User Guide

Sound System Design Reference Manual
transmission coefficient for a direct radiator as a
function of cone diameter. The solid curve is for a
single unit, and the dotted curve is for two units
positioned very close to each other. In addition to the
double power handling capability afforded by the two
units, the dotted curve shows a 3 dB increase in
transmission coefficient at low frequencies. This is
due basically to the tendency for the two drivers to
behave as a single unit with a larger cone diameter,
and hence higher efficiency. Thus, at B , we see the
relative response of a single woofer (solid curve)
compared to two such radiators (dashed curve). Note
that the upper frequency transition point for the pair
is 0.7 that of the single unit. The more such units we
combine, the lower the effective cut-off frequency
below which mutual coupling is operant.
As an example, let us pick a large cinema with
the following physical parameters:
V = 14,000 m
3
S = 3700 m
2
T
60
= 1.2 seconds
R = 2500 m
2
We will use the JBL 2242H LF transducer.
Taking into account its power rating and its dynamic
compression at full power, we note that its power
output in acoustic watts will be:
W
A
= (W
E
x reference efficiency)10
-dB/10
where W
E
is the transducer’s continuous power
rating (watts) and -dB is the transducer’s power
compression at full power.
Substituting the values of W
E
of 800 watts,
reference efficiency of .004, and power compression
of 3.3 dB, we get the value of 15 acoustical watts.
The reverberant level in a space with a room
constant of 2500 is then:
L
REV
= 126 + 10 log 15 - 10 log 2500 = 104 dB SPL
We can now construct the following table:
Number of Units Maximum Level Power Input
1 104 dB 800 W
2 110 dB 1600 W
4 116 dB 3200 W
We cannot continue this process much beyond
that shown here. What happens is that the frequency
below which mutual coupling takes place falls below
the nominal cutoff frequency of the system, and
eventually all we see is a simple 3 dB increase per
doubling of elements.
For multiple subwoofers outdoors, it is best to
assume that levels fall off according to inverse
square law.
7-8
Figure 7-6. Details of mutual coupling