Page 210 - Master Handbook of Acoustics

total absorption of room, metric sabins

Using the Sabine equation is a straightforward process, but a few notes are worth considering. The
quantity A is the total absorption in the room. For example, this accounts for the absorption of room
surfaces. (In many cases, audience absorption must be considered as well, and if desired, a value for
air absorption may be included, as described in the following text.) It would be easy to obtain the

total absorption if all the room surfaces were uniformly absorbing, but this condition rarely exists.
Walls, floor, and ceiling may be covered with quite different materials, and the doors, and windows
must be considered separately as well. Note that 1 sabin = 0.093 metric sabin.
The total absorption A can be found by considering the absorption contributed by each type of
surface. To obtain the total absorption A of the room, it is necessary to combine the respective
absorptions of the various materials lining the room by multiplying the square-foot area S of each
i
type of material by its respective absorption coefficient αi, and summing the result to obtain total
absorption. In particular, A = ΣS αi, where i represents each of the surface areas and its respective
i
absorption coefficient. The quantity ΣSα/ΣS represents the average absorption coefficient α average .
i
i i
For example, let us say that an area S (expressed in square feet or square meters) is covered with
i
a material having an absorption coefficient α , as obtained from the table in the appendix. This area
1
then contributes (S )(α ) absorption units, in sabins, to the room. Likewise, another area S is covered
1
1
2
with another kind of material with absorption coefficient α , and it contributes (S )(α ) sabins of
2
2
2
absorption to the room. The total absorption in the room is A = S α + S α + S α + …, etc. With a
2 2
3 3
1 1
figure for A in hand, it is a simple matter to use Eq. (11-1) or (11-2) and calculate the reverberation
time. This is further demonstrated in the examples at the end of this chapter.
The absorption coefficients of practically all materials vary with frequency. For this reason, it is
necessary to calculate total absorption at different frequencies. A typical reference frequency for
reverberation time is 500 Hz, and 125 Hz and 2 kHz are used as well. To be precise, any
reverberation time calculation should be accompanied by an indication of frequency. For example, a
reverberation time at 125 Hz might be quoted as RT 60/125 . When there is no frequency designation, the

reference frequency is assumed to be 500 Hz.
A word about the limitations of the Sabine equation is in order. For live rooms, the assumed
statistical conditions prevail and Sabine’s equation gives accurate results. However, in very
absorbent rooms, the equation produces erroneous results. For example, consider again the room

3
2
measuring 23.3 × 16 × 10 ft. This room has a volume of 3,728 ft and a total surface area of 1,532 ft .
If we further assume that all of its surfaces are perfectly absorbent (α = 1.0), we see that total
absorption is 1,532 sabins. Substituting these values:

Clearly, since the correct RT value in a perfectly absorbing room should be zero, the equation is
60
in error. Perfectly absorbing walls would allow no reflections. This paradox results from
assumptions upon which the Sabine equation is derived; in particular, it assumes that sound in a room
is diffuse, as in a live room. As a result, the Sabine equation is most accurate in live rooms where the
average absorption coefficient is less than 0.25.