Handbook for Sound Engineers

1240 Chapter 34

34.2.2.1 Definitions

It is conventional to use the terms Ds, D 1 , D 2 , and D 0
when referring to the distances between the elements of
this simple system.

• Ds.is the distance between the talker and the micro-

phone.

• D 0 is the distance between the talker and the listener
  (again, the farthest listener when there are many
  listeners).


• D 1 is the distance between the loudspeaker and the
  microphone.


• D 2 is the distance between the loudspeaker and the

listener (if there are many listeners, D 2 is usually

considered to be the distance between the loud-

speaker and the farthest listener).

• LP—level of pressure—more commonly known as

SPL (sound pressure level)

The terms Ds and D 0 start at the talker. The terms D 1
and D 2 are referenced to the loudspeaker. The first
member of each pair measures to the microphone, Ds
and D 1. The second member of each pair measures to the
listener, D 0 and D 2. It’s easy to remember them this way.

34.2.2.2 Attenuation with Increasing Distance

As the listener moves farther away from the loudspeaker,
the sound pressure level LP (or SPL) at the listener’s ears
will decrease. Neglecting the effect of echoes (outdoors,
away from buildings this is a good approximation), the
LP will decrease exactly 6.02 dB every time the listener
doubles the distance from the loudspeaker, Fig. 34-2).
This effect is known as the “inverse-square law” and can
be stated mathematically as

(34-1)

Example:

Let,

LP = 110 dB,

D = 4 ft,

Dc = 200 ft.

In Eq. 34-1, LP is the sound pressure level (in

dB SPL) the listener hears at distance D from the source

(the loudspeaker in the simplified system). LPc is the

new sound pressure level the listener would hear at

distance Dc from the source. If distance Dc is smaller

than distance D (the listener has moved closer to the

source), then the term 20 log (Dc/D) will be a negative

number, and the new LPc will be greater than the orig-

inal LP. Note that because the equation uses a distance

ratio, the distances may be measured in any convenient

unit (feet, yards, meters) as long as both distances are

measured in the same unit.

34.2.2.3 Acoustic Gain

Of all the reasons for a sound reinforcement system, the

most important is implied by its name, sound reinforce-

ment. That is, a sound reinforcement system reinforces

a talker’s voice so that the listener hears a louder sound

with the system on than with the system off. The term

acoustic gain describes the difference, in dB, between

the sound pressure level, LP , at the listener’s ears with

the system on and with the system off. In most cases,

the listener means the farthest listener although the

acoustic gain may be specified for any number of differ-

ent listeners in a complex system. Acoustic gain may be

described mathematically by a simple equation

(34-2)

Adequate acoustic gain is a primary design goal for a

sound reinforcement system. Techniques for reaching

this goal are described later. A simple technique for

measuring the acoustic gain of a system is to place a

sound level meter (SLM) at the position of the farthest

listener and measure the LP from the talker with the

system off. Then turn the system on and measure the LP

Lpc Lp 20 D

c

D

–= log----- -

Lpc 110 20^200

4

–= log---------

=76.0 dB

Figure 34-2. Inverse square law.

Loudspeaker

D

2D

100 dB

100 dB

Sound level

meter

Acoustic gain LPon–= LPoff