Approximate boundary conditions for diffraction by thin transmissive media

The object of this note is to describe a method that can be used to obtain useful boundary conditions to model various situations that arise in diffraction theory. In particular when wanting to apply the Wiener-Hopf technique to diffraction problems that involve thin transmissive media. Transmissive here means that the thin layer medium suffers a change in the physical quantities of density, acoustic velocity, and wave number from the surrounding medium. The present approach can be used to obtain approximate boundary conditions for other physical applications where thin strata of transmissive material arise

A note on point source diffraction by a wedge

The object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given for the three-dimensional free-space Green's function

A Green's function for diffraction by a rational wedge

In this paper we derive an expression for the point source Green's function for the reduced wave equation, valid in an angular sector whose angle is equal to a rational multiple of 77. This Green's function can be used to find new expressions for the field produced by the diffraction of a spherical wave by a wedge whose angle can be expressed as a rational multiple of n. The expressions obtained will be in the form of source terms and real integrals representing the diffracted field. The general result obtained is used to derive a new representation for the solution of the problem of diffraction by a mixed hard-soft half plane

On the roots of a Bessel function equation (problem)

For the abstract of this paper, please see the PDF file

A note on uniform asymptotic wave diffraction by a wedge

New expressions for asymptotically uniform Green’s functions for high-frequency wave diffraction when a plane, cylindrical or point wave field is incident on an ideal wedge are derived. They are useful for deriving a uniform asymptotic expression for the exact solution in terms of the high-frequency diffracted and geometrical optics far field. The present method is simple and consists of differentiating out the singularities of the integral representations and using new representations for trigonometrical sums that arise when the wedge angle is a rational multiple of π. The new results make explicit the continuity of the fields across shadow and reflection boundaries

A bifurcated circular waveguide problem

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version A D Rawlins. A bifurcated circular waveguide problem. J.I.M.A. 54 (1995) 59-81. Oxford University press is available online at: http://imamat.oxfordjournals.org/cgi/reprint/54/1/59.pdfA rigorous and exact solution is obtained for the problem of the radiation of sound from a semi-infinite rigid duct inserted axially into a larger acoustically lined tube of infinite length. The solution to this problem is obtained by the Wiener-Hopf technique. The transmission and reflection coefficients, when the fundamental mode propagates in the semi-infinite tube, are obtained. The present results could be of use for exhaust design, and as a possible instrument for impedance measurement

A note on the factorization of matrices occurring in Wiener-Hopf problems

Simple expressions for the Wiener-Hopf factors of a certain matrix considered by Daniele are given

Plane wave diffraction by a rational wedge

In this paper new expressions for the acoustic field produced when a plane wave source of sound is diffracted by a soft, hard or mixed soft/hard wedge whose angle can be expressed as a rational multiple of are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals which represent the diffracted field. The expressions are in a form which allows easy calculation of the acoustic field. Uniformly valid ex-pressions for the far field are also given for all values of the angular variable. The general result obtained includes as special cases, Sommerfeld' s solution for diffraction by a half plane, Reiche’s result for the diffraction by a right angled wedge, and a new representation for the solution of the problem of diffraction by a mixed soft/hard half plane

A trifurcated waveguide problem

We consider the diffraction of the dominant wave mode which propagates out of the mouth of a semi-infinite waveguide made of a soft and hard half plane. This semi-infinite waveguide is symmetrically located inside an infinite waveguide whose infinite plates are soft and hard. The whole system constitutes a trifurcated waveguide. A closed form solution of the resulting matrix Wiener-Hopf equation is obtained