In sound systems, it would be terrific if loudspeakers worked like spotlights: find the loudspeaker boxes with the right directional patterns, aim them where you want sound to go, and you’re done. Of course, that’s not the way it works, especially for bass. 

Ordinary bass loudspeakers are very nearly omnidirectional over their working ranges, but when you stack up a few of them, the pattern becomes more directional and more complex. Imagine if lights worked that way—a bare light bulb would illuminate the whole room, but four of them in a row would only light up some parts of it. 

To make things worse, when you use multiple woofer stacks—stage left and stage right, for example—it produces wave interference (also called “comb filtering”), causing peaks and nulls in different places in the room at different frequencies. If light worked that way, then when you lit up a room with two white lights spaced some distance apart, the room would be illuminated with a rainbow of different colors.

Even beyond that, there’s the problem of reverberation, which adds its own kinds of confusion and coloration in the time dimension.  That effect that doesn’t even have a parallel in lighting.

In the face of all these phenomena, how do audio professionals design subwoofer arrays and drive schemes that provide required qualities of coverage and fidelity?

If we succeed, then:
• The bass will be clear and will have constant tonal balance over the entire listening area.
• The bass sound level will be in correct balance with the midrange and high-frequency over the entire listening area.
• Negative effects of reverberation and reflection will be minimized.
• Efficiency of the equipment (sound power output per unit cost) will be maximized.

This article offers concepts and techniques for getting good bass. Our focus will be the frequency range from approximately 20 Hz to 150 Hz.

Wavelength
Just about everything having to do with loudspeaker array acoustics is relative to wavelength. A box or array is “large” if its dimensions—or some of its dimensions—are more than about 1.5 wavelengths across. A dimension is “small” if its dimensions are less than about a third of a wavelength.

Here are some typical wavelengths:

 
For normal air temperature, pressure, and humidity, the formulas for wavelength are:

Basic Directivity Rule
For ordinary sound sources, directivity is inversely related to dimension. If an object is small, its directivity is wide;  if large, its directivity is narrow. (See Figure 1) Remember that “small” and “large” are measured in wavelengths, not feet or meters.

Horizontal-Vertical Independence
The basic directivity rule applies independently in the horizontal and vertical planes. For example, a horizontal line of subwoofers might be large horizontally and small vertically. Therefore, its directivity would be narrow horizontally and wide vertically, as shown in Figure 2.

Multiple Sources and Lobing
Many, if not most, subwoofer installations use two separate arrays on opposite sides of the stage. Sometimes these arrays are stacked on the floor, sometimes they’re flown. 

 
Either way, the multiple sources exhibit what physicists call “wave interference”, and what audio people call “comb filtering” or “lobing”.

Figure 3 shows the directivity of a single EV Xsub woofer at 50 Hz. In this example, size of the stage is 40x20 feet. The red trace is the polar pattern. Circles are 6 dB apart. The Xsub is essentially omnidirectional.

Figure 4 shows what happens when another Xsub is added at the opposite side of the stage. The result is very different—and not better!

Because the woofers are omnidirectional, everyone in the room hears both woofers. However, the distance from each woofer to the listener is different, except in the middle. Where the distance difference equals an odd multiple of a half-wavelength, the sounds from the two woofers cancel, and the listener hears no bass, at least not directly from the woofers.

These lobes will produce uneven bass tonal balance and level in the venue. In indoor venues, the tonal balance problems are partly masked by reverberation, but the lack of clarity remains. Outdoors, there is no reverberation, and the problem is usually quite obvious.

Figure 5 shows performance of two practical cases - groundstacked rows of subwoofers, and flown subwoofer line arrays.

 
The only region that is lobe-free at all frequencies lies along a line running directly out from center stage. Along this line, the bass is strongest and clearest. This is the familiar “power alley” effect that makes the bass sound very good at the mix position, but does not give the mix engineer a good idea of what the rest of the audience is hearing.

The best solution for lobing problems is to use a single center cluster instead of separate left-right stacks. This works for both horizontal and vertical arrays. However, it is not often a practical solution for staging and rigging reasons. 

When left-right stacks are used, lobing problems can be reduced using stacking, beamforming and/or gradient woofers. In all cases, the idea is to minimize interference between the coverage areas of the two stacks.

Beamforming
Beamforming is a technique by which the sound wave emitted by a large array can be aimed and shaped. In a beamformed array, the loudspeakers are driven separately (or in small groups), and each drive signal has its own delay and level. 

Figure 6 and Figure 7 illustrate a typical effect of beamforming on a typical medium-sized subwoofer array. The illustrated array is four EV Xsub subwoofers. Figure 6 shows the array with no beamforming. In Figure 7, the delay values are chosen to direct the bass radiation offstage.  This is a typical technique for increasing side coverage.

Beamforming only works on arrays that are large (as defined above). Controlling directivity of small arrays requires gradient techniques, which will be addressed in my next installment of this article.

 
Gain Shading
The term “shading” means modifying array drive parameters for the elements on or near the ends of the array. “Gain shading” means adjusting—specifically, reducing—the drive gain for one or more elements at either end of an array.

For long arrays, shading takes the form of a gradual tapering of gain from 0 dB to about -6 dB over the last two or three elements at each end. The effect of the shading is to make the coverage pattern more regular and less frequency-dependent.

Next time, I’ll be discussing various woofer array types and applications.

NOTE: The polar patterns illustrated in this document have all been produced by the Electro-Voice LAPS 2.2A line array design program.  Starting with release 2.2A, LAPS includes a subbass pattern modeling page. 

Jeff Berryman served as the director of Jasonaudio, a touring sound company based in Canada, and is a senior scientist with Electro-Voice.

Related Articles by Jeff Berryman:
What Really Defines Good Bass In Sound Reinforcement?
Discussion & Analysis Of A Variety Of Bass Coverage Patterns