Analysis of Sound Decay in Rectangular Rooms

Abstract

Sound decay in a rectangular room, each wall of which is uniform, is analyzed in terms of the damping of normal modes of aerial vibration, as influenced by the acoustical impedance of the boundary surfaces. From two to seven decay terms may be required in the complete decay equation under different circumstances, each term representing a group of the excited modes of vibration having common properties. The analysis is given in terms of r.m.s. pressure measured for specified locations of source and receiver and includes explicitly the relative dimensions of the room. The results of the mathematical analysis are presented in form to allow determination of the complex wall impedance from consideration of the initial and final slopes of the sound decay curve, and conversely. Experimental decay curves confirm both the detailed predictions of the theory and the sufficiency of the wall impedance as a unique characterization of the influence of the wall on the behavior of sound in the room.