User Guide

Sound System Design Reference Manual
The loudspeaker is mounted at the intersection
of wall and ceiling. Its directivity index, therefore, is
assumed to be 6 dB. In this room, the critical
distance for the loudspeaker is 1.4 meters. This is
almost the same as the distance from the
loudspeaker to the microphone. Since the
microphone is located at the loudspeaker’s critical
distance, and since we have assumed a level of 71
dB for the total sound field at this point, the direct
field at the microphone must equal 71 dB minus 3
dB, or 68 dB.
The listener is 4.8 meters from the loudspeaker
(more than 3 times the critical distance) and
therefore, well into the reverberant field of the
loudspeaker. We know that the level in the
reverberant field must equal the level of the direct
field alone at the critical distance. The sound level at
the listener’s position produced by the loudspeaker
must, therefore, be 68 dB.
Step 3: Potential acoustic gain is now considered.
Since we deliberately set up the example to
represent the condition of maximum theoretical gain
for a properly equalized system, we can use these
same figures to calculate the difference in level at the
listener’s position between the unaided talker and the
talker operating with the system turned on. We have
calculated that the unaided talker produces a level at
the listener’s position of 65.4 dB. We have also
calculated that the level produced by the
loudspeaker at the listener’s position is 68 dB. The
acoustic gain of the system for this specific set of
conditions must be the difference between the two,
or only 2.6 dB. Obviously such a sound
reinforcement system is not worth turning on in the
first place.
Note that system acoustical gain is dependent
upon the distance from the microphone to the talker.
A more general concept is that of system delta.
According to the Boner paper, the maximum
theoretical ∆ of a properly equalized system is unity.
In our example, ∆ works out to be -3 dB. Why?
The Boners emphasize that for maximum
system gain the microphone must be in the direct
field of the talker and in the reverberant field of the
loudspeaker. But in our example, the microphone is
not quite in the direct field of the talker and is located
at the critical distance of the loudspeaker! To achieve
more gain, we might move the microphone to a
distance .3 meter from the talker and use a more
directional loudspeaker. This would result in a 3 dB
increase in ∆ and a potential acoustic gain at the
listener’s position of about 9 dB.
In practice, however, we cannot operate the
system at a point just below sustained feedback.
Even if we modify the system as described above,
our practical working gain will only be about 3 dB.
Our calculations merely prove what we could have
guessed in advance: in a room this small, where an
unaided talker can easily produce a level of 65 dB
throughout the room, a sound system is unnecessary
and of no practical benefit.
Figure 6-3. Relative SPL vs. distance from source in relation to critical distance
6-4