ACTIVE CONTROL OF SOUND IN ACOUSTIC WAVE-GUIDES .1. THEORY

This is the first of two papers in which the performance of active noise control systems in rigid-walled, finite-length, rectangular waveguides is discussed. The theory is developed such that optimal secondary source strengths are found to minimize three performance criteria: pressure at a selected set of points within the waveguide; potential energy in a selected volume of the waveguide; and power in the downstream region of the waveguide. The minimum pressure solution is a double summation over all the modes in the duct. This solution is difficult to interpret unless a finite number of modes are considered, and the pressure is measured to take advantage of the orthogonal properties of the high order modes in the waveguide. When evanescent energy is neglected and the pressure is measured at proper locations, the solution of the pressure minimization problem is similar to the solution of the global problem (i.e., minimization of either potential energy or power). The pressure minimum solution converges to the optimal global solution when the waveguide is infinite or when modal control strategies are implemented. © 1994 Academic Press Limited.