## Scalar Wave Diffraction by Tangent Rays

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R H Tew, S J Chapman, J R King, J R Ockendon,
B J Smith & I Zafarullah

Modern asymptotic methods are used to provide as complete as possible a
description of the scattering of a high-frequency time-harmonic acoustic
plane wave by a two-dimensional convex obstacle. The cases of infinite and
finite scatterers are considered separately, and descriptions of the
diffracted fields and the transition solutions valid across shadow boundaries
are presented.

For a finite scatterer, expressions are given for the directivity function
(or angular variation) of the scattered field in the very far field
encompassing all angular directions;
in particular this results in the prediction of a
narrow range of angles for which the directivity is an order of
magnitude lower than in general.