Transcript Physics 1251 The Science and Technology of Musical Sound

Physics 1251
The Science and Technology
of Musical Sound
Unit 2
Session 18 MWF
Room Acoustics
Physics 1251
Unit 2 Session 18
Room Acoustics
Foolscap Quiz:
Two tones of frequency 262 Hz and 264 Hz
are sounded. What do you hear?
Answer: A single tone of frequency 263 Hz
beating with a beat frequency of 2 Hz.
fmean = (f 1+ f2)/2 = (262 + 264)/2 = 263 Hz
fbeat = ⃒f 1- f2⃒ = ⃒262-264 ⃒ = 2 Hz.
Physics 1251
Unit 2 Session 18
Room Acoustics
Reflective Review:
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Wave motion is characterized by
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Reflection
Refraction
Diffraction
Doppler Shift
Beats
Interference
The Reflective
Ref
Differed
Dopily,
Beating
Interference.
Physics 1251
Unit 2 Session 18
Room Acoustics
When the surface is smooth we have
“specular” (mirror-like) reflection.
Reflection
Smooth Surface
Roughness ≲ λ
Physics 1251
Unit 2 Session 18
Room Acoustics
Refraction occurs when a wave “enters” a
medium that has a different velocity?
Refraction
V1 <
V2
Physics 1251
Unit 2 Session 18
Room Acoustics
What happens when a wave “is partially
obstructed?
Diffraction
Physics 1251
Unit 2 Session 18
Room Acoustics
Doppler Shift:
Lower f
Moving source
Higher f
fobserver = fsource [v + vobserver] / [v – vsource]
Physics 1251
Unit 2 Session 18
Room Acoustics
Beats
In phase
Out of phase
f1
f2
fmean
fbeat
Physics 1251
Unit 2 Session 18
Room Acoustics
Interference
Constructive
Destructive
Softer
Louder
Physics 1251
Unit 2 Session 18
Room Acoustics
1′ Lecture:
Factors that most determine room acoustics:
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Direct sound
Reverberant sound
Freedom from echo and interference
Background noise level
Physics 1251
Unit 2 Session 18
Room Acoustics
Greek Amphitheater
At Epidauros, Greece
Physics 1251
Unit 2 Session 18
Room Acoustics
Constructive
Interference
Physics 1251
Unit 2 Session 18
Room Acoustics
Greek Amphitheater
Acoustics
Reflected
sound
Direct sound
Physics 1251
Unit 2 Session 18
Room Acoustics
Musiksvereinssaale Vienna
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
Physics 1251
Unit 2 Session 18
Room Acoustics
Winspear Center
Edmonton, Canada
Physics 1251
Unit 2 Session 18
Room Acoustics
80/20Standards
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for “Good” Acoustics:
Clarity …little overlap of sounds
Uniformity …everywhere the same
Envelopment …sound from all directions
Smoothness …no echoes
Reverberation …appropriate length of time
Performer satisfaction …reflected to stage
Freedom from noise …no competition
Physics 1251
Unit 2 Session 18
Room Acoustics
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.
Physics 1251
Unit 2 Session 18
Room Acoustics
80/20 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.
The direct sound should arrive first.
Physics 1251
Unit 2 Session 18
Room Acoustics
Room Acoustics: Reverberation
Direct Sound
Speaker
Hearer
Reverberant Sound
Physics 1251
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Room Acoustics
Energy Lost in Reflections:
• The sound reflects many times, each time
losing energy to the reflecting surface.
• The quantity α is the absorptivity of the
surface.
• The intensity of the sound that is lost in a
reflection is ΔIlost = α Iin.
Physics 1251
Unit 2 Session 18
Room Acoustics
• The intensity of the reflected wave is
Ireflected= (1-α) Iin.
α
11
7
9
5
(1-α)
(1-α)
(1-α)3II000
α
2I I
4
6
8
10
I0 12
(1-α)
00
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Room Acoustics
• 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.
Physics 1251
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Room Acoustics
The Absorptivity
Material
α (at 500 Hz)
Acoustic tile
Plaster wall
Concrete
Person
0.6
0.1
0.02
0.8 (x1 m2)
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Room Acoustics
Wallace Sabine
(Harvard professor 1868-1919)
Asked: “How long will it take for the
sound to die down to 1 millionth (-60 dB)
of the initial value?”
80/20The
Wallace
Sabine
reverberation time is the time for the
intensity to decay by a factor of 10 –6 (- 60dB)
of its initial value.
Physics 1251
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Room Acoustics
Intensity of Sound in a Room:
~ Io
Pressure
Amplitude
I = Io ‧ 10 –6 t / TR
t = ⅙ TR
~ 1/10 Io
t = ⅓ TR
~ 1/100 Io
Time (ms)
http://hybrid.colorado.edu/~phys1240/sounds.html
Physics 1251
80/20The
Unit 2 Session 18
Room Acoustics
Sabine Equation:
I = Io ‧ 10 – 6 (t/TR)
TR = 0.16 V/Se
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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 +…
Physics 1251
Unit 2 Session 18
Room Acoustics
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= 3x3x3 = 27.0 m3.
•Walls S1 = 4 (3x3 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
Physics 1251
Unit 2 Session 18
Room Acoustics
Summary:
Direct sound should come first
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Haas or precedence effect
Reverberant sound
TR = 0.16 V/Se
0.8 sec for clear speech, 1-2 for music
Freedom from echo and interference
Use diffuse and random reflectors
Background noise level
Assure good acoustic isolation