Page 185 - The Master Handbook Of Acoustics

160 CHAPTER SEVEN

engineering computations rather than the Eyring equation or the
several derivatives thereof. Two unassailable reasons for this are
simplicity and consistency. In spite of the fact that this simpler pro-
cedure was suggested as early as 1932, and Young’s convincing argu-
ments for it were given in 1959, many technical writings have
continued to put forth the Eyring or other equations for studio use.
Even though there was authoritative backing for using Eyring for
more absorbent spaces, why continue if the commonly available coef-
ficients apply only to Sabine? These are the reasons why we use only
Equation 7-1 in this volume.
The total Sabine absorption in a room would be easy to get if all sur-
faces of the room were uniformly absorbing, but this condition rarely
exists. Walls, floor, and ceiling may well be covered with quite different
materials, and then there are the doors and windows. The total absorp-
tion, Sa, of Equation 7-1, can be found by considering the absorption
contributed by each type of surface. For example, in our imaginary
room, let us say that an area S 1 is covered with a material having an
absorption coefficient a 1 as obtained from the table in the appendix.
This area then contributes (S 1 ) (a 1 ) absorption units, called sabins, to the
room. Likewise, another area S 2 is covered with another kind of mater-
ial with absorption coefficient a 2 , and it contributes (S 2 ) (a 2 ) sabins
of absorption to the room. The total absorption in the room is Sa =
S 1 a 1 S 2 a 2 S 3 a 3 .... etc. With a figure for Sa in hand, it is a simple
matter to go back to Equation 7-1 and calculate the reverberation time.

Reverberation Calculation: Example 1
A completely untreated room will first be taken to illustrate the imple-
mentation of Sabine’s equation (Eq. 7-1). The dimensions of the room
are assumed to be 23.3 × 16 × 10 ft. Other assumptions are that the
room has a concrete floor and that the walls and the ceiling are of
frame construction with ⁄2 in gypsum board (drywall) covering. As a
1
simplification the door and a window will be neglected as having
minor effect. The tabulation of Fig. 7-22 illustrates the untreated con-
dition. The concrete floor area of 373 sq ft and the gypsum board area
of 1,159 sq ft are entered in the table. The appropriate absorption coef-
ficients are entered from the table in the appendix for each material
and for the six frequencies. Multiplying the concrete floor area of S =
373 sq ft by the coefficient a = 0.01 gives Sa = 3.7 sabins. This is