Analytical model for predicting edge diffraction in the time domain

A time domain model for predicting diffraction around half planes is presented. The model renders the directive line source model [Menounou, Busch-Vishniac, and Blackstock, J. Acoust. Soc. Am. 107, 2973-2986 (2000)] valid for times long after the diffracted signal arrival and for receivers close to the shadow boundaries, where it was not valid before. The presented model unifies diffraction by plane, cylindrically and spherically spreading incident signals (being exact for plane and approximate for cylindrical/spherical) and models diffraction as radiation from a directional line source. The terms describing the directivity and the line-source radiation are appropriately modified to handle diffraction by wedges and finite-length edges, respectively. The investigation of the derived formulation leads to (i) definition of universal parameters and quantities for the study of time diffraction, (ii) derivation of a generator curve that embodies the diffracted signals at any source-receiver configuration, and (iii) derivation of similarity conditions that determine how fast/slow diffraction evolves depending on the receiver location and that provide considerable computational benefit compared to direct computations. Furthermore, three time stages in every diffracted signal are identified, which allows a priori estimation of the diffracted signal characteristics based on the incident signal duration. Finally, the model is successfully applied to sonic boom diffraction on buildings.