L 18
Auditorium and Room
Acoustics
Dekelbaum
Concert Hall
at the
U MD
Smith Center
Paths of sound in room
Intensity vs. time for pulse
We define the reverberation time T
as the time the sound intensity
takes to decay to one millionth of
its original steady-state intensity.
This is the time taken the sound
level to decay by
10 log(1,000,000)= 60 db
Average Intensity vs. Time
for a constant tone
To calculate T, consider a room with a
hole in one wall of area A.
Call the reverberation time T.
T ˜ volume V, 1/A
T= K V/A
It has been worked out that, for V in ft3 , A
in ft2
T= 0.049 V/A
The constant is 0.16 if metric (SI) units are
used.
Let us now replace the open
window area with an absorbing
material of area S and absorption
coefficient a.
Then A= Sa. If there is more than
one type of absorbing material, the
A= S1 a1+S2a2 +S3a3+…
If you prefer, we can write
T= 0.049 V/(ΣSiai)
We call this new “area” A the “total
room absorption”, measured in sabins
(same unit as area, but a somewhat
different meaning)
If we wish to calculate T, we need
to calculate the total room
absorption- from the walls, floor,
ceiling, furniture, drapes, people,
etc.
An empty room with totally reflecting walls, ceiling,
floors, etc. has a
a) shorter T than one (empty) of comparable
dimensions with perfectly absorbing walls, ceiling,
floors, etc.
b) shorter T than one(empty) of comparable
dimensions with open windows
c) shorter T than one (empty) of comparable
dimensions with no windows and with carpets
covering the walls
d) a longer T than one of comparable dimensions
with perfectly reflecting walls , but with people
inside.
Examples of Reverberation Times
One way to respond to the question "What is a good range of
reverberation times for concert halls?" is to give examples of
some of the most famous halls in the world. For the overall
average reverberation times:
Vienna, Musikvereinsaal : 2.05 seconds
Boston, Symphony Hall: 1.8 seconds
New York, Carnegie Hall: 1.7 seconds
But the overall average reverberation time does not tell the
whole story. The variation of reverberation time with
frequency is also important.
Ideal Reverberation Times
Search youtube for Notre Dame de
Paris organ (try a Bach piece)
Intimacy
Room said to be “intimate” when the
first reverberation arrives within
20 ms of the direct sound.
Fullness vs. Clarity
Refers to the amount of
reflected sound relative to
the amount of direct sound
Warmth vs. Brilliance
Warmth increases with
increasing T for low frequencies
Acoustical Design Problems
1. Focusing of sound
2. Echoes
3. Shadows
4. Resonances
5. External noise
6. Double-valued T
Focusing of Sound
Occurs with use of
parabolic surfaces
either behind performers
or at rear of auditorium
Echoes
Highly reflective flat or
parabolic wall shapes
Flutter echos from
parallel walls
Standing waves
between parallel walls
Resonances
Parallel walls (flutter)
Rectangular practice rooms
Singing in the shower
Double-valued T
Playback room with reverberation
Concert halls with side areas
Auditorium
Design
General Design Considerations
1. Visual
2. Ventilation
3. Acoustical
a. seating
b. stage
c. room shape
d. room walls
Absorptions (in sabins)
Frequency (Hz)
Material
125
250
500 1000 2000
Unupholstered seat
0.15 0.22 0.25 0.28 0.50
Upholstered seat
3.0
3.1
3.1
3.2
3.4
Adult person
2.5
3.5
4.2
4.6
5.0
Adult/upholstered seat 3.0
3.8
4.5
5.0
5.2
Some Absorption Coefficients
Frequency (Hz)
250 500 1000 2000 4000
Material
125
Concrete/brick
Glass
Plasterboard
0.02
Plywood
Carpet
Curtains
Acoustical board
0.01 0.01 0.02 0.02 0.02 0.03
0.19 0.08 0.06 0.04 0.03 0.02
0.20 0.15 0.10 0.08 0.04
0.45
0.10
0.05
0.25
0.25
0.20
0.12
0.45
0.13
0.30
0.25
0.80
0.11
0.35
0.35
0.90
0.10
0.50
0.40
0.90
0.09
0.60
0.45
0.90
Control of TR
T = 0.050 V / A
Where:
T = reverberation time in seconds
V = room volume in cubic feet
A = total room absorption in sabins
Estimate the reverberation
time of this lecture hall
Should there be an enforced
control of sound level in listening
devices and public performance
venues?
a) yes
b) no