PHY2464 - The Physical Basis of Music
4/8/2005
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 23
23
Basics
Basics of
of Room
Room Acoustics
Acoustics –– II
II
[Reverberation]
[Reverberation]
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
2
Session
Unit 2 Session 19
19
Sam
Sam Trickey
Trickey
April
April 7,
7, 2005
2005
PHY-2464
PHY
PHY-2464
Pres. 23 Room Acoustics – Basics II
Key Elements of Wave Propagation for
Room Acoustics
Reflection
Absorption (transmission)
Diffraction
Resonances
Other issues: noise
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Observation and Query:
The public passageway shown below has brick pillars and
mirrors equally spaced along one side and a carpeted wall
along the other. What acoustic role do these architectural
elements play?
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Destructive Interference Cancellation
0.5 m
Reflection
1m
Cancellation
Cancellation
2.5 m
1m
Consequence:
No propagation
Mirror Image
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
These architectural elements attenuate propagation by
destructive interference from one side and absorption on
the other
subtract
add
Destructive Interference
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Recall:
•
•
•
Reverberation time TR is the time required to fall to 10 -6
(-60 dB) of the original sound intensity.
Except for early sound (at pulse on or pulse off), sound
intensity grows and dies away exponentially; Hall Fig.
15.3
Reverb. time is given by the Sabine equation:
TR = 0.16 V/Se
where V = room volume and Se is its acoustic effective
surface area = geometric surface times absorption
coefficient for each distinct area: Se = Σ αi Si .
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Room Acoustics: Reverberation
Direct Sound
Speaker
Hearer
Reverberant Sound
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Why is reverberation (“re-speaking”) valued?
• To even out the sound intensity throughout the
audience.
• To permit the sound to reach greater intensity.
• To give a “fullness” or “presence” to the sound.
• The downside? Loss of clarity, precision
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Sound Level in a Room:
•
•
Direct sound decreases as 1/r2 (r = distance from speaker)
Reverberant sound (in equilibrium) is constant.
How does the sound vary with distance from the speaker in
this room?
I = Ireverb [(rd /r)2 + 1]
Or
SIL = SILreverb + 10 Log[(rd /r)2 + 1]
rd = distance at which direct & reverb. sound have same
intensity
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
The Sound Level in a Room:
• rd = distance at which reverberant sound intensity
equals the direct sound intensity
3
∆SIL (dB)
2
1
0
1
5
10
r/rd
PHY2464 - The Physical Basis of Music
4/8/2005
Physics 1251 Unit 2 Session 19
Reverberation
Reverberation evens out the sound:
• Beyond rd the sound intensity is much more
uniform than it would be if there were no
reverberation.
r
rd
SIL (dB)
83
82
1/r 2 behavior, no reverb
With reverb
81
5
80 1
10
r/rd
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Winspear Concert Hall
University of North Texas
rd
rd
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Winspear Concert Hall
University of North Texas
Reverberation evens out
intensity and envelopes
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Recall Hall Fig. 15.3: Intensity in the room (from a
steady note) grows with time:
• The sound intensity level builds up if the room is
Intensity
reverberant.
Less
More
Reverberation
Reverberation
Source
Time
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Reverberation gives the sound “presence”
Intensity
Source
Room Sound
Background
Time
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Intensity
Excessively long reverberation reduces sound clarity
(“boomy”). Too short a TR makes the room “dry”.
Source
“Dry” Sound
“Boomy” Sound
Time
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
• What happens to the sound after many
reflections?
• Does sound go on forever?
• Where does the sound energy go?
• Heat is “disorganized” motion of the air
molecules.
• When the sound intensity drops below the
ambient it is masked and lost for ever.
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
Amphitheater
Epidauros, Greece
Reverberation
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Amphitheater at Epidauros Greece
V = 3.6 x 104 m3
Se = 3.0 x 103 m2
25 m
62 m
TR = 0.16 V/Se
20 m
= 0.16 (3.6 x 104/3.0 x 103)
= 1.92 sec
α = 1.0
32 m
PHYPHY-2464
8m
Pres. 23 Room Acoustics – Basics II
Reverberation Time for Physics (U. N. Texas) Room 102
S3
S5
S2
S4
Volume V
Se,Room + N (0.8 sabine/person
sabine/person)
S1
TR = 0.16 V/Se
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Reverberation Time for Physics Room 102
TR = 0.16 V/Se
TR =0.75 sec
Volume = 1600 m3
Floor
425 m2x 0.02
Tile ceiling
360 m2x 0. 60
Ceiling
65 m2 x 0.10
Walls
145 m2 x 0.10
60 People
60 m2 x 0.80
2
75 chairs 75 m x 0.60 45
Se =
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8
216
6
14
48
339
Pres. 23 Room Acoustics – Basics II
From where did the reverb.-time equation arise?
TR = 0.16 V/Se
The time required to reduce the SIL by 60 dB
corresponds a certain number of times the sound
reflects multiplied by the time it takes (on average)
to make a trip across the room.
TR = Nreflectionsx < τ>
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
The number of reflections to drop 60 dB:
10−6 = (1 − α )
so
N reflections
−6 = N reflections log (1 − α )
N reflections = −6 / log (1 − α ) ≈ 13.8 / α
Last step from properties of natural
logarithm and conversion to common log.
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
The average time between reflections:
The average time is the average distance traveled
between bounces divided by the velocity of sound:
< τ> = <d> / v
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
The average distance traveled between reflections:
Will scale as the size of the room, d.
For a cube d x d x d:
6(d3/6d2)= 6 V/S = d
For a sphere of diameter d:
6 [(π
[(πd 3/6)/(π
/6)/(πd 2)] = 6V/S = d
→ d = 6 V/S
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
The average distance traveled in a room of
dimension d:
<d> = ⅔ d
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Therefore, putting everything together:
The time required to reduce the SIL by 60 dB is
equal to the number of times the sound reflects
multiplied by the time it takes (on average) to make
a trip across the room.
TR = (13.8 / α) x (⅔) (6 V/S) /v
TR = (55.2 / v) V / (αS)
TR = 0.16 V/ (αS) = 0.16 V/ Se
PHYPHY-2464
Pres. 23 Room Acoustics – Basics II
What is the “ideal” reverberation time for a
room?
•Depends on uses and on size
Design Equations:
• Trecommended ≈ R ∛ V;
• R = 0.06 s/m for lecture, 0.07 s/m for music
• For U.N.T. Physics Room 102, V =1600 m3,
Trec ≈ R ∛ V = 0.7 → 0.9 secv
PHY2464 - The Physical Basis of Music
PHYPHY-2464
4/8/2005
Pres. 23 Room Acoustics – Basics II
Reverberation Time (s)
Recommended Reverberation:
PHYPHY-2464
3
2
1
Speech
100
a
Organ
Oper
ic
s
er Mu
Chamb
1000
10000
Volume (m 2)
Pres. 23 Room Acoustics – Basics II
Summary:
•
The reverberation time TR is the time required
to reach 10 -6 of the original sound intensity.
•
Sound intensity decays exponentially.
•
TR = 0.16 V/Se
•
The effective surface area Se of a room is the
sum of the effective surface areas of each
surface, αS.
•
<0.8 sec for clear speech, 1-2 sec for music