PHY2464 - The Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 22
22
Basics
Basics of
of Room
Room Acoustics
Acoustics
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
Unit 22 Session
Session 18
18
Sam
Sam Trickey
Trickey
April
April 3,
3, 2005
2005
PHY-2464
PHY
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Pres. 22 Room Acoustics --Basics
Basics
Key Elements of Wave Propagation for
Room Acoustics
Reflection
Absorption (transmission)
Diffraction
Resonances
Other issues: noise
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Reminder 1:
1: The intensity of a spherical sound wave
decreases as the square of the distance from the source
[“Inverse square”]
d [m] I [W/m2]
1.0
1.0
=12 /12
2.0
0.25
=12/2 2
3.0
0.11
=12 /3 2
4.0
0.068 = 12 /4 2
2
2
0.040 = 1 /5
As 1/r 2
5.0
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Pres. 22 Room Acoustics -Basics
Reminder 2: Intensity is Power per Unit Area
Why does intensity
diminish as 1/r 2?
Area = 2/3π r 2
I = Power/Area
I = I0 (A0 /A)
I= I0 (r0 / r ) 2
A = ⅔π r 2
r
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Reminder 3: Reflection and transmission when a
wave passes from one medium to another.
Case (a): the interface is smooth.
Reflection
Θin = Θout
Θout
out
Θiinn
Transmission
Medium 1
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Medium 2
Pres. 22 Room Acoustics -Basics
Case (b) The interface is rough
Diffuse
Reflection
Also
transmission
Rough Surface
Roughness > λ
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Reminder 4: What happens when a wave is partially
obstructed?
Diffraction
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Pres. 22 Room Acoustics -Basics
Reminder 4: Diffraction:
Waves “bend around” obstacles because every point
on a wave is a source; waves cannot terminate
abruptly.
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Room resonances can introduce Beats → live
and dead spots, distracting “extra pitches”
In phase
Out of phase
f1
f2
fmean
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fbeat
Pres. 22 Room Acoustics -Basics
Interference also can be a problem
Constructive
Destructive
Softer
Louder
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Greek Amphitheater
At Epidauros, Greece
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Pres. 22 Room Acoustics -Basics
Constructive
Interference
PHY2464 - The Physical Basis of Music
Physics 1251
Unit 2 Session 18
Room Acoustics
Greek Amphitheater
Acoustics
Reflected sound
Direct sound
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Pres. 22 Room Acoustics -Basics
Musiksvereinssaale Vienna
PHY2464 - The Physical Basis of Music
Physics 1251 Unit 2 Session 18
Room Acoustics
Royal Festival Hall
http://www.coxt.freeeserve.co.uk/hall.jpg
Physics 1251 Unit 2 Session 18
Room Acoustics
Morton Meyerson Symphony Center
Dallas, Texas
http://www.pcfandp.com/a/p/8103/s.html
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Winspear Center; Edmonton, Alberta, Canada
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Pres. 22 Room Acoustics -Basics
Key Fact - Standards for “Good” Performance Hall
Acoustics:
• Clarity …little overlap of sounds
• Uniformity …everywhere the same
• Envelopment …sound from all directions
…no echoes, beats
• Smoothness
…appropriate length of time
• Reverberation
• Performer satisfaction …reflected to stage
…no competition
• Freedom from noise
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Cardinal Principle of Room Acoustics
The temporal, spatial, intensity and phase
relationships between the direct and reflected
sound ultimately determine the quality of the
acoustics in a room.
A room is an instrument that can dull the most
illustrious performance by the most accomplished
musician, or
it can increase the pleasure of listening.
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Pres. 22 Room Acoustics -Basics
Haas (or Precedence) Effect
The earliest sound that arrives determines the sense
of the origin of a sound, even if the later (<100
ms) reflections are louder.
Implication:
The direct sound should arrive first.
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Room Acoustics: Reverberation
Direct Sound
Speaker
Hearer
Reverberant Sound
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Pres. 22 Room Acoustics -Basics
Energy Lost in Reflections:
• The sound reflects many times, each time losing
energy to the reflecting surface (because it is not
perfectly hard).
• The quantity α is the absorptivity of a particular
surface.
• The intensity of the sound that is lost in a
reflection at that surface is ∆Ilost = α Iin.
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
• The intensity of the reflected wave is
Ireflected= (1-α) Iin.
α
α
11
97
--αα
(1--α
(1(1
(1
α))))53IIII0I0000
10I
(1--αα)8642)12
I
I(1
(1
0 -α) I0 00
10
0
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Pres. 22 Room Acoustics -Basics
• The intensity of the reflected wave is
Ireflected= (1-α) Iin.
• Values for α, the absorptivity, for many types of
surfaces have been measured and appear in
extensive tables.
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Coefficient of Absorption or “the Absorptivity”
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Material
α (at 500 Hz)
Acoustic tile
Plaster wall
Concrete
Person
0.6
0.1
0.02
0.8 (x1 m2)
Pres. 22 Room Acoustics -Basics
Wallace Sabine
(Harvard professor 18681868-1919)
Asked: “How long will it take for the
sound to die down to 1 millionth ((-60 dB)
of the initial value?”
value?”
Wallace
Sabine
Key Fact: The reverberation time is defined as the
time for the intensity to decay by a factor of 10 –6
(- 60 dB) of its initial value.
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
Intensity of Sound in a Room:
~ Io
Pressure
I = Io x 10 –6 t / TR
t = ⅙ TR
~ 1/10 Io
Amplitude
t = ⅓ TR
~ 1/100 Io
Time (ms)
http://hybrid.colorado.edu/~phys1240/sounds.html
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Pres. 22 Room Acoustics -Basics
Key Fact: The Sabine Equation:
I = Io x 10 – 6 (t/TR)
TR = 0.16 V/Se
•
•
•
V is the volume of the room.
Se is the “effective surface area” of the walls S1 ,
floor S2 and ceiling S3 (in sabin) etc.
α is the absorptivity of the surface (in table)
Se = α1 S1 + α2 S2 + α3 S3 + α4 S4 +…
PHY2464 - The Physical Basis of Music
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Pres. 22 Room Acoustics -Basics
What is the reverberation time for 500 Hz sound in
a concrete room that is 3 x 3 x3 meters?
The Sabine Equation:
TR = 0.16 V/Se
• V is the volume of the room= 3 x 3 x 3 = 27.0 m3.
• Walls S1 = 4 (3 x 3 m2 )= 36. m2 ),
• Floor S2
= 9.0 m2
• Ceiling S3 = 9.0 m2
• α = 0.02
Se = (0.02) (36.) + (0.02) (9.0) + (0.02) (9.0) = 1.02 sabine
TR = 0.16 V/Se = 0.16 (27)/(1.02) = 4.2 sec
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Pres. 22 Room Acoustics -Basics
Summary:
•
Direct sound should come first
•
Haas or precedence effect
Reverberant sound
•
•
•
TR = 0.16 V/Se
0.8 sec for clear speech, 11-2 s for music
Freedom from echo and interference
•
•
•
Use diffuse and random reflectors
Avoid geometries that induce resonances
Background noise level
•
•
Assure good acoustic isolation