Study Hall

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Tech Topic: Friends In Low Places

Looking at the principles behind cardioid subwoofer arrays, clearing up common confusions, and learning how to deploy these arrays in the field.

Thanks to the proliferation of powered loudspeakers, active subwoofers sporting built-in “cardioid mode” DSP settings are on the rise. But what’s going on under the hood?

Let’s take a look at the principles behind cardioid subwoofer arrays, clear up common confusions, and learn how to deploy these arrays in the field.

Before digging into how to steer subwoofer coverage, let’s ask why we might want to do that. Unlike full-range loudspeakers, we can’t simply aim subwoofers in the direction we want the sound to go. It’s often repeated that subwoofers are omnidirectional, dispersing their acoustic energy in all directions. Throughout the frequency range in question, the wavelengths are so long (over 37 feet at 30 Hz) that the relatively small diameter of the loudspeaker cone can’t exert directional control over the output.

A valid objection to this statement would be that subwoofers definitely sound louder in the front. Although subwoofers are very nearly omnidirectional at the low end of the frequency range, the shorter wavelengths associated with higher frequencies means more directional control as frequency rises.

Despite crossover filters that roll off the high end of the response, our ears are far more sensitive to the energy above 100 Hz, making the subs seem more directional than they really are through their main coverage range. (For more information on this see “Minding The Gap” by Merlijn van Veen in LSI December 2017 and on ProSoundweb.)

Figure 1

Quantifying this requires a big, open outdoor space in which to set up subwoofers and measurement microphones and make a bunch of noise. What’s that, you say? Use my back yard? Great idea.

We weren’t too keen on moving the house or tool shed as part of this project, so we see some effect from those boundaries on the following measurements. The distance from which we choose to take measurements will have a pretty significant effect on the arrays’ perceived performance as well, for reasons we’ll discover shortly.

I set up a pair of single 18-inch subwoofers in the center of the yard and placed measurement mics twenty feet to the front and rear, which is as far away as I could get without ruining the garden. The two-mic setup, shown in Figure 1 from the perspective of the rear microphone, allows us to see what’s happening both “out front” of the array and “on stage.”

We start by looking at a single sub (Figure 2) and we see why there’s a demand for subwoofer beam-steering in the first place. The black trace shows the front response and the red trace shows the rear. Focusing on the two octaves of most interest to sub performance (31 – 125 Hz), we see that the front and rear response levels are similar.

From this, we can conclude that pointing a sub the other way does very little to steer its output. If we want it to be loud out front and quiet on stage, we’ll have to find another way. (Nerd Note: For visual clarity, all the transfer function traces shown use 1/12 octave averaging, although I normally use 1/24 octave resolution in practice. Temporal averaging was six seconds and the stimulus was band-limited pink noise, which the neighbors loved.)

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