Active control of sound scattering from a uniform impedance sphere: Power minimization versus backscattering cancellation

Abstract

The current paper considers the case of a locally-reacting, uniform spherical scatterer in a homogeneous fluid, subjected to a monochromatic acoustic plane-wave incidence. The scattering behaviour is controlled with a single point-monopole acoustic secondary source on the surface of the sphere. Firstly, scattered sound power is reduced by ‘least mean squares’ minimization of the spherical harmonic component contributions in the sum between primary and secondary fields. Secondly, the far-field backscattered pressure is perfectly cancelled instead. Analytical approximations and simulations show that at low relative frequencies, for a given surface impedance, the far-field scattered pressure takes the shape of a figure-of-eight after power minimization and is attenuated in the half-space associated with the controlled direction after backscattering cancellation. The scattered sound power after control is a function of frequency which varies as the same power law, regardless of control method used or the position of the source on the incidence axis. However, the second con-trol method yields less attenuation of the scattered power than the first and in some cases can even enhance the scattered power. At large relative frequencies, the directivity of the point-monopole discriminates in favour of the half-space corresponding to its position on the sphere. Thus, placing the source opposite the backscattering direction to perform the second method significantly enhances the scattered power, as well as the far-field scattered pressure in the half-space opposite the backscattering direction.

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Identifiers

ORCID for Mihai Orita: orcid.org/0000-0001-7307-0497

ORCID for Jordan Cheer: orcid.org/0000-0002-0552-5506

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