An Acoustic Space-Time and the Lorentz Transformation in Aeroacoustics

Abstract

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation of the space-time transformation, and are able to give neat and lucid derivations of the free-field Green's function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.