Sound cancellation by the use of secondary multipoles

In this paper, global free-field cancellation in the region exterior to a single compact primary source is discussed. The nature of the secondary source or sources required to achieve such cancellation, either globally or in particular regions, is a subject of current interest. In particular, results are presented that relate to global cancellation of a primary monopole’s sound field by the use of a single, multipole secondary source. The secondary multipole component source strengths required to achieve global cancellation can be found in a number of ways. For example, they may be obtained directly from a multipole expansion of the primary monopole sound field, as originally suggested by Kempton. However, improved attenuation can be achieved by choosing the secondary multipole component source strengths to minimize the total sound power radiated by the combination of primary and secondary sources. Closed form solutions for secondary multipole component strengths have been derived for both the latter case and for Kempton’s approach and are presented here along with formulae for the corresponding reductions of sound power and sound pressure. It will also be shown that it is more efficient in some instances to use a secondary multipole than an array of secondary monopoles for global cancellation. However, the primary conclusion of the present work is that useful levels of global far-field cancellation may be obtained by using secondary sources of higher than monopole order placed at a relatively large fraction of a wavelength from the primary source.