Calculation of the temporal evolution of sound pressure levels in rooms, with AcouS Propa

1. 19th INTERNATIONAL CONGRESS
ON ACOUSTICS
MADRID, 2-7 SEPTEMBER 2007
Cazard, Guillaume; Senat, Claude; Gamba, René
Gamba Acoustique & Associés, Buro Parc 2
BP 163 31676 LABEGE cedex, France
guillaume.cazard@acoustique-gamba.fr
CALCULATION OF THE TEMPORAL
EVOLUTION OF SOUND PRESSURE
CALCULATION OF THE TEMPORAL
EVOLUTION OF SOUND PRESSURE
LEVELS IN ROOMS
LEVELS IN ROOMS
Extract of RBA-10-008
Open office acoustic design –
multidimensional case studies
Fabien Krajcarz – Gamba Acoustique & Associés
Echogram at 1 kHz
125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz
0.77 0.64 0.67 0.69 0.78 0.81
0.84 0.69 0.7 0.66 0.64 0.6
Measurement (s)
Calculation (s)
Q 4cos
dsx
d
x
Source
 ' n dxx' 
n' 
dS, (x) dS', (x')
x'
( , ' ) cos θ cos θ'
I t x K x x I t d d x
  xx  
Intensity received at any point of the room for each time:
rx rx
I t d
c , x 1  x cos

dS
I t x Id t 2
, 
R R SR d
where IdSR(t) is the acoustic intensity directly received at
the receptor from the source.
The pressure level is obtain by :
  10log 1012 L t I t R
125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz
Measurement (s) 0.83 0.58 0.61 0.75 0.73 0.64
Calculation (s) 0.84 0.57 0.59 0.72 0.69 0.64
N
I t I t d
         
 
i  j 
c K Id t
j
1 
j ij i
ij
1
dij
c
N
        
Ii k  1  
j I j k  mij Kij 
Idi k
j
1
N
I IdSR I ri S
R k k i i k m ri i d
250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz
 
m dij
 
ij int
 c t
Measurement (s) 1.24 1.28 1.59 1.45 1.18
Calculation (s) 1.35 1.24 1.39 1.55 1.41
OUR MODEL
The models for predicting the sound fields based on
specular reflection assumptions use infinitely smooth
surfaces.
In case of rough surfaces and dimensions less than the
wavelength, diffuse reflection has to be taken into account.
Walls of the majority of the rooms are seldom smooth and
flat : presence of furnitures shape of the buildings
materials, floor cluttering,...
Our model is built ont he assumption that the sound waves
are totally scattered when reflected by the walls.
Ultimately, our model allows the calculation of the
echograms in every point of a room.
Thanks to the echograms, some useful criterias for room
acoustic studies can be evaluated : reverberation time,
EDT, D50, C80,...
TEMPORAL EVOLUTION OF THE
ACOUSTIC INTENSITY
Intensity of the noise at any point is made by two
superposed components :
1. Intensity directly received from the source (free field
propagation of spherical waves)
2. a component of reverberated noise received from the
walls. Walls are assimilated to virtual point sources with a
directivity factor based on the scattering assumptions.
Each component of a surface which receives energy
retransmits it towards all the surface components :
where K(x,x') is
and Id,x(t) is the intensity of the source directly received by
dS
 ,   , '  , '1  ' ' ( ) ,
'
' x x dS I t c
S
²
xx' d
K x x


rx
drx
dsr
x,dS,(x)
Receptor, xr
Source
       

 
 
S rx

   

p
ITERATIVE FORMULA
●The walls are discretised into N surface samples. We
consider that :
●
✗ absorption coefficient a is constant for a same sample
✗ surface power density is constant on all the surface S
of the sample
✗ each surface sample will be identified by its centroid
Time axis is discretised. The time sample is noted k,
temporal shift becomes
where Dt the temporal sampling step.
Function « Int »gives the closer rounded integer.
The equation is now
Thus, the intensity in every point of the room is :

          
 i 1
ri
2
1 cos 
 
COMPARISON BETWEEN CALCULATIONS
AND IN SITU MEASUREMENTS
Halle aux Grains – Samatan (32-France)
Theatre, concert hall and cinema
Volume 1,500 m3. Floor surface 250 m².
Absorbent ceilings everywhere excepting a reflecting
strip in the center of the straight ceiling.
Reflecting walls excepting the background wall
Absorbent sits
Théâtre des 3 ponts – Castelnaudary (11-France)
Both a theatre and a concert hall.
Volume 2,140 m3. Floor surface 290 m².
Absorbent ceilings everywhere
Reflecting walls excepting the background wall
Absorbent sits
Cezus Factory – Montreuil (49-France)
Volume 24,660 m3. Floor surface 2,900 m².
Highly absorbent ceilings everywhere
Absorbent walls
Highly cluttered floor (machine-tools)
Noise map in an open space office
– AcouS Propa® software
Extract of ENV-07-009
Calculate noise of wind farms
Claude Sénat– Gamba Acoustique & Associés
Noise map of wind farm – AcouS
Propa® software