User Guide

Sound System Design Reference Manual
In the frequency range of interest, the
loudspeaker is assumed to have a directivity index
along its primary axis of 9 dB. From Figure 6-6 we
find the corresponding critical distance of 4.2 meters.
The loudspeaker’s directivity index at a vertical angle
of 60° is assumed to be -3 dB, with a corresponding
critical distance of 1 meter. The unaided talker has a
directivity index of 3 dB and his critical distance must
therefore be 2 meters.
Our next step in calculating system gain is to
find the difference in level produced by an unaided
talker at the listener position as contrasted with that
at the microphone position. In this example the
listener is 12 meters from the talker and the
microphone again is .6 meters away.
The talker’s critical distance of 2 meters is more
than 3 times the microphone distance. Therefore, the
microphone is well in the direct field of the talker. The
listener is more than 3 times the critical distance and
is well into the reverberant field of the unaided talker.
Setting the level produced by the unaided talker at
70 dB for a distance of .6 meters, we calculate that
the direct field at D
C
must be 60 dB, and since the
reverberant field must also equal 60 dB, the level
produced by the unaided talker at the listener’s
position is 60 dB.
The third step is to make similar calculations for
the loudspeaker alone. The listener is located on the
major axis of the loudspeaker and is more than 3
times the critical distance of 4.2 meters. The
microphone is located at a vertical angle of 60
degrees from the loudspeaker’s major axis, and also
is more than 3 times the critical distance (at this
angle) of 1 meter. Both the listener and the
microphone are located in the reverberant field of the
loudspeaker.
If the sound level produced by the loudspeaker
at the microphone can be no greater than 70 dB (the
same level as the talker) then the level produced by
the loudspeaker at the listener’s position must also
be 70 dB, since both are in the reverberant field.
Having established these relationships we
know that the talker produces a level at the listener’s
position of 60 dB with the sound system off and 70
dB with the sound system on, or a maximum
potential gain of 10 dB. Allowing 6 dB headroom in a
properly equalized system, we still realize 4 dB gain
at the listener’s position, and the sound system can
be said to provide a small but perceptible increase in
sound level.
Figure 6-6. Critical distance as a function of room
constant and directivity index or directivity factor
6-6