Sabine equation

Sabine's reverberation equation was developed in the late 1890s in an empirical fashion. He established a relationship between the RT ₆₀ of a room, its volume, and its total absorption (in sabins). This is given by the equation:

.

where is a number that relates to the speed of sound in the room, is the volume of the room in m³, total surface area of room in m², is the average absorption coefficient of room surfaces, and the product is the total absorption in sabins.

The total absorption in sabins (and hence reverberation time) generally changes depending on frequency (which is defined by the acoustic properties of the space). The equation does not take into account room shape or losses from the sound travelling through the air (important in larger spaces). Most rooms absorb less sound energy in the lower frequency ranges resulting in longer reverb times at lower frequencies.

The reverberation time RT ₆₀ and the volume V of the room have great influence on the critical distance d _c (conditional equation):

where critical distance is measured in meters, volume is measured in m³, and reverberation time is measured in seconds.

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