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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