Approximate time domain solution for studying infinite wedge diffraction, its parameters, and characteristics

Abstract

An approximate time domain solution is derived for spherically spreading signals incident on an infinitely long rigid wedge. The solution is a short time approximation of the corresponding exact solution. The presented solution improves the accuracy of an approximate solution derived previously by the authors. The solution is extended to cylindrically spreading and plane wave incident signals. The solutions for all three types of incidence are recast in a unified form. The main advantage of this approximate solution is that it provides insight into the mechanism of diffraction. Specifically, it is shown that the time evolution of diffraction depends on a single time parameter–the diffraction delay time. Furthermore, a generator curve is presented that generates all diffraction impulse responses for all source and receiver locations, all wedge angles, and for all types of incident radiation. Finally, it is shown that any signal (irrespective of its time waveform or its type of spreading) incident on any wedge can be analyzed as an equivalent plane wave incident on a half plane. Thus, the diffraction field of a plane wave incident on a half plane (the simplest diffraction case) encompasses all wedge problems and can be considered a prototype diffraction problem.