Line Source Coupling Only Occurs At Longer Wavelengths/Lower Frequencies; The Longer The Line, The Lower The Frequencies It Will Control And The Tighter The Beam; High Frequencies Are Always Radiated From Separate Sources And Waveguides; Vertical Arrays Take One Of Three Possible Shapes - Renkus-Heinz STXLA User Manual

Line Array User's Manual

Line source coupling only occurs at longer wavelengths/lower frequencies

This is because adjacent sources have to be less than 1/2 wavelength apart in order to couple coherently. Audible
frequencies have a wide range of wavelengths, from over 50 feet at 20 Hz to about 1/2 inch at 20 kHz. Obviously
it's easy to get two sources to couple coherently at 20 Hz, because the wavelength is about 50 feet. Since high
output compression drivers have voice coils between 2 and 4 inches in diameter, it is almost impossible to
produce line source coupling at 10 kHz, where the wavelength is about 1 inch.

The longer the line, the lower the frequencies it will control and the tighter the beam

A theoretical point source, with perfectly spherical radiation, can be considered as a line with no height. For any
line of finite dimensions, the transition from line source radiation (flat or plane wave with –3 dB energy loss per
doubling of distance) to point source radiation (spherical wave with –6 dB per distance doubling) begins at the
frequency whose wavelength is twice the height of the line, and is complete one octave lower at the frequency
whose wavelength is four times the line's height. For example, a 12 deep array of STLA/9 modules will be 15.5
feet tall and will radiate as a line source above 35 Hz.

High frequencies are always radiated from separate sources and waveguides

Applying the line source calculations summarized above, it becomes clear that 2.5 voice coil compression drivers
cannot couple as a line source above 2650 Hz (6.5 inch midrange cones radiate as separate sources above 1025
Hz). Yet the compression driver must operate up to 18 or 19 kHz. Clearly, some sort of waveguide technique
that allows adjacent array modules to produce a coherent and continuous wavefront is required.
Christian Heil was the first to demonstrate that such a waveguide was possible. Since then a number of other
approaches have been used successfully. Interestingly enough, all of these have been used for decades to control
microwave radiation, which happens to have many of the same characteristics as high frequency sound. Renkus-
Heinz has employed the acoustic lens technique in its Isophasic Wave Generator. One advantage of an acoustic
lens is that the technique is equally successful with a wave model (i.e. at lower octaves) and with a ray model
(higher octaves). Therefore the lens technique is effective at controlling a broader range of frequencies than
reflection-based designs which are only operative on rays (very high frequencies). Another advantage of the
acoustic lens is that the wavefront curvature is independent of the path length from the driver to the waveguide
exit.
Vertical arrays take one of three possible shapes: flat (line, straight or "|"arrays, symmetrically curved or ")"
arrays and asymmetrically curved or "J" arrays.
The flat shape is a pure line source, at least at low frequencies. Curving the line array broadens the dispersion.
Curving the bottom of the line array only widens dispersion in the lower section (coincidentally this is the section
that is closest to the audience). It also tilts the main beam of the array downward.

Variants of the "J" produce the best results in the vast majority of applications

By "best" we mean the "most consistent amplitude and frequency response from the front to the rear of the
audience."
As a point of reference, horizontal arrays are pie sections of a spherical source: their energy is reduced by 6 dB
with each doubling of distance. In the typical large venue with a distance ratio of 4:1 from the closest to the
farthest seats, this means that the front rows are 12 dB louder than the back. Look closely at the Aimware
screens shown on the following pages. They illustrate how the three vertical array shapes behave in this type of
venue.
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