Ensemble statistics of active and reactive sound intensity in reverberation rooms

Abstract

This paper examines fundamental statistical properties of the active and reactive sound intensity in reverberant enclosures driven with pure tones. The existing theory for sound intensity in a diffuse sound field, which is based on Waterhouse's random wave model and therefore limited to the region of high modal overlap, is extended to the region of low modal overlap by taking account of the random fluctuations of the sound power emitted by the source that generates the sound field. The validity of the extended model is confirmed by experimental and numerical results.

Two definitions of the inner product of modes and their use in calculating non-diffuse reverberant sound fields

“…It is apparent that the sound field is strongly reactive, as indicated by the presence of a standing wave in the z-direction. These results agree with theoretical predictions [24][25][26][27]. In the damped room, the magnitudes of the active and reactive intensities are lower than in the undamped case.…”

Sound Energy Field in a System of Coupled Rooms

“…Thus, according to Eqs. (6), (8) and (9), the active intensity I is zero, both at vortex centers and stagnation points, whereas the reactive intensity Q is zero at vortex centers. The rst property is clearly visible in Fig.…”

“…where w p = P 2 /4ρc 2 is the potential energy density. Equation (9) conrms that the reactive intensity vector Q is always irrotational. On the contrary, the active intensity I represents a rotational vector eld because the curl of right-hand side of Eq.…”

“…The connection between the mean energy velocity, the reverberation time and the angular momentum density has been studied by Stanzial and Schirer [8]. Statistical properties of the sound intensity in reverberant rooms subjected to pure-tone excitation have been examined by Jacobsen and Molares [9]. In recent papers of the present author [1012], space distributions of energy density and sound intensity in a steady-state acoustic eld inside coupled rooms and irregular enclosures were analyzed using the modal expansion method supported by computer implementations.…”

Numerical investigation of acoustic field in enclosures: Evaluation of active and reactive components of sound intensity

“…The connection between the mean energy velocity, reverberation time, and angular momentum density has been investigated by Stanzial and Schiffrer [26]. Statistical properties of the active and reactive intensities in reverberant enclosures subjected to pure-tone excitation have been studied by Jacobsen and Molares [27]. Behavior of scalar and vector characteristics of steady-state sound field inside coupled rooms and irregular enclosures has been analyzed by the author in papers [28][29][30][31].…”