622 Chapter 17
nulls and lobes, and it causes the off-axis impulse
response of a line array to contain multiple discrete
arrivals.
It is often incorrectly asserted that a line array
behaves, or can behave, as a line source. A line source
is largely a theoretical construct. It consists of a long,
narrow radiator that radiates sound with perfect unifor-
mity at every point on its surface. This assumption of
perfect uniformity, while impossible to achieve in prac-
tice, simplifies the mathematics required to model the
behavior of a line source. When used for illustrative
purposes in texts, line sources may additionally be
assumed to have infinite length, making possible even
further simplification of the mathematical model. The
same model has been employed in texts on electromag-
netic theory, for the same reasons.
The two assumptions—continuous radiation and infi-
nite length—lead to two interesting results. First, due to
symmetry, the frequency response of an infinitely long,
continuous line source is not a function of observation
position along the line. For example, if the line is
assumed to be coincident with the Z-axis in a cylindrical
polar coordinate system, then its response will not vary
with changes in the Z-coordinate of an observation posi-
tion (i.e., for movement in a direction that is parallel to
the line). Second, due to the infinite length of the source,
the wavefront (a collection of isophase points) will form
a cylindrical, rather than a spherical, shape. For this
reason, the intensity of radiation in the outward direction
falls off as the inverse of the first, rather than the second,
power of the distance from the line.
As interesting and attractive as the two above results
may be, they are not achievable in any physically realiz-
able array. The effects of radiation that is neither contin-
uous nor uniform, and of finite array length, cannot be
neglected in discussing the behavior of real-world
systems. Unfortunately, these issues have been glossed
over or completely ignored in the information that is
provided regarding the performance of commercially
available line array products.
Full-range line arrays characteristically have rela-
tively narrow vertical radiation patterns. The details of
these radiation patterns vary widely with frequency and
typically contain undesirable off-axis nulls (deep
response notches) and lobes (response peaks). The same
phenomena that produce off-axis response variations in
a noncoaxial, multiway loudspeaker—interference
caused by variations in the relative distances between
multiple sources and the listener—create this directivity.
At high frequencies, the angular separation between the
first two nulls—and therefore the useful coverage
angle—may be on the order of 5q or less.
A number of remedies to the problem associated with
line arrays have been implemented over the past 50
years. There are two primary areas in which the line
array intrinsically poses challenges to the designer: total
array length and individual device spacing. Both must
be addressed in order to produce a well-behaved system.
One means to address the issue of total array length
is to implement a tapered array. In this type of array,
only the innermost elements carry the highest frequen-
cies. The signals applied to the more outwardly placed
elements in the array are low-pass filtered at succes-
sively lower frequencies. The goal of this approach is to
make the effective length of the line array become
shorter at higher frequencies. An alternative way of
stating this goal is that one desires the ratio between the
effective length of the array and the wavelength of
sound to be invariant. With the ability via DSP
processing to create filters of essentially arbitrary
amplitude and phase response, it has become relatively
straightforward to create tapered arrays. Additionally,
the availability of frequency-independent delay makes
lobe steering possible.
The matter of device spacing poses another set of
challenges. The smaller the spacing can be made rela-
tive to wavelength, the better a line array can approxi-
mate the behavior of a continuous radiator. When
device spacing becomes large relative to a wave-
length—roughly in the range of a full wavelength—the
off-axis response of the array will contain many lobes
and nulls. It is likely that one or more of these off-axis
lobes will approach the level of the on-axis radiation.
When one considers the small wavelengths of the higher
audible frequencies—the wavelength of 10 kHz is
34.4 mm (1.35 inch)—the challenge of achieving
optimal device spacing for higher frequencies becomes
apparent. The continued reduction in size of motor
assemblies through the use of high-powered magnetic
materials has been helpful in addressing this issue.17.8.5 CrossoversMultiway loudspeakers incorporate a crossover network.
A crossover network is a collection of electrical filters,
each of which allows a specific portion of the frequency
spectrum to pass through it. The filtered signal is then
applied to one of the bands in the loudspeaker. The types
of electrical filters used to execute the crossover function
are low pass, high pass, and bandpass.
The simplest crossover network consists of a low
pass and a high-pass filter for use in a two-way loud-
speaker. Choices that must be made regarding the filters
in this crossover are: