Physics of Music Lecture 8

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Physics of MusicLecture 8

• Room Acoustics
• Prof. Charles E. Hyde-Wright
• Berg Stork Chapter 8

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Reverberation

• Sound bounces off the walls.
• The listener hears both direct sound and
  (multiply) reflected sound.
• With each bounce, the intensity I0 drops to aI0,
  where alt1 is the reflectivity of the wall.
• After n-bounces, the intensity is anI0.

Response to a sustained tone
Response to a Sound impulse
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Exponential Decay of Intensity

• If d is a typical dimension of the room, then the
  average time between bounces is d/S, and in a
  time t there are n(t S /d) bounces (S speed of
  sound).
• The sound intensity as a function of time is
• I(t) I0 a(t S /d) exponential decay with
  time
• Exponential decay law can be written
• I(t) I0 10(-6 t / tR) tR -6 d / S loga
• Reverberation time tR is time for intensity to
  decay by 106 (60dB)

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Reverberation Time

• Exponential decay with time
• I(t) I0 a(t S /d) I0 10(-6 t / tR)
• tR -6 (d/S) / loga
• Dimension d proportional to volume/surface-area
• For a cube, d 6V/A
• Reflectivity a 1-a, aabsorption coefficient
• If altlt1, then loga log(1-a) -a log(2.718)
• tR 55.2 V/(SAeff)
• Aeffa1A1 a2A2
• Ai area of surface i., V volume of room
• ai1-ai absorption coefficient of surface i.

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Reverberation Time and Absorption CoefficientstR
55.2 V/S (a1A1 a2A2 )

• tR time for the sound intensity to decay by a
  factor of 106 60 dB
• In time tR/2, sound decays by 30 dB (1/1000)
• In time 2 tR, sound decays by 120 dB (1/1012)
• Notice that reverberation time is frequency
  dependent

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Ideal Reverberation Time

• Speech, Different music styles prefer different
  reverberation times.

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Reverb Time for OCNPS 146

• Front and rear walls 3m x 5m
• Wall board, a(500,2000Hz) (0.1, 0.04)
• Side walls 3m x 15 m
• Floor and ceiling 5m x 15 m
• Concrete a(500,2000Hz) (0.02, 0.02)
• Acoustic board a(500,2000Hz)(0.80,0.90)
• A(500Hz)
• 2(15m2)0.1 2(45m2)0.1 (75m2)0.02
  (75m2)0.873.5m2
• tR 55.2 V/(SA) 55.2 (3x5x15m3)/(73.5m2340m/s)
  
• 0.5 sec

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Subjective/Objective Qualities in Acoustics

• Liveness
• Long reverb time live
• Short reverb time dead
• Out-of-doors is very dead, tR0
• Intimacy
• How close do the performers seem to be?
• Time delay between direct sound and first reverb.
• Short time delay intimate (sounds like small
  room)
• Improve intimacy with reflectors close to
  musicians.
• Reflectors also increase total volume of sound.

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Fullness / Clarity

• Full sound has a lot of reflected sound
• Slow music prefers fullness
• Clarity implies very little reflected sound
• Speech, fast music requires clarity
• Fullness is almost synonymous with liveness, or
  long reverb time.

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Warmth / Brilliance

• Warmth results when reverb time is longer at low
  frequencies than at high frequencies
• Fullness in bass, Clarity in treble
• Brilliance is the opposite
• Predominance of high frequencies in reflected
  sound
• Too much brilliance gives a unpleasant ringing.
• Most soft wall materials (curtains, acoustic
  tile) will automatically give warmth, hard wall
  materials give brilliance (Table 8-3)

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Texture

• Texture is the envelope of the decaying sound
• A smooth envelope requires many closely spaced
  reverberations, rather than a few widely spaced
  strong echoes.
• Smooth texture is obtained by breaking up the
  wall and ceiling into many irregular reflecting
  surfaces.
• OCNPS 200 initially had a very long reverb, with
  strong echoes. Mostly cured by adding acoustic
  paneling.
• Graduation speeches in SCOPE were
  incomprehensible.

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Blend Ensemble

• Blend is uniformity of sound intensity received
  by listener from all members of ensemble
• Ensemble is the ability of all members of the
  orchestra to hear each other
• Reflectors near ensemble (remember Intimacy) must
  be diffuse or irregular, scattering the sound in
  all directions

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Amplified (live) sound

• Indoors or outdoors, amplified sound should
  provide all of the features discussed previously.
• Speakers staggered throughout the audience must
  have appropriate delay, since electricity travels
  faster than sound.
• Speakers facing back towards stage can provide
  reverb, essential to intimacy, warmth, texture.
• Or you can just crank it up to ear-splitting
  noise.