# Reverberation Time

The persistence of sound in an enclosure after a sound source has stopped. Reverberation time is the time in seconds required for sound pressure at a specific frequency to decay 60 dB after a sound source is stopped.

For the ISO standard the reverberation time is measured over a -5 to -35dB sound pressure level below the constant sound source level as measured prior to it being switched off. When a sound source excites a room, forced oscillations are generated. These are characterised by the spectrum of the sound and the position of it in the room. When the sound source stops, the sound field changes in that only the normal modes of oscillation will persist. The rate of decay of these oscillations will depend on the absorption of the walls at the reflection and to a lesser extent air damping. The Q factor of the eigenmodes is thus determined by the absorption coefficient of the wallls and the mean free path between reflections. As the mean free path is generally longest for the axial modes they will have a longer reverberation time than the longitudinal and oblique modes.

In general bigger spaces will have longer reverberation times than smaller spaces.

Optimum reverberation times at 1kHz for a number of different room sizes and uses.

Long reverberation times degrade speech perception of hearing-impaired persons far more than normal-hearing persons.

The initial rate of decay of reverberant sound appears to be more important than the total reverberation time. A rapid initial decay is interpreted by the human ear as meaning that the reverberation time is short.

### Sabine Formula

The average sabine absorption coefficient, is defined as:

Where

A = total absorption in square metres [m2]
S = total surface area [m2]

The reverberation time is:

Where

V = room volume [m3]

### Norris Eyring Formula

The mean distance between reflections from the walls of a rectangular enclosure is:

Therefore, the number of reflections per second is:

At each reflection the sound energy is reduced by a factor:

Where

= area average random incidence energy absorption coefficient

Over a time interval of T the total attenuation of the sound energy is:

The definition of reverberation time is that the sound intensity level must drop by 60dB.

Therefore:

for T this gives:

### Millington-Sette Formula

Note that if any value of is equal to 1 then T goes to zero.