EELE 217 Reverb Topics

Basic Considerations for Reverberation

The reverberation time of a large room is specified by the number of seconds required for the sound pressure level to decrease 60 dB once the sound source is stopped.  Reverberation time is often specified with the notation RT60 or T₆₀.  Because reverberation generally differs from one frequency range to another, it is important to specify T₆₀ at a range of different frequencies in order to adequately describe a particular room.

Estimating room reverberation:  The Sabine equation

The Sabine equation is a way to estimate the reverberation time for a large room.  The actual measured reverberation time will likely be different than the Sabine estimate, but the equation is often useful in guiding the selection of surface treatment types and sizes.

                   T60 = 0.161 * V / SUM{ S_i * a_i  }      Sabine Reverberation Time (estimate) [seconds]

V = total volume in m³

S_i = area of surface i in m²

a_i = absorptivity of surface i

When located close to a sound source in a reverberant room, the sound field consists of the direct sound from the source plus the reverberant sound from the room.  As one moves away from the source, the sound pressure level associated with the direct sound from the source decreases by 6dB for every doubling in distance, while the reverberant sound level remains roughly constant throughout the room.  Thus, the direct-to-reverberant ratio changes from being dominated by the direct sound when near the source, to being mostly reverberant sound when located far from the source.

Example of Sabine reverberation time calculation

Consider a rectangular room with floor dimensions 15m x 20m and a ceiling height of 4m.

For this example, let’s assume that:

Floor material has absorptivity a = 0.2
Ceiling a = 0.4
Wall material has a = 0.6

There are six surfaces:

Floor area = 15x20 = 300 m²
Ceiling area = 15x20 = 300 m²
Front and back walls = 15x4 = 60 m² each
Side walls = 20 x 4 = 80 m² each

And the Volume of the room is:  L x W x H = 15 x 20 x 4 m³ = 1200 m³

Using the Sabine formula with volume V and total absorption A = SUM( surface absorptions ), the numerator becomes  0.161 V = 0.161 x 1200 = 193.2

The denominator is the sum of each surface area times its absorptivity:

Floor:  300 x 0.2 = 60
Ceiling:  300 x 0.4 = 120
Front:  60 x  0.6 = 36
Back:  60 x 0.6 = 36
Side1: 80 x 0.6 = 48
Side2: 80 x 0.6 = 48

Sum in denominator = 348

 So the estimated T₆₀ for this example room is  193.2 / 348 = 0.56 seconds

Typical target values for reverberation time

Room reverberation:  the critical distance

The distance at which the direct sound level and the reverberant sound level are roughly equal is known as the critical distance for the room, often specified by the symbol r_d.

An estimate of the critical distance is given by the equation:

                              r_d = 0.25 * sqrt(  SUM{ S_i * a_i  }  / π  )

S_i = area of surface i in m²

a_i = absorptivity of surface i

Roughly speaking, a microphone located closer to the source than the critical distance will pick up mostly the direct sound and proportionately less reverb, while a microphone located farther than the critical distance will receive mostly reverberant sound.

Table 12.5.1 Representative Sabine absorptivities and absorptions

                                                                                                Sound Absorption A in m²