Handbook for Sound Engineers

Acoustics for Auditoriums and Concert Halls 149

1000 Hz or the four octave bandwidths 500 Hz,
630 Hz, 800 Hz, and 1000 Hz, and referred to as the
mean reverberation time.
The desirable convenient value of the reverberation
time RT 60 depends on the kind of performance (speech
or music) and the size of the room. For auditoriums and
concert halls, the desired values of the mean reverbera-
tion time for between 500 Hz and 1000 Hz with a room
occupation of between 80% and 100% are given in
Fig. 7-1 and the admissible frequency tolerance ranges
are shown in Figs. 7-2 and 7-3. This shows that in order
to guarantee a specific warmth of sound with musical
performances, an increase of the reverberation time in
the low frequency range is admissible (see Section
7.2.1.2), while with spoken performances a decrease of
the reverberation time is desirable in this frequency
range (see Section 7.2.2.9).

The reverberation time of a room as defined by
Eyring mainly depends on the size of the room and on
the sound absorbing properties of the boundary surfaces
and nonsurface forming furnishings:

(7-4)

where,

RT 60 is the reverberation time in seconds,

V is the room volume in cubic meters (cubic feet),

is Atot/Stot which is the room-averaged coefficient of

absorption,

Atot is the total absorption surface in square meters

(square feet),

Stot is the total room surface in square meters (square

feet),

m is the energy attenuation factor of the air in m–1 (see

Fig. 7-4).

The correlation between the mean sound absorption

coefficient and the reverberation time for different rela-

tions between room volume V and total surface Stot is

graphically shown in Fig. 7-5.

The total sound absorption surface of the room Atot

consists of the planar absorption surfaces with the corre-

sponding partial surfaces Sn and the corresponding

frequency-depending coefficient of sound absorption

plus the nonsurface forming absorption surfaces Ak

consisting of the audience and the furnishings.

(7-5)

For an average sound absorption coefficient of up to

= 0.25, the Eq. 7-4 by Eyring^2 can be simplified by

means of series expansion according to Sabine^4 to

(7-6)

Figure 7-1. Recommended value of the mean reverbera-

tion time RTrecommended between 500 Hz and 1000 Hz for

speech and music presentations as a function of room

volume V.

Figure 7-2. Frequency dependent tolerance range of rever-
beration time RT 60 referred to RTrecommeded for speech
presentations.

(^1) » 3
Figure 7-3. Frequency-dependent tolerance range of rever-
beration time RT 60 referred to RTrecommended for music
presentations.
RT 60 0.163 V
–4ln  1 +aStot+ mV
= ------------------------------------------------------
0.049 for U.S. units
a
Dn
Atot DnSn
n

¦ Ak

k

= +¦

a

RT 0.163* V

Atot+ 4 mV

= ---------------------------

*0.049 for U.S. units