Room Acoustics: Reverberation

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Room Acoustics Reverberation
Introduction to Acoustics

• University of Salford
• Acoustics Audio and Video Group

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Learning Outcomes

• Explain reflection, absorption, energy density,
  sound decay and reverberation.
• Understand the energy balance equation in rooms
• Explain and use Sabine's reverberation time
  equation

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Sound in Rooms

• reflection
• absorption
• rays or waves?

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The Sound Field

• Imagine a large number of rays emitted from a
  sound source
• Growth of sound field described by energy
  density, D
• D acoustic energy (in a sound field) per unit
  volume

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Energy balance (in)

• Energy in room DV
• Energy is supplied by sound source of power W
  Watts
• Energy per second supplied W

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Energy balance (out)

• At each reflection, let the proportion of energy
  absorbed be called a
• ( it can be shown that) the rate at which energy
  falls on wall area S is

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Energy Balance

• Rate of change of energy in room power input -
  power lost

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Reverberant Sound Decay

• If source switched off at time t 0

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Example
A lecture theatre has the following parameters V
1200 m3 S 700 m2 a 0.5 A loudspeaker is
left running in the room for some time and then
switched off. How long does it take the sound
energy density to reach a millionth of its
steady-state value? (Take c 343 ms-1)
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Reverberation Time

• Definition Reverberation time T is the time
  taken for D to fall to D0 / 106
• Sabines equation
• A total absorption in room (m2)

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Conclusions

• Sound field in a room is controlled by an energy
  balance
• Decaying sound field is described by
  reverberation time
• Sabines equation can be used to predict
  reverberation time - important for good room
  acoustics