Plane wave diffraction by a semiinfinite soft/hard parallel-plate waveguide

The diffraction of acoustic plane waves by a semi-infinite parallel plate waveguide satisfying Dirichlet (soft) and Neumann (hard) boundary conditions on its exterior and interior faces, respectively, is investigated rigorously by using the Fourier transform technique in conjunction with the mode-matching method. This mixed method of formulation gives rise to a scalar Wiener-Hopf equation of the second kind, the solution of which contains infinitely many constants satisfying an infinite system of linear algebraic equations. A numerical solution of this system is obtained for various values of the thickness of the parallel plate waveguide and the incidence angle, through which the effect of these parameters on the diffraction phenomenon is studied