Diffraction of sound around corners and over wide barriers

Formulas and procedures are described for the estimation of sound pressure amplitudes at locations partially shielded from the source by a barrier. The analytical development is based on the idealized models of a wave from a point or extended source incident on a rigid wedge or a three-sided semi-infinite barrier. Versions of the uniform asymptotic solution for the wedge problem which are convenient for numerical predictions are derived in terms of auxiliary Fresnel functions by means of complex variable techniques previously employed by Pauli from a generalization of the exact integral solution developed by Sommerfeld, MacDonald, Bromwich, and others and are interpreted within the spirit of Keller's geometrical theory of diffraction. The Kirchhoff approximation in terms of the Fresnel number is obtained in the limit of small angular deflections from shadow zone boundaries. An approximate and relatively simple expression for the double-edge diffraction by a thick three-sided barrier is given based on the single wedge diffraction solution and on concepts inherent to the geometrical theory of diffraction which reduces to finite and realistic limits when either source or listener are near the extended plane of the barrier's top. A simple approximation suggested by Maekawa based on the replacement of actual barriers by an equivalent thin screen with diffraction treated by the Kirchhoff approximation is discussed in terms of the present theory and it is concluded that in some instances this approximation may lead to sizeable errors. An alternate scheme is suggested whereby one approximates the actual barrier by a three-sided barrier wholly contained within the actual barrier.