Analytical models of sound diffraction by barriers: A review

Abstract

During the past few years, considerable success has been achieved in the further development and numerical implementation of analytic solutions for barrier diffraction. The older Fresnel‐Kirchhoff theory of diffraction has proven to be inadequate for many cases of practical application, but is an unnecessary oversimplification because simple formulas (including the Fresnel number approximation) result in the uniform asymptotic expansion limit for the exact solution of diffraction by a rigid wedge. Although the MacDonald solution in its original form is cumbersome to apply to general source‐listener configurations, numerical calculations become simple when contour deformation techniques are employed. Also significant is Medwin's application of FFT algorithms to the transient solution of Biot and Tolstoy, which we now know is equivalent to MacDonald's solution. Williams' and Maliuzhinetz's solution for impedance wedges has led to approximate models for nonrigid barriers. Three‐sided barriers can be handled using Keller's geometrical theory of diffraction (GTD), which also allows the theory for plane wave diffraction to be used when the source is localized and when the barrier rests on the ground. Hayek and others have used creeping wave expansions for curved barriers; Fock's theory allows a smooth transition into the shadow zone.