Some thoughts on multipolar sources in a moving medium and the structure of the wave equation

Abstract
The procedure of derivation of the wave equation is reviewed, it been pointed out that, while for a medium at rest there is a clear correspondence between point multipole sources originating from the expansion of a general source term and with multipoles resulting from singularities in the continuity and momentum equations, this is not so for a moving medium. Thus, a classification of source multipole order based on the expansion of a general source may lack physical significance. Starting from "natural" monopole and dipole operators, identified in the source function, different families of multipole operators are defined, based on the expansion of the appropriate terms. It is shown that the wave operator has a structure similar to that of the source function, being composed of particular multipole operators. Applications of these features in analyzing different formulations for the aerodynamical noise problem and in optimizing the choice of equivalent source terms are highlighted.