Active Control of High Order Acoustical Modes in a Semi-Infinite Waveguide

This paper presents an analysis of the effectiveness of active noise control methods for control of high order modes in rigid-walled, semi-infinite waveguides. The waveguides examined in this investigation are terminated at one end with a rigid end. The case studies performed reconfirmed that n control actuators can control n propagating modes (including the plane wave) in a waveguide if the actuators are properly placed. The results also confirmed that the control actuators should be located at the node surfaces of the most significant evanescent modes to avoid various problems that evanescent modes cause active control systems. A significant new finding is the effect of the rigid waveguide termination on the active controller. The reflected energy from the termination causes standing waves in the region between the rigid termination and the secondary sources. At certain frequencies which correspond to resonant conditions, the standing wave amplitudes become large and the control actuator strength must be high. At these frequencies the effects of the evanescent modes become significant even when the mode is not close to its cut-on frequency. Similar resonant effects can be expected to affect active noise control performance for any case where there are significant reflections in the waveguide upstream of the control actuators.