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Auditorium <strong>Acoustics</strong> 2011, Dublin<br />
Diffusion in Concert halls analyzed as a function<br />
of time during the decay process<br />
Claus Lynge Christensen<br />
&<br />
Jens Holger Rindel<br />
Odeon A/S, Lyngby, Denmark
Agenda<br />
• Why investigate diffusivity?<br />
• Directional Diffusion and Steady State Diffusivity<br />
• Defining the Dynamic Diffusion Curve (DDC)<br />
• Normalising the DDC<br />
• Typical features of the DDC<br />
• DDC in (models of) 12 concert halls<br />
• DDC as a function of distance in 2 halls<br />
• DDC and flutter echo<br />
• Conclusions<br />
Auditorium <strong>Acoustics</strong> 2011 2
Motivation, why investigate diffusivity?<br />
• Diffusivity is assumed to be important for the quality of<br />
concert halls<br />
• Efforts are put into promoting diffuse reflections;<br />
– making surfaces scatter sound<br />
– shape of geometry<br />
– distribution of materials<br />
Therefore we should understand better how given designs<br />
affect diffusivity in rooms.<br />
Auditorium <strong>Acoustics</strong> 2011 3
Steady State Diffusivity<br />
Thiele (1953) defined Directional Diffusion (d in %) as<br />
d<br />
=<br />
(1 −<br />
µ<br />
) × 100%<br />
µ<br />
0<br />
=<br />
E −<br />
E<br />
I<br />
× 100%<br />
where E is sound energy and I is sound intensity<br />
Directional Diffusion is usually close to 100%, so instead<br />
we may prefer to define Steady State Diffusivity in dB as:<br />
D ( ss)<br />
= 10 × log<br />
10<br />
( E)<br />
−10<br />
× log<br />
10<br />
( I<br />
)<br />
[dB]<br />
2 2 2<br />
Note!<br />
I = I + I + I<br />
8x<br />
8x<br />
8z<br />
Auditorium <strong>Acoustics</strong> 2011 4
Steady State Diffusivity<br />
Example on D(ss) at different locations<br />
Diffusivity(ss) (dB) at 1000 Hz >= 11,8<br />
Receiver in side gallery with<br />
no visible no sight<br />
10,5<br />
9,8<br />
Odeon©1985-2011 Licensed to: License information /dongle unavailable at start up!<br />
8,9<br />
19.2 dB@1000Hz<br />
P1<br />
8,1<br />
7,3<br />
6,5<br />
5,8<br />
Receiver at floor<br />
6.4 dB@1000Hz<br />
4,9<br />
4,2<br />
3,4<br />
2,6<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Dynamic Diffusivity Curve – DDC<br />
energy and intensity curves<br />
Backwards integrated squared impulse response curve<br />
t<br />
∫ = t = ∞<br />
E( t ) = 10 × log<br />
10<br />
E(<br />
t)<br />
dt [ dB]<br />
n<br />
t n<br />
Backwards integrated intensity curve<br />
t = tn<br />
t = t<br />
2<br />
n<br />
t = t<br />
2<br />
n<br />
2<br />
10<br />
( ∫ I ( t)<br />
8x<br />
dt)<br />
+ ( ∫ I ( t)<br />
8 y<br />
dt)<br />
+ ( I ( t)<br />
8z<br />
dt)<br />
t=∞<br />
t =∞<br />
t=∞<br />
I ( t ) = 10 × log<br />
∫<br />
n<br />
Auditorium <strong>Acoustics</strong> 2011 6
Dynamic Diffusivity Curve – DDC<br />
example; energy and intensity curves<br />
Schröder curve<br />
Backwards integrated<br />
Intensity curve<br />
D(ss)<br />
SPL (dB)<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
Decay curves at 1000 Hz, T30=3,22<br />
Zoomed decay T(10,57, -21,35)=2,90 s<br />
DDC(n)<br />
gfedc<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedcb<br />
E, Simulated<br />
E, Integrated<br />
E, Corrected<br />
I, Simulated<br />
I, Integrated<br />
-15<br />
-20<br />
-25<br />
0 0,2 0,4 0,6 0,8 1<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
1,2<br />
1,4<br />
Auditorium <strong>Acoustics</strong> 2011 7
Dynamic Diffusivity Curve – DDC<br />
DDC is the difference between energy and intensity curves<br />
DDC<br />
( n)<br />
=<br />
E(<br />
n)<br />
−<br />
I ( n)<br />
= 10 × log<br />
10<br />
∫<br />
t = t<br />
n<br />
t =∞<br />
E(<br />
t)<br />
dt<br />
t = t<br />
∫<br />
∫<br />
∫<br />
10<br />
n<br />
2<br />
n<br />
2<br />
n<br />
−<br />
10 ×<br />
log<br />
10<br />
(<br />
I<br />
(<br />
t<br />
)<br />
8<br />
x<br />
dt<br />
)<br />
+<br />
(<br />
I<br />
(<br />
t<br />
)<br />
8<br />
y<br />
dt<br />
)<br />
+<br />
(<br />
I<br />
(<br />
t<br />
)<br />
8<br />
t =∞<br />
t = t<br />
t =∞<br />
t = t<br />
t = ∞<br />
z<br />
dt<br />
)<br />
2<br />
[dB]<br />
Auditorium <strong>Acoustics</strong> 2011 8
Comparing DDC for rooms with different T30<br />
Box shaped room 12 x 14 x 16<br />
1<br />
P1<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Diffusivity (dB)<br />
24<br />
22<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0<br />
0,5<br />
Dynamic diffusivity curves<br />
1 1,5 2 2,5 3 3,5 4<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
4,5<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
T30=3.24s@1000 Hz<br />
All hard surfaces<br />
Low scattering<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
Diffusivity (dB)<br />
22<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0<br />
0,5<br />
Dynamic diffusivity curves<br />
1 1,5 2 2,5 3 3,5 4<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
4,5<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
T30=1.65s@1000 Hz<br />
hard surfaces+absorbing ceiling<br />
High scattering<br />
Auditorium <strong>Acoustics</strong> 2011 9
Normalising DDC<br />
• Use Schröder curve for normalization<br />
• Substitute time axis with decay [dB]<br />
-16<br />
-18<br />
-20<br />
-22<br />
Decay curves at 1000 Hz, T30=3,24<br />
Zoomed decay T(-15,69, -27,37)=3,25 s<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedc<br />
gfedc<br />
E, Simulated<br />
E, Integrated<br />
E, Corrected<br />
I, Simulated<br />
I, Integrated<br />
SPL (dB)<br />
-24<br />
-26<br />
-28<br />
-30<br />
-32<br />
0 0,1 0,2 0,3 0,4<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
0,5<br />
0,6<br />
Auditorium <strong>Acoustics</strong> 2011 10
Normalising DDC<br />
Diffusivity (dB)<br />
Dynamic diffusivity curves<br />
24<br />
22<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz 22<br />
DDC -125 Hz 20<br />
DDC -250 Hz<br />
18<br />
DDC -500 Hz<br />
16<br />
DDC -1000 Hz<br />
DDC -2000 Hz 14<br />
Diffusivity (dB)<br />
DDC -4000 Hz 12<br />
DDC -8000 Hz 10<br />
DDC fit -63 Hz<br />
8<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
6<br />
DDC fit -500 Hz 4<br />
Dynamic diffusivity curves<br />
DDC fit -1000 Hz2<br />
DDC fit -2000 Hz<br />
0<br />
DDC fit -4000 Hz 0 -5 -10 -15 -20 -25 -30 -35 -40<br />
DDC fit -8000 Hz<br />
Decay (dB)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
T30=3.24s@1000 Hz<br />
All hard surfaces<br />
Low scattering<br />
T30=1.65s@1000 Hz<br />
hard surfaces+absorbing ceiling<br />
High scattering<br />
Auditorium <strong>Acoustics</strong> 2011 11
Typical features of DDC<br />
• Initial value Dss is lower that later values<br />
• A peak appears within the first 5 (to 10) dB<br />
• DDC reaches its plateau level after some 5 to 10 dB decay<br />
• The plateau can have ripples e.g. in case of a flutter echo<br />
Auditorium <strong>Acoustics</strong> 2011 12
12 Concert halls (models)<br />
Source mid stage – receiver mid-parterre<br />
Dss, Peak and Plateau levels
Two examples for comparison
Diffusivity(Dss) – Boston Symphony Hall<br />
Floor level, only<br />
0 10 20 30 40 metres<br />
Diffusivity(total) (dB) at 1000 Hz >= 9,9<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
8,9<br />
25 metres<br />
20<br />
15<br />
10<br />
5<br />
0<br />
P1<br />
8,2<br />
7,5<br />
6,8<br />
6,1<br />
5,4<br />
4,7<br />
4,0<br />
3,3<br />
2,6<br />
1,9<br />
1,2<br />
0,5<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Auditorium <strong>Acoustics</strong> 2011<br />
15<br />
Dss and Plateau levels<br />
as a function of distance<br />
Boston Symphony Hall<br />
12<br />
10<br />
Diffusivity (dB)<br />
8<br />
6<br />
4<br />
2<br />
Dss (dB)<br />
Plateau (dB)<br />
0<br />
8,6 11,6 14,6 17,6 20,6 23,6 26,6 29,6 32,6 35,6 38,6 41,6<br />
Distance (Source-Receiver) in metres<br />
Auditorium <strong>Acoustics</strong> 2011 16
DDC variation with distance in BSH<br />
Dynamic diffusivity curves<br />
35 40 metres<br />
0 5 10 15 20 25 30<br />
20 metres<br />
15<br />
P1<br />
10<br />
12 11 10 9 8 7 6 5 4 3 2 1<br />
5<br />
0<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Diffusivity (dB)<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35<br />
Decay (dB)<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
20<br />
Diffusivity (dB)<br />
18<br />
16<br />
Auditorium <strong>Acoustics</strong> 2011<br />
Diffusivity (dB)<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
R01<br />
R05<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
R09<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
17<br />
Odeon©1985-2011 Licensed to: Odeon A/S
Diffusivity(Dss) – Royal Festival Hall<br />
Floor level, only<br />
0 10 20 30 40 50 metres<br />
Diffusivity(total) (dB) at 1000 Hz >= 9,9<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
8,9<br />
20 metres<br />
10<br />
0<br />
P1<br />
8,2<br />
7,5<br />
6,8<br />
6,1<br />
5,4<br />
4,7<br />
4,0<br />
3,3<br />
2,6<br />
1,9<br />
1,2<br />
0,5<br />
Odeon©1985-2011 Licensed to: Odeon Auditorium A/S <strong>Acoustics</strong> 2011<br />
18<br />
Dss and Plateau levels<br />
as a function of distance<br />
Royal Festival Hall<br />
12<br />
10<br />
Diffusivity (dB)<br />
8<br />
6<br />
4<br />
2<br />
Dss (dB)<br />
Plateau (dB)<br />
0<br />
6,0 9,0 12,0 15,0 18,0 21,0 24,0 27,0 30,0 33,0 36,0<br />
Distance (Source-Receiver) in metres<br />
Auditorium <strong>Acoustics</strong> 2011 19
DDC variation with distance in RFH<br />
40 45 50 metres<br />
0 5 10 15 20 25 30 35<br />
30 metres<br />
25<br />
20<br />
P1<br />
15<br />
11 10 9 8 7 6 5 4 3 2 1<br />
10<br />
5<br />
0<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Auditorium <strong>Acoustics</strong> 2011<br />
Diffusivity (dB)<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
Dynamic diffusivity curves<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Diffusivity (dB)<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
R01<br />
R05<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
20<br />
Diffusivity (dB)<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
R09<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
20<br />
Odeon©1985-2011 Licensed to: Odeon A/S
Queen’s Hall, Copenhagen<br />
DDC and Flutter Echo<br />
4 reflector panels tilted slightly<br />
inwards – creating a flutter echo<br />
P1<br />
1<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Source: 1<br />
Surface: *Receiver*<br />
Refl.: 2<br />
Path : 26,50<br />
Time : 77<br />
Diffusivity (dB)<br />
13<br />
12<br />
11<br />
10<br />
9<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0<br />
0,5<br />
1 1,5 2 2,5<br />
Time (seconds rel. direct sound)<br />
3<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Auditorium <strong>Acoustics</strong> 2011 21
Queen’s Hall, Copenhagen<br />
DDC and Flutter Echo<br />
4 reflector panels tilted slightly<br />
inwards – creating a flutter echo<br />
P1<br />
1<br />
Dynamic diffusivity curves<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
Source: 1<br />
Surface: *Receiver*<br />
Refl.: 2<br />
Path : 26,50<br />
Time : 77<br />
1<br />
1,5<br />
2<br />
2,5<br />
Time (seconds rel. direct sound)<br />
Diffusivity (dB)<br />
13<br />
12<br />
11<br />
10<br />
9<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0<br />
0,5<br />
1 1,5 2 2,5<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
3<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
DDC fit -2000 Hz<br />
DDC fit -4000 Hz<br />
DDC fit -8000 Hz<br />
Auditorium <strong>Acoustics</strong> 2011 22
DDC and flutter echo<br />
Dynamic diffusivity curves<br />
Before treatment<br />
with scattering<br />
surfaces<br />
Diffusivity (dB)<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
DDC -63 Hz<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
After treatment<br />
with scattering<br />
surfaces<br />
Diffusivity (dB)<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
Dynamic diffusivity curves<br />
0 -5 -10 -15 -20 -25 -30 -35 -40<br />
Decay (dB)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
DDC -63 Hz<br />
Auditorium <strong>Acoustics</strong> 2011 23<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedc<br />
gfedcb<br />
DDC -125 Hz<br />
DDC -250 Hz<br />
DDC -500 Hz<br />
DDC -1000 Hz<br />
DDC -2000 Hz<br />
DDC -4000 Hz<br />
DDC -8000 Hz<br />
DDC fit -63 Hz<br />
DDC fit -125 Hz<br />
DDC fit -250 Hz<br />
DDC fit -500 Hz<br />
DDC fit -1000 Hz
Conclusions<br />
• Dynamic Diffusion Curve DDC is suggested for investigating<br />
dynamic behavior of diffusion during decay<br />
• Features for rooms without echoes;<br />
– Starts with Steady State Diffusion – in auditoria 2-7 dB,<br />
– Peak value typically within first 5-10 dB of decay<br />
– Plateau level (rev. diffusion) – in auditoria 5-12 dB<br />
• Features for rooms with echo problems, e.g. flutter echo;<br />
– Ripples (xx dB?)<br />
• Further research, optimum values, JND’s, better tools than<br />
DDC?, extract other information from the DDC etc…<br />
Auditorium <strong>Acoustics</strong> 2011 24
Example<br />
Integrated energy and intensity curves<br />
Schröder curve<br />
D(ss)<br />
Backwards integrated<br />
Intensity curve<br />
SPL (dB)<br />
-15<br />
-20<br />
-25<br />
-30<br />
-35<br />
-40<br />
-45<br />
Decay curves at 1000 Hz, T30=3,24<br />
Zoomed decay T(-15,69, -47,39)=3,24 s<br />
DDC(n)<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
E, Simulated<br />
E, Integrated<br />
E, Corrected<br />
I, Simulated<br />
I, Integrated<br />
-50<br />
-55<br />
0 0,2 0,4 0,6 0,8 1 1,2<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
1,4<br />
1,6<br />
Auditorium <strong>Acoustics</strong> 2011 25
Integrated energy and intensity curves<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
Decay curves at 1000 Hz, T30=3,22 s at 1000 Hz<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
gfedcb<br />
E, Simulated<br />
E, Integrated<br />
E, Corrected<br />
I, Simulated<br />
I, Integrated<br />
SPL (dB)<br />
-15<br />
-20<br />
-25<br />
-30<br />
-35<br />
-40<br />
-45<br />
0 0,5 1 1,5 2 2,5<br />
Time (seconds rel. direct sound)<br />
Odeon©1985-2011 Licensed to: Odeon A/S<br />
3<br />
Auditorium <strong>Acoustics</strong> 2011 26
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