Page 187 - The Master Handbook Of Acoustics

162 CHAPTER SEVEN

Reverberation Calculation:
4 Example 2
The goal now is to correct the reverberation
Reverberation time - seconds 3 2 A of curve A of Fig. 7-23. It is evident that

much absorption is needed at midband
frequencies, a modest amount at higher fre-
quencies, and very little at lower frequen-
cies. The need is for a material having an
1
absorption characteristic shaped more or
B
less like the reverberation curve A. Skip-
0 ping the laborious thumbing through of
125 250 500 1 k 2 k 4 k 3
Frequency - Hz handbooks, 4-in acoustical tile seems to
have the right shape. Giving no thought at
FIGURE 7-23
this point to how it is to be distributed,
The calculated reverberation characteristics of a 23.3 × what area of this tile is required to correct
16 × 10 ft room: (A) the “as found,” untreated condi- for Fig. 7-23A?
tion of Example 1, (B) treated condition of Example 2.
A new table, Fig. 7-24, is set up to orga-
nize the calculations. Everything is identi-
3
cal to Fig. 7-22 except that the ⁄4-in acoustical tile has been added with
coefficients from the appendix. What area of tile is required? In Fig.
7-22 a total of 53.9 sabins is noted at the peak reverberation time at
1 kHz and 339.8 sabins at 125 Hz at which the reverberation time is a
reasonable 0.54 sec. How much ⁄4-in acoustical tile would be required
3
to add 286 sabins at 1 kHz? The absorption coefficient of this material
is 0.84 at 1 kHz. To get 286 sabins at 1 kHz with this material would
require 286/0.84 = 340 sq ft of the material. This is entered in Fig. 7-24
and the calculations extended. Plotting these reverberation time points
gives the curve of Fig. 7-23B. Obtaining reverberation time this uniform
across the band on the first trial is unusual, but satisfying. The overall
precision of coefficients and measurements is so poor that the devia-
tions of curve B from flatness are insignificant.
No carpet has been specified in this example and people usually
demand it. The use of carpet would change everything as much
absorption in the high frequencies is added.

Reverberant Field

In our 23.3 × 16 × 10 ft room the volume is 3,728 cu ft. The inner sur-
face area is 1,533 sq ft. By statistical theory (geometrical ray acoustics