User Guide

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 direc-
tional 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
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