Handbook for Sound Engineers

Sound System Design 1245

four questions are important enough that, in the next

section, they form the basis for an expansion of the

simplified system to cover the effects of reverberation

on indoor systems.

34.2.3 Indoor Sound Reinforcement System Model

So far, the discussion of sound reinforcement has been
simplified by neglecting the effects of echoes and rever-
beration. Now, however, it’s time to modify the mathe-
matical model of the sound reinforcement system to
include these effects. Doing this, of course, creates a
much more useful model, one that can be used success-
fully both indoors and out.
The equations presented in this section used to deter-
mine indoor attenuation, critical distance, potential and
needed acoustic gain, and electrical power required are
derived from concepts presented by Hopkins and
Stryker. The equation for Alcons was derived by Peutz
and Klein. The acoustic gain (potential, and needed)
equations were developed by Don Davis of
Syn-Aud-Con. The critical distance (Dc) equation was
developed by Don Davis and Mel Sprinkle. The equa-
tions have been manipulated and modified by a number
of writers to make them more useful to sound system
designers. The most notable of these writers are Don
and Carolyn Davis.
The equations presented here are basically the same
as those used in Sound System Engineering by Don and
Carolyn Davis.^4 However, as presented here, the equa-
tions have been algebraically manipulated by this author
to make them somewhat easier to explain and to make
them more adaptable to computer analysis. As in the
simplified model, the equations in this section help the
designer answer the four questions.

34.2.3.1 Echoes and Reverberation

Echoes and reverberation are both reflections of sound.
A reflection is called an echo if the time between the
original sound and the reflection is long enough that
both sounds can be heard distinctly (about 70 ms or
greater). If a room has lots of reflections and they are
closely spaced in time so that distinct echoes are not
audible, this large number of reflections is known as
reverberation. A much more detailed discussion of
echoes, reverberation, and general room acoustics can
be found in Chapters 1, 3, 5, and 7.

34.2.3.1.1 When an Echo Is a Problem

Some rooms have one or more distinct echoes but very

little reverberation. A conference room with carpeting,

draperies, padded seating, and acoustical ceiling tile, for

example, may have little or no reverberation. That same

room, however, may have a hard rear wall that produces

a single slap-back echo (so called because it slaps back

at talkers every time they try to speak from a location in

the front of the room). Other, larger, rooms may have

multiple distinct echoes. Superdome-sized rooms are an

obvious example. In most cases, problem echoes must be

dealt with by acoustic treatment. In some cases, in fact, a

sound system will only aggravate an echo problem.

34.2.3.1.2 Can a Reflection Be Useful?

Reflections add to the level perceived by the listener but

this additional level may or may not be useful. Mid- to

high-level late reflections, which arrive at the listener’s

ear more than 50 ms after the direct sound, can muddy

the sound or may even be perceived as echoes. Mid- to

high-level early reflections, which arrive at the lis-

tener’s ear less than 20 ms after the direct sound, cause

comb filtering which degrades the system frequency

response. Reflections between 20 ms and 50 ms, how-

ever, can add to the level in a way that is beneficial to

intelligibility and pleasing to the sound quality.

Thus, audible reflections can be useful, questionable,

or undesirable, depending primarily on the difference in

the arrival time at the listener’s ears (and somewhat on

the difference in level between the direct and reflected

sound).

Note that the sound from multiple loudspeakers can

arrive at a listener’s ears at multiple different times.

This effect mimics early reflections and may or may not

be useful as discussed above.

34.2.3.1.3 When Reverberation Is Useful

Some reverberation is often desirable, especially for a

musical performance. The reverberation of a large

cathedral, for example, enhances the organ and choir

sound. Some musical compositions, like those written

for a pipe organ, are actually intended for a large, rever-

berant room.

A small amount of reverberation can also enhance a

speech reinforcement system. Reverberation can fill out

a vocal sound to make it more natural. Those reflections

in a reverberant field that reach the listener’s ears a

short time (but not too short a time) after the source can