User Guide

Sound System Design Reference Manual
The Concept of Acoustical Gain
Boner (4) quantified the concept of acoustical
gain, and we will now present its simple but elegant
derivation. Acoustical gain is defined as the increase
in level that a given listener in the audience
perceives with the system turned on, as compared to
the level the listener hears directly from the talker
when the system is off.
Referring to Figure 4-3, let us assume that both
the loudspeaker and microphone are omnidirectional;
that is, DI = 0 dB and Q = 1. Then by inverse square
loss, the level at the listener will be:
70 dB - 20 log (7/1) = 70 - 17 = 53 dB
Now, we turn the system on and advance the
gain until we are just at the onset of feedback. This
will occur when the loudspeaker, along the D
1
path,
produces a level at the microphone equal to that of
the talker, 70 dB.
If the loudspeaker produces a level of 70 dB at
the microphone, it will produce a level at the listener
of:
70 - 20 log (6/4) = 70 - 3.5 = 66.5 dB
With no safety margin, the maximum gain this
system can produce is:
66.5 - 53 = 13.5 dB
Rewriting our equations:
Maximum gain =
70 - 20 log (D
2
/D
1
) - 70 - 20 log (D
0
/D
s
)
This simplifies to:
Maximum gain =
20 log D
0
- 20 log D
s
+ 20 log D
1
- 20 log D
2
Figure 4-2. Electrical response of a sound system 3 dB below sustained acoustical feedback
Figure 4-3. System gain calculations, loudspeaker and microphone both omnidirectional
4-2