1. 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

2. 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

3. 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.

4. 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.

5. 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

6. 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)

7. Rooms reverberation times (RT 20)
source
room
neighbouring
room

8. Sound level distribution
coupling area S2

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

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

11. 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

12. 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.

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