A discussion on nonradiating sources

Abstract

The fact that a given source sound field can be generated by more than one source distribution is quite well known but is frequently given an overexaggerated importance. This paper discusses the structure of sources of silence, the name given by Doak [Proc. I.O.A., 10-2, 693–700 (1988)] to the reactive part of a source distribution, i.e., to the part with no far field and which is responsible for the ambiguity. It is shown that, since all ambiguities can always be traced back to the impossibility of distinction between the sound fields of a point monopole and of an isotropic point quadrupole, a simple criteria can be established for identifying a general source distribution as active or reactive. The particular case of the velocity field due to a point dipole (i.e., to a point force) in an homogeneous medium at rest is worked out in detail, since it contains a source of silence (associated with the vorticity at the source point) which is frequently mishandled. The concepts presented are applied to aeroacoustic wave equations, to discuss optimization of the choice of dependent variable as well as some case of identification of nonradiating sources found in the literature.