asa vancouver 1 experimental validation of a diffusion equation-based modeling of the sound field in...
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![Page 1: ASA Vancouver 1 Experimental validation of a diffusion equation-based modeling of the sound field in coupled rooms Alexis Billon a, Vincent Valeau a, Judicaël](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bfe91a28abf838cb6d21/html5/thumbnails/1.jpg)
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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 AmericaVancouver, 20th May 2005
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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
t
wwD 2
Diffusionequation for acoustic energydensity w
3
cD
( room mean free path, c sound speed)
Diffusion coefficientwith
Recent works [Picaut et al, Acustica 83,1997] proposed an extension of the concept of diffuse sound field:
This concept allows non-uniform energy density
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Model Presentation (2)
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.
It has been applied successfully analytically for 1-D long rooms or streets [Picaut et al., JASA 1999]
,
4
n
wJ D hw
nc
with h
wall()
nJ
Sound absorption at walls is taken into account by a mixed boundary condition [Picaut et al., Appl. Acoust. 99]:
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Modeling coupled room acoustics with a diffusion equation
Room boundary V hw
n
wD
(mixed boundary conditions)
Source
source room
)t,r(Q
),( trQt
wwD 2
neighboring room
DR
hR
DS
hS
Simulations characteristics:- Finite Element Model (FEM) solver (Femlab)- Unstructured mesh with about 3000 nodes;
- stationary response Sound intensity LevelComputing time: about 10 seconds
- impulse response Sound decayComputing time: about 1 minute.
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Statistical theory model of coupled rooms
Source room (S) Neighbouring room (R)
sound source Coupling aperture cS
EsER
mean energy densities
Power balance
cRR
S c R
SEk
E S A
10log( )S R RL L k
coupling factor 0<kR<1
Energy decay
11 22exp( 2 ) exp( 2 )1 /
SS I II
II s
kE t E t E t
11 22exp( 2 ) exp( 2 )1 /
RR I II
I r
kE t E t E t
S
[Cremer &Müller, 1978]
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Experimental set-up
Two coupled classrooms (University of La Rochelle)
Software DSSF3 – Signal: Time-Stretched pulse (TSP)
glass windowscoupling area
concrete wall
partitions
partitions
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Rooms reverberation times (RT 20)
sourceroom
neighbouring room
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Sound level distribution
S1
S2
),( trQwD 2
coupling area
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Sound attenuation measurements and simulations
S2
S1
S2
S1
stat.meas.
diff.
S1
stat.
diff.meas.
S1
stat.
diff.
meas.
S2
diff.
meas.stat.
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Mean sound level difference
stat.
diff.
meas.
S1
meas.
diff.
stat.
S2
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Sound decay : simulation and measurements
coupling
no coupling
frequency (hz)
RT (s)
Source roomstat.
meas.
diff.CATT
frequency (hz)
Source room
coupling
no coupling
Coupled room
frequency (Hz)
meas. stat.diff.
CATT
Neighbouring room
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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:The authors would like to thank the ADEME (french agency for environmental studies) for supporting this work.
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Shape definition
Sound source
Meshing
Modeling coupled room acoustics with a diffusion equation (2) – Example for a stationary source
Problem definition
01 wD
02 wD
SS VWwD / Mixed boundary cond. (absorption)
dBFEM calculation