Handbook for Sound Engineers

1248 Chapter 34

ical distance depends on the Q of the source and the
absorption in the room; thus, it can vary with frequency,
and this test shows only a broadband approximation of
critical distance.
For a given loudspeaker in a given room, critical
distance can be found from

(34-12)

where,
Q is the Q of the source,
S is the total surface area of the room,
is the average absorption coefficient for the surfaces
in the room,
N is the total number of loudspeakers producing the
same acoustic power as the loudspeaker pointed at the
farthest listener.

Example:
Let
Q = 5,
S = 28,000 ft^2 ,
= 0.35,

N = 1.

For a more detailed discussion of the concept of N, see
Section 34.3.2.10.

34.2.3.3 Attenuation of Sound Indoors

The first part of the indoor sound reinforcement system

model will tell us what happens to a sound at increasing

distances from the source in an indoor environment. The

inverse-square law, Eq. 34-1, is still correct indoors, but

only for the direct sound. The reverberant sound level is

assumed to be the same everywhere—that is, the rever-

berant sound level does not change with distance from

the source. Thus, the total sound level, at any distance

from a source, is the sum of the direct sound, which has

been attenuated by inverse-square law, and the reverber-

ant sound, which does not change with distance

(34-13)

where,

D is the original distance from the source,

Dc is the new distance from the source,

LP is the original LP at D,

LPc is the new LP at the distance Dc,

g(x) is found from the equation

(34-14)

where,

x is any distance.

Note that the equation for indoor attenuation is

exactly the same as Eq. 34-1 for the simplified system

(outdoor) attenuation (inverse-square law) except for

the final term, which can be interpreted as a contribu-

tion from the indoor reverberant field.

Example:

Let

LP = 90 dB,

D = 4 ft,

Dc = 125 ft,

Dc = 31.2 ft.

To compare to outdoor attenuation, Eq. 34-1, simply

ignore the term

Indoor attenuation can also be found from another

equation

if

Figure 34-7. Critical distance. Courtesy JBL Professional.

Relative SPL–dB

+18 +12 +6 0 -6 -12 -18

20

0

15

10

5

0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 10

Direct-to-reverberant sound ratio–dB

Ratio of distance from source to critical distance

Calculated from 10 log (1+1/X^2 ) where X is the

ratio of distance from source to critical distance

Dc QSa

16 SN

--------------=

0.141 QSa

N

= -----------

a

a

Dc 5 28 000^  0.35

16 S 1

= -------------------------------------

=31.2 ft

Lpc LP 20 Dc

D

log------ 10 gD^ c

gD

–= ©¹§·+ log--------------

gx Dc

2

x

2

+=

Lpc 90 20^125

4

log--------- 10 g^125

g 4

–= + log-----------------

=72.3 dB.

10 gD^ c

gD

log--------------