A principle of sound field control based on the Kirchhoff-Helmholtz integral equation and the theory of inverse systems

摘要

In order to control sound inside a three-dimensional region perfectly, based on the conventional theory of sound field control which includes sound field reproduction and active noise control, a sufficient number of acoustically transparent loudspeakers must be located continuously over the entire surface of the region. In this paper, the "Boundary Surface Control (BSC) principle", which is a new principle of sound field control based on the Kirchhoff-Helmholtz integral equation and the theory of inverse systems, is proposed. The system based on the BSC principle enables us to control sound perfectly in a three-dimensional region without using such an unrealistic condition of loudspeakers. First, we adopt an interpretation of the Kirchhoff-Helmholtz integral equation which is different from the conventional interpretation, i.e. Huygens principle, and combine it with the theory of inverse systems to describe the BSC principle. Although this principle can be applied to both sound field reproduction and active noise control, this paper is confined to reproduction. Second, based on the BSC principle, two types of sound field reproduction systems are designed. The transfer functions of these systems are determined so that the pressure and its gradient on the surface of the reproduced region in the secondary field are identical to those on the surface of the recorded region in the primary field. Third, the results of the computer simulation indicate the possibility of the realization of this principle and also that the eigenvalue problem and the uniqueness between the pressure and its gradient, which are the essential properties of the Kirchhoff-Helmholtz integral equation, are related to the BSC principle. [References: 22]