Sound diffraction by knife-edges of finite length: Integral solution, dimensionless parameters, and explicit formulas

Abstract

Sound diffraction by knife-edges of finite length is considered in the frequency domain. An approximate analytical solution in integral form is derived from a previously published time domain solution. Unlike the well-established finite length diffraction solution by Svensson et al. [Acta Acust. Acust. 95(3) 568-572 (2009)], the presented solution contains no singularities and both solutions agree, except very close to the diffracting edge. It is shown that finite length diffraction can be studied based on two dimensionless parameters: one expressing the receiver's proximity to the shadow boundary and one associated with the edge length. Depending on the dimensionless parameters, a given edge can be considered a short edge, an infinitely long edge or an edge of medium length, each case with different characteristics. Furthermore, a nomograph and the corresponding database are presented. They provide the normalized diffracted field for any source/receiver location, any source frequency, and any edge length. Also, easy to compute explicit mathematical expressions are presented to approximate the analytical integral solution. These expressions, along with the database method, accelerate diffraction calculations by order of magnitude compared to the presented integral solution or the Svensson solution. Finally, predictions from all proposed methods agree reasonably well with experimental data.