Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 2
• Session 18 MWF
• Room Acoustics

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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- f2? ?262-264 ? 2 Hz.
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Reflective Review
• Wave motion is characterized by
• Reflection
• Refraction
• Diffraction
• Doppler Shift
• Beats
• Interference

The Reflective Ref Differed Dopily, Beating
Interference.
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Physics 1251 Unit 2 Session 18 Room Acoustics

• When the surface is smooth we have specular
  (mirror-like) reflection.

Reflection
Smooth Surface Roughness ? ?
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Refraction occurs when a wave enters a medium
  that has a different velocity?

Refraction
V1 lt V2
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Physics 1251 Unit 2 Session 18 Room Acoustics

• What happens when a wave is partially obstructed?

Diffraction
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Physics 1251 Unit 2 Session 18 Room Acoustics
Doppler Shift Moving source
Higher f
Lower f
fobserver fsource v vobserver / v
vsource
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Physics 1251 Unit 2 Session 18 Room Acoustics
Beats f1 f2
In phase
Out of phase
fmean
fbeat
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Physics 1251 Unit 2 Session 18 Room Acoustics
Interference
Constructive
Destructive
Softer
Louder
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Physics 1251 Unit 2 Session 18 Room Acoustics

• 1' Lecture
• Factors that most determine room acoustics
• Direct sound
• Reverberant sound
• Freedom from echo and interference
• Background noise level

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Physics 1251 Unit 2 Session 18 Room Acoustics

• Greek Amphitheater
• At Epidauros, Greece

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Physics 1251 Unit 2 Session 18 Room Acoustics
Constructive Interference
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Greek Amphitheater
• Acoustics

Reflected sound
Direct sound
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Musiksvereinssaale Vienna

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Physics 1251 Unit 2 Session 18 Room Acoustics

• Royal Festival Hall
• http//www.coxt.freeeserve.co.uk/hall.jpg

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Physics 1251 Unit 2 Session 18 Room Acoustics

• Morton Meyerson Symphony Center
• Dallas, Texas

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Physics 1251 Unit 2 Session 18 Room Acoustics

• Winspear Center
• Edmonton, Canada

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Physics 1251 Unit 2 Session 18 Room Acoustics

• 80/20Standards for Good Acoustics
• Clarity
• Uniformity
• Envelopment
• Smoothness
• Reverberation
• Performer satisfaction
• Freedom from noise

little overlap of sounds
everywhere the same
sound from all directions
no echoes
appropriate length of time
reflected to stage
no competition
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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.

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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
  (lt100 ms) reflections are louder.
• The direct sound should arrive first.

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Physics 1251 Unit 2 Session 18 Room Acoustics

• Room Acoustics Reverberation

Speaker
Hearer
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Energy Lost in Reflections
• The sound reflects many times, each time losing
  energy to the reflecting surface.
• The quantity a is the absorptivity of the
  surface.
• The intensity of the sound that is lost in a
  reflection is ?Ilost a Iin.

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Physics 1251 Unit 2 Session 18 Room Acoustics

• The intensity of the reflected wave is
• Ireflected (1-a) Iin.

a
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Physics 1251 Unit 2 Session 18 Room Acoustics

• The intensity of the reflected wave is
• Ireflected (1-a) Iin.
• Values for a, the absorptivity, for many types of
  surfaces have been measured and appear in
  extensive tables.

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Physics 1251 Unit 2 Session 18 Room Acoustics

• The Absorptivity
• Material a (at 500 Hz)
• Acoustic tile 0.6
• Plaster wall 0.1
• Concrete 0.02
• Person 0.8 (x1 m2)

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Physics 1251 Unit 2 Session 18 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 reverberation time is the time for the
  intensity to decay by a factor of 10 6 (-
  60dB) of its initial value.

Wallace Sabine
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Intensity of Sound in a Room

Io
I Io ? 10 6 t / TR
t ? TR
1/10 Io
Pressure Amplitude
t ? TR
1/100 Io
Time (ms)
http//hybrid.colorado.edu/phys1240/sounds.html
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Physics 1251 Unit 2 Session 18 Room Acoustics

• 80/20The Sabine Equation
• I Io ? 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.
• a is the absorptivity of the surface (in table)
• Se a1 S1 a2 S2 a3 S3 a4 S4

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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
• a 0.02Se (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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Physics 1251 Unit 2 Session 18 Room Acoustics

• Summary
• Direct sound should come first
• 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