Scattering of plane acoustic waves by a circular semi-infinite pipe with a rigid end face placed axially in an infinite circular duct

Abstract

In this paper, the propagation of acoustic waves along a duct system, where a semi-infinite circular rigid pipe with a rigid end face is placed axially inside an infinite circular rigid pipe is analyzed rigorously. First, direct Fourier transform is applied and the problem is reduced into the solution of a modified Wiener-Hopf equation of the second type from which the reflection and transmission coefficients are determined. Then the bifurcated circular waveguide problem is solved by applying direct Fourier transform again to reduce the problem into the solution of a Wiener-Hopf equation and the resulting transfer coefficients are taken into account when applying the building block method. Building block method is one of the scattering matrix techniques where reflection and transmission characteristics of each discontinuity in a duct are first determined independently and then taken into account as scattering matrices in order to analyze the original problem. At the end of the analysis, numerical results are presented comparing two approaches of formulation and illustrating the effects of the radii of the pipes and frequency. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim