On the significance of reflection coefficients produced by active surfaces bounding one-dimensional sound fields

Active boundary surfaces intended to control reverberation or other characteristics of enclosed sound fields have often been investigated using plane wave tubes. This paper presents an analysis of actively terminated semi-infinite and finite-length plane wave tubes to provide needed clarification of the effects of these surfaces. By considering relationships between complex pressure-amplitude reflection coefficients and acoustic energy quantities, the investigation reveals that increases in reflection coefficient moduli at terminations do not always produce corresponding increases in total energy or energy flux in adjacent fields. These relationships are shown to depend upon physical properties of the acoustic spaces, sources, and source positions. The investigation also demonstrates how the impact of reflection coefficients with moduli exceeding unity may be easily misinterpreted.