In spite of the present focus on numerical techniques, there are still theoretical problems that are fascinating and relatively simple, but have not yet been solved. One of these is the diffraction of a plane wave at skew incidence on a wedge of arbitrary angle subject to impedance boundary conditions on the two faces of the wedge. This is an important element in any physically-based model of propagation in an urban or interior environment.

A simpler problem, which presents the same mathematical difficulties, is a half plane with anisotropic impedance boundary conditions. Recent work now enables this problem to be solved, and the solution is outlined.