Approximate expressions are obtained for the field produced when an electromagnetic plane wave is diffracted by an arbitrary angled dielectric wedge, whose refractive index is near unity. The solution is obtained from an application of the Kontorovich-Lebedev transform and a formal Neumann-type expansion. The diffraction problem is solved by firstly solving a related wedge diffusion problem and then using analytic continuation to obtain the solution for the diffraction problem. The results have applications in diffusion and wave propagation into a wedge.

SynopsisThe diffraction of a line source of sound by an absorbing semi-infinite half plane in the presence of a fluid flow is examined. It is found that the radiated sound intensity, in the half space in which the source is located, can be considerably reduced by a suitable choice of the absorption parameter. For subsonic flow the system exhibits no acoustic instabilities.

A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing fining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.

No abstract

A direct method is described for effecting the explicit Wiener-Hopf factorisation of a class of (2 x 2)-matrices. The class is determined such that the factorisation problem can be reduced to a matrix Hilbert problem which involves an upper or lower triangular matrix. Then the matrix Hilbert problem can be further reduced to three scalar Hilbert problems on a half-line, which are solvable in the standard manner. The factorisation technique is applied to the matrices that arise from two problems in diffraction theory, thus permitting these diffraction problems to be solved in closed form (at least in principle).