Alexis Billon

On the use of a diffusion model for acoustically coupled rooms

A numerical model is proposed to predict the reverberant sound field in a system of two coupled volumes that are connected through an open aperture. The model is based on the numerical implementation of a diffusion model that has already been applied to predict the sound-energy distribution and the sound decay in single rooms. In comparison with the statistical theory, the proposed approach permits the prediction of the sound field by taking into account the sound source location and the receiver locations as well as the transition from one room to the other at the coupling aperture. Moreover, the diffusion model results match satisfactorily the experimental data in terms of sound-pressure level and reverberation times, both in the room containing the source and in the receiving room. Simulations with a ray-based model are also carried out, leading to results similar to those of the diffusion model, but at a cost of larger computation times.

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.

Acoustic Predictions in Industrial Spaces Using a Diffusion Model

Industrial spaces are known to be very noisy working environment. This noise exposure can be uncomfortable, tiring, or even harmful, at worst. Industrial spaces have several characteristics: they are often huge flat volumes fitted with many obstacles and sound sources. Moreover, they are usually surrounded by rooms where low noise levels are required. The existing prediction tools can seldom model all these phenomena accurately. In this paper, a prediction model based on a diffusion equation is presented. The successive developments carried out to deal with the various propagating phenomena met in industrial spaces are shown. For each phenomenon, numerical or experimental examples are given to highlight the validity of this model. It is also shown that its computation load is very little in comparison to ray-tracing-based methods. In addition, this model can be used as a reliable and flexible tool to study the physics of the coupling between rooms. Finally, an application to a virtual factory is presented.

Numerical evidence of mixing in rooms using the free path temporal distribution

The ergodic propriety of a room has strong effects on its reverberation. If the room is ergodic, the reverberation can be broken up in two steps: a deterministic process followed by a stochastic one. The late reverberation can be then modeled by a reverberation algorithm instead of more computationally consuming methods. In this study, the free path temporal distribution obtained by ray-tracing is used as an indicator of the rooms mixing: the energetic average of the path lengths is computed at each time step. Ergodic rooms are thus characterized by rapidly convergent distributions. The free path value becomes independent of time. On the other hand, path selection mechanism and orbits are observed in non-ergodic rooms. The transition time from the deterministic process to the stochastic one is also studied through the evaluation of the rooms time constant. It is shown that its value depends only on the mean free path and the boundaries scattering value. An empirical expression is obtained which agrees well with simulations carried out in a concert hall. This transition time from a deterministic model to a stochastic one can be used to speed up the acoustical predictions and auralizations in ergodic rooms.

Experimental validation of a diffusion equation-based modeling of the sound field in coupled rooms

Sound modeling in coupled rooms (i.e., two acoustically coupled rooms separated by an open area) has attracted considerable attention in the past. However accurate and operational models are still needed, principally when three or more rooms are coupled. In recent papers, a diffusion equation‐based model has been applied to unusual room shapes. For the coupled rooms geometry, this diffusion model has been validated successfully by comparison with the classical statistical theory in a parametrical study of the coupling parameters [Billon et al., J. Acoust. Soc. Am. 116, 2553 (2004)]. In the present work, the diffusion model results are validated by means of a comparison with experimental results, both in terms of sound attenuation and reverberation time. A comparison is also provided with results given by the statistical theory and a ray tracing program. For this purpose, experiments have been conducted in two coupled classrooms with two different sound source locations. The results show a very good agreem...

Influence d'images évocatrices et distractrices sur une tâche de jugement en acoustique des salles

In the context of the design of a multimodal environment for room acoustics evaluation, we investigate the link between a projected image and the sound of an acoustic simulation. 54 subjects have been tasked to judge the level of reverberation of a sound in a control situation (without image) and in an experimental situation. In this experimental condition, half the subjects were presented a coherent image aiming at supporting the evaluation task and the other half, a disturbing image. Our results show a positive influence from the evocative images, and no influence from the distractive images.

Predictions of sound pressure levels in streets using a diffusion model: numerical validations and experimental comparisons

Predictions of sound propagation in urban areas have attracted a considerable over the years. If the sound energy is assimilated to particles with a constant energy, their movement can be described by a transport equation. In canyon streets, this transport equation can be reduced to a diffusion equation whose expression is more simple. In this presentation, sound absorption at the boundaries (buildings facades and ground), as well as atmospheric sound attenuation are introduced. The problem is then solved numerically using a finite elements method for the configuration of a canyon street. A systematic validation of the obtained model is carried out in terms of sound pressure level by comparison to numerical simulations taken from the literature. Comparisons with experimental data are then conducted. Finally, applications in more complex configurations are presented.

Reverberated sound field modeling in coupled rooms using a diffusion equation

Sound modeling in coupled rooms has attracted considerable attention in the past, but accurate and operational models are still needed. In recent papers, a diffusion equation based model has been applied with success to unusual room shapes. This approach allows nonuniform repartition of energy, and is especially relevant in room acoustics for long rooms or complex spaces such as networks of rooms. The present work aims at validating the behavior of the diffusion model in the case of two acoustically coupled rooms separated by an open area. In this purpose, the time‐dependent diffusion equation is solved in three dimensions using a finite‐element solver. It allows one to predict both sound attenuation and reverberation time at any point of the coupled rooms. Parameters influencing the coupling, i.e., room relative sizes, aperture size and room absorption areas, are investigated. Results are then compared with the classical statistical theory of coupled rooms. Finally, a comparison with experimental data in two coupled classrooms is also provided.