Acoustic wave propagation from a moving point source

Abstract

A method for obtaining a type of progressing waves is introduced. The method is applied to show that [ ( c t − z cosh ⁡ α ) 2 + r 2 sinh ⁡ 2 α ] − 1 / 2 F [ sinh ⁡ − 1 ( c t − z coshα r sinh ⁡ α ) + i θ ] ( α being a constant) is a progressing wave satisfying the wave equation c 2∇2 φ = ∂2φ/∂ t 2 in cylindrical coordinates r , θ and z , for an arbitrary analytic function F of a complex variable. In terms of this and other similar progressing waves, we consider the problem of wave propagation from a moving point source in two semi-infinite fluid spaces. Both the subsonic and supersonic cases are included. The solutions for a fixed line source and for a stationary point source are obtained as limiting cases.