Multipole sources for cancellation of radiated sound fields

It is of interest to be able to cancel the sound field generated by a noise source everywhere exterior to the source. The nature of the secondary source or sources required to achieve that cancellation is a subject of current interest. It has recently been suggested that the sound radiation from coherent, finite-size radiators may be represented as a superposition of monopole fields [G. H. Koopman etal., J. Acoust. Soc. Am. 86, 2433–2438 (1989)]. It has also been observed that a monopole source may be represented by an infinite-order multipole source placed elsewhere [A. J. Kempton, J. Sound Vib. 48, 475–483 (1976)]. In principle it is thus possible to create a single multipole source that could represent, and thus cancel, the sound field generated by an arbitrary coherent radiator. In this paper, the initial results of a study to determine the feasibility of such an approach are presented. In particular, the realizable far-field attenuation will be considered as a function of frequency, secondary source order, and primary–secondary source separation distance. It will be shown that useful levels of low-frequency far-field attenuation may be obtained using secondary sources truncated at quadrupole order and positioned within several meters of the primary source. It has thus been concluded that the approach suggested here may find application in the active control of low-frequency exterior sound fields.