Diffraction of Acoustic Waves by a Semi-Infinite Pipe with Finite Impedance Discontinuity

A rigorous solution is presented for the problem of diffraction of acoustic waves emanating from a ring source by a semi-infinite cylindrical pipe with a partial exterior impedance. By the application of Fourier-transform technique, the diffraction problem is described by a modified Wiener-Hopf equation of the third kind. By performing the Wiener-Hopf factorization and decomposition procedure, the modified Wiener-Hopf equation is reduced to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations.