Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness

An asymptotic high-frequency solution is presented for the problem of diffraction of acoustic waves emanating from a ring source by a semi-infinite cylindrical pipe of certain wall thickness having different internal, external and end surface impedances. Through the application of the Fourier-transform technique in conjunction with the Mode Matching method, the diffraction problem is described by a modified Wiener–Hopf equation of the second kind and then solved approximately. Various numerical results illustrating the effects of the parameters of the problem on the diffraction phenomenon are presented.