Modeling Reverberation Time

Sabine is credited with modeling the reverberation time with the simple relationship which is called the Sabine formula:

where V is the volume of the enclosure and

and a is the absorption coefficient associated with a given area S.

Sound Absorption Coefficient

When a sound wave in a room strikes a surface, a certain fraction of it is absorbed, and a certain amount is transmitted into the surface. Both of these amounts are lost from the room, and the fractional loss is characterized by an absorption coefficient a which can take values between 0 and 1, 1 being a perfect absorber.

The effective absorbing area is a factor in determining the reverberation time of an auditorium. The absorption coefficient of a surface typically changes with frequency, so the reverberation time is likewise frequency dependent. A table of absorption coefficients can be used in calculations of reverberation time with the Sabine formula.

Sabine Formula Discussion

The Sabine formula works reasonably well for medium sized auditoriums but is not to be taken as an exact relationship. It tends to overestimate the reverberation times for enclosures of high absorption coefficient. A better approximation for such enclosures utilizes an overall average absorption coefficient:

Note that this reduces the calculated reverberation time. The Sabine formula also neglects air absorption, which can be significant for large auditoriums.

Table of Absorption Coefficients

Air Absorption

Air absorption is usually neglected in calculations of reverberation times for auditoriums, but for large enclosures it may become significant. Air absorption is greater for high frequencies and is dependent upon air temperature and relative humidity. Rossing reports the following values and the modification of the Sabine formula:

Air absorption m per cubic meter: Air at 2000 Hz 4000 Hz 8000 Hz 20°C, 30% RH 0.012 0.038 0.136 20°C, 50% RH 0.010 0.024 0.086

Air absorption m per cubic foot: Air at 2000 Hz 4000 Hz 8000 Hz 20°C, 30% RH 0.004 0.012 0.041 20°C, 50% RH 0.003 0.007 0.026