Experimental validation of a diffusion equationbased modeling of

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 149 th Meeting of the Acoustical Society of America Vancouver, 20 th May 2005 ASA Vancouver

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) ASA Vancouver 2 This concept allows non-uniform energy density

Model Presentation (2) 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: ASA Vancouver 3 – stationary responses; – impulse responses; • validation by comparison with experimental results.

Modeling coupled room acoustics with a diffusion equation source room neighboring room oo R DS m h. S DR y r da un bo Source h. R (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 ASA Vancouver 4 - impulse response Sound decay Computing time: about 1 minute.

Statistical theory model of coupled rooms Source room (S) sound source Es Neighbouring room (R) Coupling aperture ER mean energy densities Power balance ASA Vancouver 5 coupling factor 0<k. R<1 Energy decay [Cremer &Müller, 1978]

Experimental set-up Ø Two coupled classrooms (University of La Rochelle) partitions concrete wall glass windows coupling area ASA Vancouver 6 Software DSSF 3 – Signal: Time-Stretched pulse (TSP)

Rooms reverberation times (RT 20) source room neighbouring room ASA Vancouver 7

Sound level distribution S 1 S 2 ASA Vancouver 8 coupling area

Sound attenuation measurements and simulations S 1 S 2 S 1 diff. meas. stat. ASA Vancouver 9 S 1 S 2 diff. meas. stat.

Mean sound level difference S 1 S 2 stat. meas. diff. ASA Vancouver 10 stat. meas. diff.

Sound decay : simulation and measurements Neighbouring room Coupled room Source room stat. meas. no coupling RT (s) CATT ASA Vancouver 11 coupling stat. coupling meas. diff. frequency(hz) frequency (Hz) frequency no coupling CATT

Conclusion 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: ASA Vancouver 12 The authors would like to thank the ADEME (french agency for environmental studies) for supporting this work.

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Modeling coupled room acoustics with a diffusion equation (2) – Example for a stationary source d. B FEM calculation Shape definition Problem Meshing Sound source ASA Vancouver 14 Mixed boundary cond. (absorption)