Cédric Foy

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.

Introducing atmospheric attenuation within a diffusion model for room-acoustic predictions

This paper presents an extension of a diffusion model for room acoustics to handle the atmospheric attenuation. This phenomenon is critical at high frequencies and in large rooms to obtain correct acoustic predictions. An additional term is introduced in the diffusion equation as well as in the diffusion constant, in order to take the atmospheric attenuation into account. The modified diffusion model is then compared with the statistical theory and a cone-tracing software. Three typical room-acoustic configurations are investigated: a proportionate room, a long room and a flat room. The modified diffusion model agrees well with the statistical theory (when applicable, as in proportionate rooms) and with the cone-tracing software, both in terms of sound pressure levels and reverberation times.

An Empirical Diffusion Model for Acoustic Prediction in Rooms with Mixed Diffuse and Specular Reflections

In this paper, a modification to the room-acoustic diffusion model is proposed to take different amounts of wall scattering into account. An extensive set of numerical simulations using a cone-tracing software has first been carried out, in order to highlight the impact of the scattering coefficient on the diffusion process in rooms, in terms of sound pressure levels. An iterative method is then proposed to identify, for a given value of the walls scattering coefficient, the diffusion constant that allows the stationary sound field to be governed by a diffusion process, regardless of the rooms geometry. Using this method, an empirical law can be proposed between the diffusion constant and the scattering coefficient. The empirical diffusion model is then compared to scale model experiments, as well as to other models from the literature, with a satisfactory agreement for the sound pressure level. However, the empirical diffusion model fails to predict the sound decay for rooms with perfectly specularly reflecting surfaces, due to the inherent concept of a diffusion process.

Some contributions of Murray Hodgson to room acoustics modeling

This presentation focuses on some of the many contributions of Murray Hodgson (1952–2017) concerning room-acoustic modeling. The concepts of sound field diffuseness and diffuse reflections have always been of major interest for Murray, his studies associating most of the time numerical modeling and measurements on scale models or real-scale rooms. His most cited paper [JASA 89, 1990] proposes to include diffuse surface reflections in ray-tracing simulations, and is a milestone in room acoustics prediction as most standard room-acoustic prediction softwares now include surface diffusivity. Another extensively cited paper [App. Ac. 49, 1996] discusses the applicability of diffuse field theory according to room shape and to absorption distribution and magnitude. The conclusions of this study are still greatly useful to researchers, students, and practitioners. Another important focus of Murray’s research has been the acoustics of « fitted » rooms (i.e., rooms containing many obstacles such as industrial work...

Modeling the inhomogeneous reverberant sound field within the acoustic diffusion model: A statistical approach

In room acoustics, starting from the sound particle concept, it is now well established that the reverberant field can be modeled from a diffusion equation function of the acoustic density and a gradient equation function of the acoustic intensity. The main works on the development of an acoustic diffusion model have highlighted the major role of a coefficient of the model, the so-called diffusion coefficient. Indeed, the main phenomena influencing the reverberant sound field can be modeled by proposing an appropriate expression of this diffusion coefficient. The work presented here deals with the modeling of inhomogeneous reverberant sound fields induced by geometric disproportions, and investigates, in particular, the case of long rooms. Previously, the ability of the acoustic diffusion to model adequately the spatial variations of the sound field along the room has been demonstrated by considering a diffusion coefficient that is spatially dependent. We propose here to extend this work by determining an empirical law of the diffusion coefficient, depending on both the scattering and absorption coefficients of the walls of the room. The approach proposed here is statistical and is based on the least squares method. Several linear models are proposed, for which a rigorous statistical analysis makes it possible to assess their relevance.

Including scattering within the room acoustics diffusion model: An analytical approach

Over the last 20 years, a statistical acoustic model has been developed to predict the reverberant sound field in buildings. This model is based on the assumption that the propagation of the reverberant sound field follows a transport process and, as an approximation, a diffusion process that can be easily solved numerically. This model, initially designed and validated for rooms with purely diffuse reflections, is extended in the present study to mixed reflections, with a proportion of specular and diffuse reflections defined by a scattering coefficient. The proposed mathematical developments lead to an analytical expression of the diffusion constant that is a function of the scattering coefficient, but also on the absorption coefficient of the walls. The results obtained with this extended diffusion model are then compared with the classical diffusion model, as well as with a sound particles tracing approach considering mixed wall reflections. The comparison shows a good agreement for long rooms with uniform low absorption (α = 0.01) and uniform scattering. For a larger absorption (α = 0.1), the agreement is moderate, due to the fact that the proposed expression of the diffusion coefficient does not vary spatially. In addition, the proposed model is for now limited to uniform diffusion and should be extended in the future to more general cases.

On the use of diffusion equations to model the acoustics of coupled rooms

The acoustics of coupled rooms are characterized by energy exchanges through apertures and/or partition walls. The use of systems of diffusion equations allows to predict the temporal and spatial energy distributions in these configurations quite accurately. In this presentation, the diffusion formalism for room acoustics‐prediction is summarized. The systems of equations to be solved in the case of coupling through an aperture and through a partition wall are presented. For two rooms coupled through an aperture (two classrooms connected through an open door), the results obtained with the diffusion model are compared to experimental data, in terms of sound pressure levels and sound decays. On the other hand, for the case of two classrooms connected through a partition wall, the diffusion model is compared to experimental data in terms of sound pressure level difference only. Finally, an engineering application is presented in the configuration involving a workroom including multiple sound sources (e.g., ...