfy the Helmholtz equation (3) are to be determined with the aid of the following boundary and continuity relations. The boundary condition on the absorbing surface can be given in terms of the potential funcitons and…”

“…Analysis of sound wave propagation in waveguides with discontinuities has received wide attention due to its importance in acoustics. Up until now, numerous analytical and numerical studies have been derived [1][2][3][4][5][6]. One method of reducing noise is to introduce linings to absorb the noise as it travels along the pipe.…”

Sound Transmission in a Duct with Sudden Area Expansion, Extended Inlet, and Lined Walls in Overlapping Region

“…So the main objective of this paper is to reveal the influence of the partial lining on the transmitted field and to present an alternative method of formulation. The method previously employed in [10,11] consists of expanding the field in the overlap region into a series of complete set of orthogonal eigenfunctions and using the Fourier transform technique elsewhere. The problem is then reduced directly into a Wiener-Hopf equation whose solution involves a set of infinitely many unknown expansion coefficients satisfying an infinite systems of linear algebraic equations.…”