It would be impossible to construct one specific low frequency array whose energy radiation is optimized for all of these positions. For instance, an array over a stage would need to radiate minimal energy straight down, yet maintain a broad horizontal coverage pattern. The same array placed on stage left or stage right could radiate excessive energy to allow distant miking - an application where a null toward the stage might be desirous. The first step of implementing an array therefore becomes the decision as to where it must be placed; something determined by the physical constraints and conditions that exist in all venues.

Polar response of spaced radiators at a single frequency as a function of wavelength. (Note: Polars will be mirror-imaged for omnidirectional radiators.)
From Acoustical Engineering

The variables that determine the polar response of an array are:

I. The number of devices
2. The spacing between the devices
3. The frequency (wavelength of interest)
4. The time offset between the devices (delay)
5. The polarity of the devices
6. The relative levels of the devices

All of these parameters can be readily input into the computer, and the polar responses generated.

The following pages depict some arrays that have been optimized for each type of placement. pb

Horizontal spacing: 3 wavelengths at 100 Hz (33 ft) This is not a recommended placement, but does serve to show the lobing caused by split subwoofers.

Array Guidelines

Some conclusions can be drawn from the array models:

I. For most venues, sub arrays should be stacked vertically to narrow vertical coverage and maintain horizontal coverage.

2. If subs are to be split horizontally, they should be as far apart as possible (>5 wavelengths).

3. If subs MUST be arrayed horizontally, con sider the Bessel array.

4. Cardioid subwoofers can be useful for control ling rear radiation.

5. Remember that the polars are frequency dependent, and a good polar at one frequency will produce the opposite effect at twice (or half) that frequency. For this reason, it may be necessary to use multi-way subwoofer systems with each passband optimized for the desired polar.

6. The room’s response will interact with the subwoofer array response, and can nullify the ben efits of the array.

7. A ridgid boundary near a subwoofer (floor, wall, ceiling or combination) will produce a reflection that can be treated as another low frequency source. The princip of subwoofer spacing apply, and the best coupling takes place within 1/8 wavelength of the sur face, producing a mirror image that couples with the sound source as though separated by 1/4 wavelength.

Interested designers can perform these investigations using ArraySHOW’ software from EVI Audio (Customer Service Department: 1-800-234-6831 Phone 616-955-6831 Fax.)

From Joe Etrick... A “Cardioid” subwoofer from an AES paper authored by George Augspurger: Device B is located 1/4 wavelength behind the device A (34” at 100 Hz), inverted in polar- iv and delayed by 2.5 ms. A good choice when rear radiation must be reduced.

Five subs lined up horizon rally within 1/4 wavelength. Note the narrowing of the horizontal coverage. This is a useful configuration if rotated 90 degrees, which “swaps” the horizontal and vertical patterns.

The same configuration as above, but with each sub “splayed” by 15 degrees forming an arc array. When located over a stage, the low frequency spill prevents good gain-before-feedback.

The same configuration as above, but with the subs con figured as a Bessel array. The outside loudspeakers (A and E) are reduced in level by 3 dB, and loudspeaker B or D is connected reverse-polarity This can be useful f the subs MUST be located in front (or under) the stage and a broader horizontal radiation pattern is desired.

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