Statistical aspects of active control in harmonic enclosed sound fields

Joseph, P., Elliott, S. J. and Nelson, P. A. (1994) Statistical aspects of active control in harmonic enclosed sound fields. Journal of Sound and Vibration, 172 (5), 629-655. (doi:10.1006/jsvi.1994.1203).

Abstract

This paper deals with the active control of harmonic enclosed sound fields, special emphasis being given to the low and high frequency limits. A general statistical approach is adopted which seeks to quantify the performance of some well known active control strategies by specifying the mean acoustic potential energy reduction and, where possible, the variance about the mean. This paper is divided into two parts. The first deals with the active control of harmonic enclosed sound fields at low frequencies where the frequency response function is composed of distinct, well isolated modal resonances. In this frequency regime the sound field in the room is amenable to global control: for example, minimizing the total acoustic potential energy in the enclosure. At the resonance frequency of the dominant mode, substantia} reductions in sound pressure level are readily achieved throughout the enclosure. At much higher frequencies, however, the response of the room is not dominated by a single mode, but rather the contributions from a much larger number of modes of roughly equal amplitude, In this frequency range, the complete suppression of the dominant mode, or of a small number of dominant modes, does not afford significant reductions in the average sound pressure level of the sound field. In this instance such a global approach to active control is obviously ineffective and one must resort to local control schemes. This paper is concerned with the effect of cancelling the pressure at a single point remote from the sources, the result of which is to produce a small localized zone of quiet centred on the point of cancellation. Experimental measurements of this quiet zone are presented together with an analysis of the secondary source strength statistics. Also presented in this paper is an expression for the distribution of the acoustic potential energy after control as the source and cancellation positions are varied randomly around the room.

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Contributors

Author: P. A. Nelson

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