User Guide

Sound System Design Reference Manual
From our calculations of critical distances, we
see that the unaided talker will produce a sound level
at the listener of 59 dB in an empty room and about
55 dB with a full audience. For a usable working
delta of -6 dB, the calculated acoustic gain at the
listener’s position is about 5 dB in an empty room
and about 9 dB when full.
Can we get more gain by turning off the
loudspeaker directly over the microphone? Not in a
densely packed array such as this. The loudspeakers
are mounted close together to produce a uniform
sound field at ear level. As a result, the contribution
of any one loudspeaker is relatively small. However,
by turning off all the loudspeakers in the performing
area and covering only the audience, some increase
in system gain may be realized.
In the example just given, each loudspeaker is
assumed to have a directivity index in the speech
frequency region of +6 dB at 0°, +3 dB at 45°, and
0 dB at 60°. Suppose we use only the 25
loudspeakers over the audience and turn off the 15
loudspeakers in the front of the room. In theory, the
increase in potential gain is only 1 dB with a single
listener or 2 dB when the audience area is filled.
Even if we allow for the probability that most of the
direct sound will be absorbed by the audience, it is
unlikely that the gain increase will be more than 3 dB.
The calculations required to arrive at these
conclusions are tedious but not difficult. The relative
direct sound contribution from each of the
loudspeakers at microphone and listener locations is
calculated from knowledge of polar patterns and
distances. By setting an arbitrary acoustic output per
loudspeaker, it is then possible to estimate the sound
level produced throughout the room by generally
reflected sound (reverberant field) and that produced
by reflected plus quasi-direct sound.
System Gain vs. Frequency Response
In the preceding examples we have not defined
the frequency range in which gain calculations are to
be made. In most sound systems the main reason for
worrying about system gain is to make sure that the
voice of a person talking can be amplified sufficiently
to reach a comfortable listening level in all parts of
the seating area. Therefore, the most important
frequency band for calculating gain is that which
contributes primarily to speech intelligibility: the
region between 500 and 4000 Hz.
Below 500 Hz the response of the system can
be gradually shelved, or attenuated, without seriously
degrading the quality of speech. Above 4 kHz sound
systems tend to take care of themselves, due to the
increase in overall acoustical sound absorption. At
very high frequencies, most environments are
substantially absorptive, the air itself contributes
considerable acoustical absorption and loudspeaker
systems tend to become directional. These factors
make it highly unusual to encounter feedback
frequencies much above 2500 Hz.
To make sure that a sound reinforcement
system will successfully amplify speech, it is a good
idea to make gain calculations in at least two
frequency bands. In a well-designed system, if
calculations are made for the regions centered at 1
kHz and 4 kHz, chances are that no unforeseen
problems in achieving desired system gain will be
encountered.
However, the region below 500 Hz cannot
simply be ignored. The room constant and the
directivities of the loudspeaker system and the
microphone should be checked in the 200 - 500 Hz
range to make sure that there are not substantial
deviations from the calculations made at 1 and 4
kHz. If the room has very little absorption below 1
kHz, and if the loudspeaker system becomes
nondirectional in this region, it may be impossible to
achieve satisfactory system gain without severely
attenuating the mid-bass region. The result is the all
too familiar system which provides satisfactory
speech intelligibility, but which sounds like an
amplified telephone.
The Indoor Gain Equation
From the foregoing discussions, we can
appreciate the complexity of indoor system gain
analysis and the need for accurately calculating the
attenuation of sound along a given path, from either
talker or loudspeaker, noting when we leave the
direct field and make the transition into the
reverberant field. If we were to attempt to establish a
general system gain equation, we would have a very
difficult task. However, in the special case where the
microphone is in the talker’s direct field, and both
microphone and listener are in the loudspeaker’s
reverberant field, then the system gain equation
simplifies considerably.
Let us consider such an indoor system, first
with the system turned off, as shown in Figure 6-10.
If the talker produces a level L at the microphone,
then the level produced at the listener will be:
6-9