Acoustics

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Acoustics

• Reverberation

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What is Reverberation?

• Reverberation is multiple, random, blended
  repetitions of a sound.
• Three parts Direct Sound, Early Reflections,
  Later Reflections.
• Reverberation Time (Decay Time) is the time
  required for the sound in a room to decay 60 dB
  (also known as RT60). This represents a change in
  sound intensity or power of 1 million (10 log
  1,000,000 60 dB, or a change in sound pressure
  level of 1,000 (20 log 1,000 60 dB).

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Growth Decay of Sound

• W. C. Sabine, the Harvard pioneer in acoustics
  introduced the concept of RT60.

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Measuring Reverberation Time

• A common approach to measuring reverberation
  time. Figure B is a more common occurrence than
  figure A.

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Measuring Reverberation Time

• The sound sources used to excite the room must
  have enough energy throughout the spectrum to
  ensure decays sufficiently above the noise to
  give the required accuracy.
• Both impulse sources and those giving a
  steady-state output are used.

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Impulse Sources

• Common impulse sources are balloon pops and
  starter pistols. The diagram shows the reverb
  decays at several different octave ranges using a
  starter pistol.

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Steady-State Sources

• Bands of random noise give a steady and
  dependable indication of the average acoustical
  effects taking place.
• Octave and 1/3 octave bands of random noise
  (white or pink) are most commonly used.

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Mode Decay Variations

• The fluctuations in the decays result from beats
  between closely spaced modes.
• The differences in the four decays is due to the
  random nature of the noise.
• It is good practice to record several decays for
  each octave for each mic position of a room.
• Acoustical flaws can often be identified from
  aberrant decay shapes.

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Room Modes

• When sound is emitted in a room with parallel
  opposing walls, the room exhibits a resonance at
  a specific frequency determined by the equation
  f0 1,130/2L (or 565/L), where L is the length
  (in feet) of space between the two walls.
• A similar resonance occurs at 2f0, 3f0, 4f0, etc.
• These resonances are called modes specifically,
  axial modes.

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Frequency Beats
500 Hz
500 505 Hz
505 Hz
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Modal Interaction with Decay

• The diagram shows four different axial mode
  frequencies in the octave centered on 63 Hz.
• The lower the frequency, the less axial modes
  there are, so the more noticeable the beats
  become.

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Types of Room Modes

• Axial modes are derived from two walls,
  tangential modes are derived from four walls, and
  oblique modes are derived from all six surfaces.

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Frequency Effect

• This diagram shows typical fluctuation due to
  modal interference.

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Variation with Mic Position

• There is enough variation of reverb time from one
  position to another in most rooms to justify
  taking measurements at several positions.
• The average gives a better statistical picture of
  the behavior of the sound field in the room.
• If the room is symmetrical, measure only one side
  to minimize time and effort.

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Acoustical Coupling

• Acoustically coupled spaces are quite common in
  large public gathering spaces, but are also found
  in offices, homes, and other smaller spaces.
• Assuming that slope A is correct for the main
  room, persons subjected to slope B would hear
  inferior sound.

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Electroacoustical Coupling

• What is the overall effect when sound picked up
  from a studio having one reverberation time is
  reproduced in a listening room having a different
  reverberation time?
• The combined reverb time is greater than either
  alone
• If the reverb time of each room alone is the
  same, the combined reverb time is 20.8 longer
  than one of them.

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Optimum Reverberation Time

• The best reverb time for a space in which music
  is played depends on the size of the space and
  the type of music.
• Spaces for speech require shorter reverb times
  than for music.

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Optimum Reverb Time Examples
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Optimum Reverb Time Examples
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Bass Rise

• Taking the 1 kHz value as a reference, rises of
  80 at 63 Hz and 20 at 125 Hz were found to be
  acceptable in studios designed for voice
  recording.

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Living Room Reverb Times

• The average reverb time decreases from 0.69
  seconds at 125 Hz to 0.4 seconds at 8 kHz.

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The Sabine Equation
The absorption coefficients published by
materials manufacturers are typically Sabine
coefficients and can be applied directly in the
Sabine equation.
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Absorption and Absorption Coefficients

• Absorption in acoustics, the conversion of sound
  energy to heat.
• Absorption Coefficient the fraction of sound
  energy that is absorbed at any surface. It has a
  value between 0 and 1 and varies with the
  frequency and angle of incidence of the sound.
• Multiplying the surface area (in sq. ft.) by the
  absorption coefficient results in absorption
  units (sabins).

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Reverberation Calculations

• The diagram shows an example of the RT60
  calculations using the Sabine equation.

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Reverb Time (RT60) Calculations

• 1) Calculate the total areas of each type of
  surface
• 2) Find the absorption coefficients for each type
  of surface for the six frequencies 125 Hz, 250
  Hz, 500 Hz, 1 kHz, 2 kHz, 4 kHz
• 3) Multiply the area by the coefficient to
  determine the absorption units (sabins)
• 4) Add all sabins to find total sabins for each
  frequency
• 5) Plug all info into the Sabine equation to find
  the reverb time (RT60) for the room.

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Determining Room Treatments

• The result of the RT60 calculations show a short
  reverb time at low frequencies, long reverb time
  in the midrange, and medium reverb time in the
  high frequencies.

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Determining Room Treatments

• 1) Find treatments that will achieve the desired
  response
• 2) Determine how much treatment (in sq. ft.)
  would be necessary to add the desired amount of
  absorption (sabins) by dividing the sabins by the
  absorption coefficient. The result will be the
  amount of treatment in sq. ft.