Acoustic wave propagation from a moving point source
Abraham Albert Ungar, Zipora Alterman · 1973
A method for obtaining a type of progressing waves is introduced. The method is applied to show that F'sinh- 1/ct- z cosh~' ~ iO " [(ct-zc°sh~)2+r2sinhZ~]-1/2 [ ~ rsin~- ~)+] ( ~ being a constant) is a progressing wave satisfying the wave equation c2VZq ~ = 82q~/Ot 2 in cylindrical coordinates r, 0 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. [NTRODUCTION The reflection and the refraction of cylindrical or spherical waves at a plane boundary have already been investigated by many authors. A reference may be made to Cagniard (1962) for the spherical wave H(ct-R) /R, to Garvin (1956) for the cylindrical wave