Pressure-amplitude reflection coefficients of active impedance tube terminations and their relationships to energy-related quantities of adjacent sound fields

Abstract

Active boundary surfaces intended to control reverberation or other characteristics of enclosed sound fields have often been investigated using impedance tubes. Unfortunately, the significance of pressure-amplitude reflection coefficients produced by these surfaces and their relationships to acoustic energy quantities in enclosed spaces has remained obscure. This paper accordingly presents a straightforward analysis of an actively terminated impedance tube to provide needed clarification. It demonstrates that increases in reflection coefficient moduli at the termination do not necessarily produce proportional increases in total enclosed energy in the tube or energy flux toward the enclosed field. Very large reflection coefficients (i.e., with moduli much greater than unity) produce both total enclosed acoustic energies and vector magnitudes of net active intensity approaching those present under an anechoic boundary condition. Large relative changes in total enclosed energy occur only when active termination reflection coefficient moduli roughly approach unity. Energy-related effects of actively produced reflection coefficients are generally frequency-dependent functions of distinct enclosed spaces and acoustic fields generated by primary sources in these spaces. Hence, correlations between reflection coefficient moduli and energy quantities of adjacent sound fields are not necessarily simple or consistent. They depend upon important physical properties of acoustic spaces, sources, and source arrangements.