User Guide
Sound System Design Reference Manual
How Much Gain is Needed?
The parameters of a given sound reinforcement
system may be such that we have more gain than we
need. When this is the case, we simply turn things
down to a comfortable point, and everyone is happy.
But things often do not work out so well. What is
needed is some way of determining beforehand how
much gain we will need so that we can avoid
specifying a system which will not work. One way of
doing this is by specifying the
equivalent
, or
effective,
acoustical distance
(EAD),
as shown in Figure 4-6.
Sound reinforcement systems may be thought of as
effectively moving the talker closer to the listener. In
a quiet environment, we may not want to bring the
talker any closer than, say, 3 meters from the
listener. What this means, roughly, is that the
loudness produced by the reinforcement system
should approximate, for a listener at
D
0
, the loudness
level of an actual talker at a distance of 3 meters.
The gain necessary to do this is calculated from the
inverse square relation between
D
0
and
EAD
:
Necessary gain = 20 log D
0
- 20 log EAD
In our earlier example, D
0
= 7 meters. Setting
EAD = 3 meters, then:
Necessary gain = 20 log (7) - 20 log (3)
= 17 - 9.5 = 7.5 dB
Assuming that both loudspeaker and
microphone are omnidirectional, the maximum gain
we can expect is:
Maximum gain =
20 log (7) - 20 log (1) + 20 log (4) - 20 log (6) - 6
Maximum gain = 17 - 0 + 12 - 15.5 - 6
Maximum gain = 7.5 dB
As we can see, the necessary gain and the
maximum gain are both 7.5 dB, so the system will be
workable. If, for example, we were specifying a
system for a noisier environment requiring a shorter
EAD
, then the system would not have sufficient gain.
For example, a new
EAD
of 1.5 meters would require
6 dB more acoustical gain. As we have discussed,
using a directional microphone and a directional
loudspeaker would just about give us the needed 6
dB. A simpler, and better, solution would be to reduce
D
s
to 0.5 meter in order to get the added 6 dB of gain.
In general, in an outdoor system, satisfactory
articulation will result when speech peaks are about
25 dB higher than the A-weighted ambient noise
level. Typical conversation takes place at levels of 60
to 65 dB at a distance of one meter. Thus, in an
ambient noise field of 50 dB, we would require
speech peaks of 75 to 80 dB for comfortable
listening, and this would require an EAD as close as
0.25 meter, calculated as follows:
Speech level at 1 meter = 65 dB
Speech level at 0.5 meter = 71 dB
Speech level at 0.25 meter = 77 dB
Let us see what we must do to our outdoor
system to make it work under these demanding
conditions. First, we calculate the necessary
acoustical gain:
Necessary gain = 20 log D
0
- 20 log EAD
Necessary gain = 20 log (7) - 20 log (.25)
Necessary gain = 17+ 12 = 29 dB
4-4
Figure 4-6. Concept of Effective Acoustical Dustance (EAD)