Is there anybody to explain Sabein's formula for reverberation time briefly?

Question

Is there anybody to explain Sabein's formula for reverberation time briefly?

Answer 1

Ugh I distrust empirically established formulae...All the formula really does is relate the time it takes for the reflection of a sound to decay to a certain level below the original sound, to the surface area of the container and absorption coefficient.  A version of formula is:

Reverb. Time (60 decibels below original) = 0.16 * V / (S * a)

where V is volume of the room, S is surface area, and a is absorption coefficient.  It makes sense too...eg, If two rooms A and B have the same volume, with walls of the same material, but A has a much larger surface area, then by the formul, the time it takes for the reverb sound in room A to decay will be much less than that for B, as we would expect since a larger surface area means a much more "wrinkled and creviced" surface, which isnt too kind to reverb.

Answer 2

1) The reverberation time depends on the frequency of the sound wave because absorption coefficient of most of the materials increases with frequency. Hence high frequency would have shorter reverberation time. Prof. Wallace C. Sabine (1868-1919) summarized his results in the form of the following equation:

Reverberation Time T  Ã¢ÂˆÂž (Volume of the Hall, V) / (Absorption Time, A)

Or T = KV / A -> (1), where K is proportionally constant. It is found to have a value of 0.161 when the dimensions are measured in metric units. Thus,T = (0.161V) / A, where A is given by ΣαS -> (2). Here the value of α depends on the nature of the material as well as the frequency of sound and S is the surface area of the material. Using (1) and (2) Sabine’s formula is rewritten as T = (0.161V) / ΣαS

2) Sabine’s work made the breakthrough to link the scientific knowledge to design applications by developing the reverberation formula (Sendra, 1999). RT=0.163V/A (1.1)

Where RT reverberation time,

V room volume,

A room absorption.

The virtue of this formula is not only its simplicity, but also its clear recognition and definition of reverberation time as a design goal. As Sabine considered architectural acoustics as two domains. One is pure physical investigation of sound propagation and its interaction with enclosure, and the other is subjective perception of musical effects and its quantification. Sabine’s formula is used to predict the reverberation time, while the reverberation time is used as the critical parameter influencing music appreciation and its optimum range is investigated. The establishment of Sabine’s formula is considered as the starting point of architectural acoustics (Sendra, 1999).This formula also proves to be the most useful and popular tool in concert hall design.

AJM