User Guide

directional radiators. Of most interest when designing line

arrays is the term directivity index. The directivity index,

di = 10 log base 10(Q), represents the acoustic gain associated

with the increased directional radiation of higher Q devices.

The fundamental operation of a vertical source of radiators

or a line array depends heavily on gain related to directivity

index. These gains, of course, are also dependent on having

the directivity index be constant with regards to frequency.

(Constant gain versus frequency is a critical operating parameter

for uniform SPL distribution).

Figure 14 is another Array Show representation illustrating

the concept of beamwidth, Q and directivity index. Here two

point sources, again spaced 12 inches apart, are shown. The

applied frequency is 1250 Hz. In this condition the spacing B

is approximately the equivalent to the wavelength associated

with 1250 hz. In Figure 14 the beamwidth is 30 degrees, the

Q is 2 and the directivity index associated with that Q is

slightly over a 3 dB gain.

It can also be seen from Figure 14 that the lobing pattern

begins to suggest that spacings greater than those equal to

the radiated wavelength begin producing unacceptable polar

lobing errors. For this reason, successful application of full band

with line arrays requires that the spacing always be less than

the radiated wavelengths. Figure 15 now takes our two point

sources and begins to build a continuous vertical orientation of

sources. Although still theoretical in nature, the representation

shown in Figure 15 is exactly what is used to generate the proper

mathematical description of the line array. The sources still have

a separation of B but now we’ve replaced two sources with N

number of sources. A theoretical line array occurs when the

spacing B tends toward 0 and the number of sources grow towards

infinity. Again, although both conditions are impossible to

satisfy in real world applications, the designer’s challenge is to

approximate small source separation and as great a number of

sources as geometry, physical spacing, and safe hanging practice

will allow. It should also be noted that one of the key points

to all line array discussions is noted in Figure 15, and that is

all sources must be both equal in magnitude and of equal phase.

Figure 12

Figure 13

Figure 14

Figure 15