Acoustic energy density distribution and sound intensity vector field inside coupled spaces

Abstract

In this paper, the modal expansion method supported by a computer implementation has been used to predict steady-state distributions of the potential and kinetic energy densities, and the active and reactive sound intensities inside two coupled enclosures. The numerical study was dedicated to low-frequency room responses. Calculation results have shown that the distribution of energetic quantities in coupled spaces is strongly influenced by the modal localization. Appropriate descriptors of the localization effect were introduced to identify localized modes. As was evidenced by numerical data, the characteristic objects in the active intensity field are vortices positioned irregularly inside the room. It was found that vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. Finally, an impact of the wall impedance on the quantitative relationship between the active and reactive intensities was analyzed and it was concluded that for very small sound damping the behavior of the sound intensity inside the room space is essentially only oscillatory.

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

“…(16) and then using Eq. (21) for the complex sound intensity [29]. The active intensity I describes the acoustic energy transfer in the sound field and, as seen from Eqs.…”

“…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].…”

An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

“…Other versions of this method may be found in (Xu, Sommerfeldt, 2010). The Fourier method is difficult to apply for rooms with complex shapes and complex boundary conditions, and in more practical cases it is unusable (Meissner, 2012;2013a;2013b).…”

Prediction of Reverberant Properties of Enclosures via a Method Employing a Modal Representation of the Room Impulse Response

“…The most common among these methods are the normal mode analysis (Morse, Bolt, 1944), which is the oldest and simplest type of modal analysis, the classical modal analysis (Dowell, 1978) developed by using the Green's theorem, the asymptotic modal analysis (Kubota, Dowell, 1992), and the hybrid modal analysis (Xu, Sommerfeldt, 2010) that combines the free field Green's function and a modal expansion. Methods employing the modal expansion approach are more difficult to apply for rooms with complex shapes (Li, Cheng, 2004; Sum, Pan, 2006) but it fully describes the wave nature of a sound field such as degeneration of modes (Meissner, 2009a) and modal localization (Félix et al, 2007;Meissner, 2009b), as well as creation of energy vortices in the sound intensity field (Meissner, 2012;2015a). Their disadvantages are a significant increase in computation times at higher frequencies, usually slow convergence speed, and occurrence of modal coupling in the case of the classical modal analysis.…”