Experimental validation of a diffusion equation-based modeling of the sound field in coupled rooms Alexis Billona, Vincent Valeaua, Judicaël Picautb, Anas Sakouta a LEPTAB, University of La Rochelle, France b LCPC, Nantes, France 149th Meeting of the Acoustical Society of America Vancouver, 20th May 2005

This concept allows non-uniform energy density Model Presentation (1) The diffuse field assumption in closed spaces assumes that sound energy is uniform in the field. This is wrong especially for complex closed spaces or long rooms Recent works [Picaut et al, Acustica 83,1997] proposed an extension of the concept of diffuse sound field: Diffusion equation for acoustic energy density w with Diffusion coefficient ( room mean free path, c sound speed) This concept allows non-uniform energy density

Model Presentation (2) Scope of this work: Sound absorption at walls is taken into account by a mixed boundary condition [Picaut et al., Appl. Acoust. 99]: wall (a) It has been applied successfully analytically for 1-D long rooms or streets [Picaut et al., JASA 1999] Scope of this work: application to a simple configuration of two coupled rooms, for evaluating: stationary responses; impulse responses; validation by comparison with experimental results.

Modeling coupled room acoustics with a diffusion equation source room neighboring room DS hS DR hR Source Room boundary (mixed boundary conditions) Simulations characteristics: - Finite Element Model (FEM) solver (Femlab) - Unstructured mesh with about 3000 nodes; - stationary response Sound intensity Level Computing time: about 10 seconds - impulse response Sound decay Computing time: about 1 minute.

Statistical theory model of coupled rooms Source room (S) Neighbouring room (R) sound source Coupling aperture ER Es mean energy densities Power balance Energy decay [Cremer &Müller, 1978] coupling factor 0<kR<1

Experimental set-up Two coupled classrooms (University of La Rochelle) partitions partitions concrete wall coupling area glass windows Software DSSF3 – Signal: Time-Stretched pulse (TSP)

Rooms reverberation times (RT 20) source room neighbouring room

Sound level distribution coupling area S2

Sound attenuation measurements and simulations stat. diff. meas. stat. meas. diff. S1 S2 diff. meas. stat. S1 stat. diff. meas.

Mean sound level difference stat. diff. meas. S1 meas. diff. stat. S2

Sound decay : simulation and measurements coupling no coupling frequency (hz) RT (s) Source room coupling no coupling Coupled room stat. meas. diff. CATT frequency (hz) Source room frequency (Hz) meas. stat. diff. CATT Neighbouring room

Conclusion - the sound intensity difference between the rooms; The diffusion model shows good agreement with experimental data for evaluating: - the sound intensity difference between the rooms; the reverberation time. Predicts the sound level distribution and spatial variations of sound decay Low calculation times Future work : Comparison with experimental data for networks of coupled rooms (hall connected with a set of coupled rooms). Acknowledgements: The authors would like to thank the ADEME (french agency for environmental studies) for supporting this work.

Modeling coupled room acoustics with a diffusion equation (2) – Example for a stationary source dB FEM calculation Shape definition Meshing Problem definition Sound source Mixed boundary cond. (absorption)