Radiation of Sound Waves from a Semi-Infinite Rigid Duct by Local Outer Lining

Radiation of sound waves from a semi-infinite rigid duct by local outer lining (Fig. 1) is investigated rigorously by the Wiener-Hopf technique. Through the application of Fourier-transform technique in conjunction with the Mode-Matching method, the radiation problem is described by a modified Wiener-Hopf equation of the third kind and then solved approximately. The solution involves a set of infinitely many expansion coefficients satisfying 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 radiation phenomenon are presented.