The diffracted sound field due to an impedance half plane and the field due to a right angle wedge with impedance surfaces are analyzed with a review of the previous works in this area. Maliuzhinetz's diffraction coefficient is modified in order to yield an explicit and simple expression that makes it easy to investigate the dependence of diffracted sound field on the surface impedances. Numerical examples are given for the cases of various combinations of surface impedances. This results show the effectiveness of the surface treatment on the dark surface with absorptive materials as well as on the bright surface. Generally the former treatment gives less effect than the latter on the sound field in shadow zone.
The effect of absorptive side walls of a slotted geometry on the sound propagation from a line source inside the slot is investigated analytically. The problem is modeled as a rectangular waveguide with a reflective baffle whose side walls have finite acoustic impedances. The source is located along the axis of the waveguide. The acoustic field inside the waveguide is represented by a series of mode functions with unknown coefficients and the field outside the waveguide is represented by an inverse cosine transform of an unknown function. The unknown coefficients and unknown function are determined from the boundary conditions inside the waveguide, radiation condition and the continuity of both pressure and normal velocity on the aperture plane. Edge condition for an impedance wedge is deduced with the aid of energy principle. An infinite system of linear equations is truncated by a finite one and its error is evaluated using the edge conditions. Thougn numerical examples are given for a wedge with small acoustic admittances, the effect of absorptive walls is apparently shown. Limiting cases are compared with the earlier results by Howard [J. Math. Phys. 13, 482-490 (1972)] who treated the same geometry with perfectly reflective and absorptive walls.
