The active minimization of harmonic enclosed sound fields, part I: Theory

Abstract

An analysis is presented of the effectiveness with which active methods can be used for producing global reductions in the amplitude of the pressure fluctuations in a harmonically excited enclosed sound field. The total time averaged acoustic potential energy is expressed as a quadratic function of the complex strengths of a number of secondary sources of sound introduced into the enclosure. For a given number and location of secondary sources, there is a unique set of source strengths which determines the minimum value of this function. The analysis is applied to the case of a lightly damped enclosure excited by a point primary source at a frequency above the Schroeder cut-off frequency. It is demonstrated that substantial reductions in the total time averaged acoustic potential energy are possible only if the secondary sources of sound are located at a distance from the primary source which is less than half a wavelength at the frequency of interest.