Multi-scattering in active noise control

Abstract

This paper follows up on an earlier paper of the author [1] dealing with the issue of multi-scattering in a typical active noise control system. This work concerns the effects of the presence of a neighboring wall on the performance of an active noise cancellation system when the dimension of sources is added to the analysis. Effect of the adjacent wall is taken into account using the image method, and multi-scattering is also allowed for by the spherical harmonic addition theorem. The recognized method of separation of variables and appropriate wave field expansions in spherical coordination are used to derive the required analytical solutions. A primary spherical source radiates at different modes, and a secondary source is modeled as a radially vibrating cap which resembles a real sound speaker. Our particular interest in this work is to investigate effects of multi-scattering at intermediate working frequencies of ANC, e.g., about 100–500 Hz. In addition to emphasizing the importance of multi-scattering, this work endeavors to find the appropriate cap angle of the control source to achieve acceptable noise attenuation for different vibrating modes of the primary source (monopole, dipole). Numerical results reveal that the presence of a rigid wall will considerably change the adequate velocity of the secondary source and also show that using a baffled spherical piston instead of a monopole control source will obviously improve the sound minimization efficiency when the primary source vibrates in the n = 1 mode in a low frequency range.