Electro-Voice LINE ARRAY BROCHURE

Line Arrays — History and Theory

Mention is made of the vertical orientation of sound
sources as far back as 1896. Line arrays were also popular in
the 1950s and 60s because of the ability to provide excellent
vocal range intelligibility in reverberant spaces. Figure 1,
Figure 2 and Figure 3 are excellent representations of high
performance “vocal range” line arrays. These line arrays, like
all vertically oriented sources in the past were, what could best
be termed, limited bandwidth line arrays.

Figure 3 shows an Electro-Voice line array from the 1970s.
It represents a relatively elegant solution to achieving high vocal
intelligibility. It should be noted that the source separation of

this design is roughly six inches, relating to a wavelength of

2.26kHz. The line array behaved very well up to that 2 kHz range.
It should also be noted in the Figure 3 that a high

frequency horn was employed above that frequency limit in
order to achieve appropriate extended bandwidth and fidelity
up to and beyond 10 kHz. This is a classic embodiment of a
limited bandwidth line array and as we shall see in this presen­tation, only recently have solutions been brought to the state
of the art to enable line array technology to truly be full band­width and extend beyond the 10-15 kHz region.

Before we begin discussing bandwidth for modern day line

arrays, it is important to begin with a discussion of basic
radiation of sound. Figure 4 represents a spherical shape
whose radius “r” can vary with time.

Figure 5, Equation 1 describes the acoustical performance

of this pulsating sphere. This pulsating sphere, or simple
source is a useful theoretical tool describing the mathematics
of radiating sound.

Figure 5, Equation 1

ρ

AV

=

(ka)

2

p.c ( Vs2) ave (4πa2)

1 + (ka)

2

Where: K = W/

C

ρ

AV

= time averaged power

VS= velocity

Figure 5, Equation 2

Condition:Ka << 1

or
λ >> a

Line Arrays

Figure 1

Figure 2

Figure 4

b=6''
ƒ = 2.26 KHz

Figure 3

1

One of the key requirements of this pulsating sphere, or
simple source, is that KA is always much less than 1 (Figure 5,
Equation 2). That is to say the wavelength must always be
much greater than the dimensions of the radiating device
itself. An ideal simple source is almost infinitely small and
thereby meets the requirement that KA is always much, much
less than 1.

Simple sources, of course, don’t exist in the real world as
radiating devices always some dimension and those dimensions,
in order to radiate sufficient acoustic power, become large
compared to most audio frequencies. (It is important to define
the term high frequency and low frequency at this point. When
one considers the term high frequency, one always assumes a
particular value associated with that frequency. One could
assume 5 kHz to be a relatively high frequency and it certainly
would be if the radiating device were an 18-inch direct radiating
loudspeaker. 5 kHz conversely, is a very low frequency if the
device radiating that wave front were a very small dimension, a
high frequency super tweeter, for example. The important thing
to note here is that the term high frequency or low frequency
is a term that describes the wavelength in comparison to the
dimensions of the radiating device itself. Throughout this
discussion of line arrays, whenever the term high or low
frequency is used, it is always assumed that a low frequency
has an associated wavelength much longer than the dimensions
of the radiating source and the term high frequency relates to
wavelengths that are much shorter than the dimensions of the
radiating source.)

Figure 6 is an Array Show representation of a theoretical
simple source. As can be seen from this slide, the radiation is
purely omnidirectional, implying that any wavelength radiated
is always long compared to the dimensions of the radiating
device. It is common in sound reinforcement practice to
assume that subwoofers or bass enclosures are essentially
omnidirectional.

Figure 7 shows an Electro Voice XDS subwoofer enclosure.
Although the 100 Hz being radiated is a relatively low frequency
(wavelength approximately 11.3 ft), examination of the associated
polar in this figure shows that the radiation at + and – 90
degrees from the central axis is 6dB to 7dB down from that on
axis and the radiation at 180 degrees opposite the main lobe is
also 7dB to 8dB down. The XDS is a relatively large subwoofer
from a physical standpoint. (36''H x 45.92''W x 29.88''D). The
radiator is not omni directional.

To further illustrate the point, Figure 8 shows an Electro
Voice TL15-1 base enclosure. This is a single 15-inch, direct
radiating enclosure of very small dimension. It can still be seen
from examination to polar response in this figure that the
response at +/- 90 degrees is still 3 dB down from that on axis.
Again, not omni directional radiation. These figures, indicate
the importance of the radiated frequencies being substantially
longer than the dimensions of the device if true omni direc­tional radiation is to occur. Given the initial descriptions of
these theoretical simple sources or pulsating spheres it is now
appropriate to bring a second sphere into the discussion.

Figure 6

Figure 7

Figure 8

2

Figure 9 represents two spheres or simple sources separated
by a distance B. The assumption here is that B is always much,
much less than the radiated wavelengths. If this condition
occurs, than the two point sources will generate double the
pressure and the directivity is still that of a single point (omni).
This is a simple and intuitive case where two radiating sources
simply generate twice the pressure of the single source.

Figure 10 shows these two point sources separated by a
distance of 12 inches. The polar response shown is that of
those two point sources radiating 100 hz signal. Again, the
space in B is much, much less than the wavelength, and as a
result, the radiation continues to be that of an omni-directional
condition. (Again, this is only a theoretical case, as point
sources do not exist in practice.) This representation is
extremely useful when we look at Figure 11, which is the same
two point sources as that of Figure 10. The distance continues
to be 12 inches, but now the frequency has been raised to 630
hz. (B approximately equivalent to 1/2 of the wavelength.)

Examination of Figure 11 shows that at 0 degrees on axis
and at 180 degrees the radiation is summing coherently and
the radiation at –90 degrees and +90 degrees (-y/,+y on the
Array Show polar plot) is experiencing cancellation. The
radiation of +x and –x, or that of the radiation on axis, has
seen a 3 dB gain in pressure associated with the pressure
addition of the two sources. Figure 11 begins to illustrate the
principles underlying successful application of a continuous line
of vertical sources (that of a line array).

Figure 12 is extremely interesting as well as it explains
the “historical” applications where line arrays were limited
bandwidth devices, such as those referenced in Figure 1,
Figure 2 and Figure 3 earlier in this discussion. The two point
sources continue to be spaced by 12 inches, but now the
frequency has been raised to 2500 hz. In this case, the space
B is equal to twice the wavelength. Examination of the polar
response shows substantial polar lobing errors. It describes
exactly the response of any group of sources, whether they are
vertically oriented or horizontally oriented when the wave­lengths become shorter than the device spacing.

Figure 12 is a clear representation of difficulties that
system designers face when trying to provide full bandwidth
radiation (i.e. greater than 16 kz) with real world radiating
sources. The peaks and nulls in the diagram of Figure 12 are
easily heard in real world applications and have always been
taken as a “necessary evil” when orienting sources. The
previous polar diagrams also require some explanation.

In definition of terms, Figure 13, the beamwidth is
defined as the included angular separation between the –6 dB
points, reference to the 0 db (+x) axis. The term Q is the ratio
of the acoustic intensity on that reference axis at some
reference distance to a true point source radiating the identical
acoustic power. Again, the true point source is useful from a
mathematical standpoint to enable us to define the acoustic
intensity ratio of real world devices to theoretical omni

Figure 9

Figure 10

Figure 11

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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

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