The Wiener–Hopf technique and scattering of acoustic waves in ducts

Abstract

The reactive silencer is the standard product for attenuating noise in ducts with flue gases. A model problem is solved for such a silencer by calculating the scattering of acoustic waves at sharp edges in a two-dimensional waveguide. In this waveguide the walls are considered acoustically hard and to ensure the existence of a unique solution an edge condition is applied. An exact analytical solution is found using the Wiener–Hopf technique, which relies heavily on the Fourier transform with assumptions on regularity of the solution. Control methods are employed to check the theory and the accuracy of the numerical results. One of the control methods is derived from the energy conservation principle. Symmetries, so-called reciprocity relations, are found for the reflection and transmission matrices and are first used to check the analytic calculation and later to reduce the numerical work. A quasistationary model is also used for control purposes. It is valid for low frequencies and checks the phase of the transmission and reflection coefficients, while the energy method only covers the corresponding absolute values. Physical results as the behavior of the reflection and transmission coefficients are also presented. These coefficients are analyzed as functions of both frequency and geometry.