On non-radiating sources

Abstract

Following the analysis by P.E. Doak on the radiating (active) and non-radiating (reactive) parts of a source distribution and their effect on the identification of sources, this paper discusses the possible structure of non-radiating sources, i.e., of sources which produce a null field outside the source region. It is shown that these sources can be of three types, two of them only with arbitrary time dependence. In this case, the non-radiating sources are forcibly formed by the difference of two source distributions which generate, outside the region limited by the sources in question, the same field. In the type discussed by Doak, one source distribution encircles the other and cancelation is attained as a global effect. In the other, emphasized by Ffowcs Williams, the two source distributions are superimposed and cancelation is produced locally. The latter type of non-radiating source is discussed in detail, it being shown that, while they do not represent physical sources, they provide valuable information on non-radiating effects. The third type refers to single frequency sources and involves a particular match of wavelength, geometry and source strength distribution so that the acoustic energy gets trapped inside the source region. Of these three types of non-radiating sources, only the first one—that focused by Doak—can influence the identification of the active part of a source distribution from measurements made outside the source region. Evanescent waves, associated with a purely reactive field, are also discussed. It is pointed out that evanescent waves obtained in the decomposition of the field of a vibrating body of finite extent, although useful for representing certain aspects of the field, do not exist physically. Aspects affecting the identification of sources are also briefly tackled.