Reproduction of plane wave sound fields

The problem of reproducing a desired sound field in space, not just at a number of discrete points, but over a continuous two-dimensional area, is investigated. In theory, any sound field can be reconstructed perfectly in a given region by using a continuous monopole/dipole layer, but this is obviously not possible in practice. This paper attempts to give some quantitative measures of the extent to which a given sound field can be reproduced by using a number of discrete monopole sources. Some of the physical limitations that apply to any sound reproduction system are illustrated by studying a simple model. The desired sound field is a plane wave, the sources are ideal monopoles in a free field, and the optimal source accelerations are calculated using the traditional least-squares method. All calculations are undertaken in the frequency domain, and three different loudspeaker arrangements are studied. The results clearly demonstrate that the quality of the reproduced sound field is mainly determined by the size of the receiver area and the angles between the sources as seen from the center of the receiver array.