## Calculation of Reverberation Time

Reverberation time is the time required for a steady-state sound to reach one millionth or -60dB of its original intensity.

There are several models used in calculating the reverberation time but the first and most commonly used is that of Wallace Sabine (1868-1919). The Sabine equation

states that the reverberation time (Tr, in seconds) is directly proportional to the volume of the room (V, [m3]) and inversely proportional to the room's effective surface area (A, [m2]). The effective surface area is the sum of the product of an area covered by a particular material and the material's absorption coefficient.

The units of aA are sabins.  For a surface of area A and with absorption coefficient a, aA can be thought of as the equivalent area of a perfect absorber (open window). The absorption coefficient varies with frequency and so the reverberation time is a function of frequency.

The above table was scanned from page 324 of Donald Hall's Musical Acoustics text published by Brooks/Cole, ISBN 0-534-13248-0.

another table can be found at this link.

Example: Calculate the reverberation time at 125Hz, 500Hz, and 2000Hz for a classroom that is 8m wide by 12m long by 3m high. The floor is vinyl tile on concrete, the walls are made of 1/2" drywall (gypsum) board, and the ceiling is acoustic tile suspended in frames.

 Surface Area [m2] a125*Area [sabins] a500*Area [sabins] a2000*Area [sabins] Walls 120 36 6 8.4 Floor 96 1.9 2.9 2.9 Ceiling 96 48 57.6 67.2 Total Effective Area 85.9 66.5 78.5 Frequency 125 Hz 500Hz 2000Hz Reverb Time 0.55 sec 0.70 sec 0.60 sec

Sample Reverb Calculation for 125 Hz

This room will have an appropriate reverb time for speech but is too short at all frequencies for any type of musical performance. The room will be bright with a high degree of clarity but because of the parallel surfaces will suffer from resonances. The surfaces are close enough that no echoes will be detected. Adding wood/metal seating will not change the reverb time very much, but allowing the seats to be occupied will greatly increase the effective area and lower the reverb time.