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Subwoofer Arrays: Discussion & Analysis Of A Variety Of Bass Coverage Patterns
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We often describe bass as non-directional. This is because we’ve learned that loudspeakers much smaller than the wavelengths they’re radiating are normally non-directional, and we know that bass wavelengths are long - 20 feet at 55 Hz, for example.
In reality, bass is just low-frequency sound that obeys the same rules as sounds of other frequencies. In these rules, all dimensions are proportional to wavelength.

For bass, practical directivity issues arise because the wavelengths involved are so large.

Some have a hard time actually believing that a big subwoofer box is actually non-directional in its operating range, but under “pure conditions,” it is.

By pure conditions, I mean: a) the box is by itself, not stacked or hung in an array of some kind; and b) the box is free enough from distortion that it isn’t putting out a directional beam of distortion harmonics that mask the real (non)directivity of the fundamental.

Directive distortion harmonics (point b above) are the usual reason for individual subwoofers seeming directional. Stand in front of a single box and you hear clear bass; stand off to the side and you hear muffled bass.

The conclusion is that the box is directional. The problem is that the only directional part is the part you don’t want - distortion.

When a bunch of subwoofers are stacked into a big array, the dimensions of the stack are large enough to create strong directional effects.

Sometimes these effects help, sometimes they don’t. What happens depends upon the shape and size of the array, and on how the subwoofers are powered.

Also, with multiple bass arrays (one array on each side of the stage, for instance), the interactions between/among them have powerful directional effects.

Let’s take a look at some of the more common types of subwoofer arrays and modeling graphs that show their horizontal directivities.

The graphs shown with this article were generated by a simple bass array modeling program I wrote back in the 1980s. The program still works, which may not be too surprising since the laws of physics don’t change.

The graphs all assume a generic type of subwoofer box about 2 feet tall by 4 feet wide. Bass array directivity doesn’t depend much on individual box details.

All curves are calculated for a listening distance of 150 feet on the floor. A 60-foot-wide stage is assumed.

Classic left and right stacks. This is the configuration most often used, with the subwoofers in flat-front stacks at stage left and right. This is popular for several reasons: easy set up, little interference with sightlines, and creation of a platform for stacking fill loudspeakers.

It also adds a pair of little stage extensions for the star to leap onto in peak moments.

Figure 1 shows that the bass coverage from such arrays is kind of lumpy, and there’s quite a bit of sound coming off the back. In practice, the amount of sound coming off the back of the array isn’t as much as the modeling program shows. 

Figure 1: Classic left and right subwoofer stacks.

However, the depiction of the lobing is accurate. Notice the lobe up the middle, surrounded by nulls. This is the classic “power alley” phenomenon observed by FOH mixers.

The lobing problem is serious - the circles on the graphs are 10 dB apart, so there are big differences between the peaks and the valleys.

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