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Optimizing The Low End: Run & Gun Subwoofer Arraying Techniques
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Of all the tweaking I apply as a system tech, the most common is fixing mediocre subwoofer setups.

Problems in this area are so prevalent that many of us take them for granted or assume there is no room for improvement. In fact, most of the time there is a better solution. 

Further, that method is usually free and can be accommodated by most system layouts.

Let’s use visual depictions of subwoofer response in a free field (i.e., outdoors) to show that subwoofer coverage is often inadequate, and by how much it can be improved.

First, a quick primer on how sound waves operate. Typical subwoofer frequencies are between 30 and 100 Hz, which corresponds to wavelengths of between 38 feet and 11 feet. Above these frequencies wavelengths continue to shorten. At 20 kHz, commonly accepted as the upper limit of human hearing, the wavelength is three-quarters of an inch. Why is wavelength significant? (See *Note On Examples* and **Determining Wavelength** at the conclusion - page 4 -  for more information on the data used for this article.)

Figure 1 represents a “perfect” omnidirectional subwoofer. Because this single sound source is acoustically “small” relative to the size of the waves it reproduces, it has negligible effect on them. 

A source is acoustically “small” when no dimension of the source is larger than one-quarter wavelength at the frequency of interest. Any “small” source will exhibit near-perfect omnidirectional response. This is great, because it means that the sound given off by the source will be the same regardless of how it is oriented, and makes it very predictable and easy to work with. Fortunately most individual subwoofers meet this criterion.

Figure 1 (click to enlarge)

Unfortunately, problems quickly develop in even modestly sized sound systems. One-quarter wavelength at 80 Hz (a common subwoofer crossover frequency) is merely 3.5 feet. While there are plenty of subwoofers that are less than 3.5 feet across, there is no individual subwoofer I’m aware of that has enough output for larger audiences in this footprint. 

When you take a perfectly good subwoofer that has a lovely omnidirectional pattern and place it next to 2, 4, 8 or more of its peers, the resulting arrangement no longer has anything like an omnidirectional pattern.  What happens is the dimensions of the subwoofer array have far exceeded the 3.5 feet mark, and the collection of sources are no longer within one-quarter wavelength of each other. The increasing size of an array causes something called “pattern narrowing” that is demonstrated in Figure 2 and Figure 3.

Figure 2 (click to enlarge)
Figure 3 (click to enlarge)

To understand why this narrowing occurs, one needs to have a working knowledge of phase. Phase is the offset between two waves, measured in degrees, as shown in Figure 4. If you imagine a wheel, one full revolution of the wheel would be 360 degrees of phase, or one full cycle of the wave. Half a revolution would be 180 degrees, or half the wave, and so on.

Figure 4 (click to enlarge)

The behavior of two waves interacting depends on their phase (and amplitude, but let’s assume equal amplitude for now) relative to each other. That is to say, two waves perfectly in phase (0 degrees difference) will add coherently, for 6 dB of gain. Two waves 180 degrees out of phase will cancel perfectly. Any other phase relation will result in somewhere between perfect addition and perfect cancellation.

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