User Guide

Sound System Design Reference Manual
Step 1: Calculate relative sound levels produced
by the talker at microphone and listener.
We begin with the sound system off. Although
the calculations can be performed using only relative
levels, we will insert typical numbers to get a better
feel for the process involved.
The microphone is .6 meter from the talker, and
at this distance, the direct sound produces a level of
about 70 dB. Since D
C
for the unaided talker is only
1 meter, the microphone distance of .6 meter lies in
the transition zone between the direct field and the
reverberant field of the talker. By referring to Figure
6-3, we note that the combined sound levels of the
reverberant field and the direct field at a distance of
.6 meter must be about 1 dB greater than the direct
field alone. Therefore, since we have assumed a
level of 70 dB for the direct field only, the total sound
level at the microphone must be 71 dB.
Next, we use a similar procedure to calculate
the sound level at the listener’s position produced by
an unaided talker:
The listener is located 4.2 meters from the
talker, more than 3 times the critical distance of 1
meter, and therefore, well into the reverberant field of
the talker. We know that the sound level anywhere in
the reverberant field is equal to that produced by the
direct field alone at the critical distance. If the level
produced by direct sound is 70 dB at a distance of .6
meter, it must be 4.6 dB less at a distance of 1 meter,
or 65.4 dB, and the level of the reverberant field must
also be 65.4 dB. The sound level produced by the
unaided talker, at the listener’s position, therefore is
65.4 dB.
At this point, let us consider two things about
the process we are using. First, the definition of
critical distance implies that sound level is to be
measured with a random-incidence microphone. (For
example, we have chosen a non-directional system
microphone so that it indeed will “hear” the same
sound field as that indicated by our calculations).
Second, we have worked with fractions of decibels to
avoid confusion, but it is important to remember that
the confidence limits of our equations do not extend
beyond whole decibel values, and that we must
round off the answer at the end of our calculations.
Step 2:The sound field produced by the
loudspeaker alone.
Now let us go back to our example and
calculate the sound field produced by the
loudspeaker. Our system microphone is still turned
off and we are using an imaginary test signal for the
calculations. We can save time by assuming that the
test signal produces a sound level at the microphone
of 71 dB — the same previously assumed for the
unaided talker.
Figure 6-2. Indoor sound system gain calculations
6-3