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Diffraction of sound waves from a rigid circular cylindrical cavity with an acoustically absorbing internal surface is investigated rigorously by a modified version of the Wiener‐Hopf technique. The solution involves a set of infinitely many expansion coefficients satisfying an infinite system of linear algebraic equations. The numerical solution of this system is obtained for different parameters of the problem such as the cavity radius, cavity depth, cavity internal surface impedance, and their effects on the diffraction phenomenon are shown graphically.

Analytical solutions for the problem of radiation of sound from a duct with flow have been shown to serve as an important first model for acoustic engine-aircraft engineering applications, useful for understanding the physics and for validating and benchmarking numerical solutions.The probably most important steps were taken by Levine & Schwinger and Munt. He showed that application of the Kutta condition, in order to determine the amount of vorticity shed from the trailing edge, goes together with excitation of the Kelvin-Helmholtz instability wave of the jet.In the present work we will extend this work further by considering the effect of lining on the centerbody and on the afterbody, which is mathematically a much different problem. The lining is of impedance type, while the Ingard-Myers boundary condition is taken to include the effect of the mean flow. The flow is assumed to be subsonic. Differences in the (otherwise uniform) mean flow velocity, density and temperature are taken into account. A vortex sheet which separates the jet from the outer flow emanates from the edge. Due to this velocity discontinuity of the mean flow the jet is unstable. An analytical solution satisfying the full or partial Kutta condition at the trailing edge is found by means of the Wiener-Hopf technique. The jet instability wave is taken apart from the rest of the solution and the effect of applying the Kutta condition to the scattered field is shown, both in far field and near field. The influence of lining on the radiation is displayed graphically.The problem of a lined afterbody is of particular interest, because its Wiener-Hopf solution embodies a novel application of the so-called "weak factorization".It should be noted that our primary goal here is to archive the mathematical solution, rather than to unravel all physical possibilities and explore the whole spectrum of problem parameters and their combinations.

Aft fan noise radiating from a lined bypass exhaust duct with lined afterbody is modelled in a way that allows an analytical solution of generalised Wiener-Hopf type. A preliminary set of numerically evaluated examples, based on the experiments by Tester at al. seem to confirm their conclusions that the beneficial effect of a lined afterbody is mainly found without mean flow.

In the present work the radiation of sound from a bifurcated circular waveguide formed by a semi‐infinite rigid duct inserted axially into a larger infinite tube with discontinous wall impedance is analyzed. The formulation of the boundary‐value problem in terms of Fourier integrals leads to a matrix Wiener‐Hopf equation which is uncoupled by the introduction of infinite sum of poles. The exact solution is then obtained in terms of the coefficients of the poles, where these coefficients are shown to satisfy infinite system of linear algebraic equations. This system is solved numerically and the influence of the parameters such as the outer cylinder radius and the discontinuity of the surface impedances on the radiation phenomenon is shown graphically.