Diffraction by a slit in an infinite porous barrier

The diffraction of an acoustic wave by a slit in an infinite, plane, porous barrier is investigated. The barrier is modeled as a rigid material filled with narrow pores, normal to the plane of the barrier, that provide sound damping. However, the barrier is thin enough that sound transmission takes place. An approximate boundary condition is derived that models both these effects. The source point is assumed far from the slit so that the incident spherical wave is locally plane. The slit is wide and the barrier thin, both with respect to wavelength. The principal purpose of the barrier is to reduce the reflected and transmitted sound so that we assume that the flow resistance of the pores is large. The diffracted field is calculated using integral transforms, the Wiener-Hopf technique and asymptotic methods. While a formal solution to the complete problem is given, only the diffracted wavefield is studied, and that only in the farfield of the slit. The diffracted field is the sum of the wavefields produced by the two edges of the slit and an interaction wavefield. The dependence on the barrier parameters of the power removed from the reflected wavefield by the diffraction at the slit is exhibited.