Sub Arrays: End-Fire, Cardioid and Spacing
Sub arrays use spacing, delay and polarity to make bass add where the crowd is and cancel where it is not wanted: on stage, behind the rig, towards the neighbours. A single sub is close to omnidirectional; a correctly timed group of them is not.
Why one sub goes everywhere
Wavelength is speed of sound ÷ frequency. At 50 Hz that is 343 ÷ 50 = 6.9 m, several times the size of any 18" cabinet, and a source much smaller than the wavelength radiates almost equally in all directions. Horn and scoop cabinets gain some directivity in their working band but spread widely below it. See horn loading explained.
To steer bass you need a source that is large compared with the wavelength. Several subs, spaced and delayed correctly, make one. Everything below depends on correct phase and polarity.
Spacing a row of subs
Subs placed together couple and add on axis. Space them more than about half a wavelength apart at a given frequency and the pattern breaks into lobes: loud and weak zones across the floor.
- Half-wavelength rule: at 100 Hz, half a wavelength is 1.7 m. Keep box centres closer than that across the sub band for even coverage.
- Tight blocks are predictable. A close cluster behaves as one large source.
- Separated left and right sub stacks on a wide stage produce power alley: a strip of extra bass down the centre with cancellation zones either side. A centre cluster or a close ground-stacked row avoids it.
End-fire
Subs in a line, one behind another, all facing the audience. Each box further forward is delayed by the time sound takes to travel from the rear box to it. In front, every output arrives together and adds; behind, arrivals are staggered and partly cancel.
- Spacing is commonly a quarter wavelength at a target frequency: 1.07 m at 80 Hz.
- Delay per step = spacing ÷ 343 m/s: 1.07 m gives 3.1 ms.
- Rear rejection is strongest near the design frequency and weaker away from it.
- It takes floor depth: four boxes at 1 m centres need more than 3 m front to back.
Cardioid (gradient)
A compact alternative: forward-facing subs with one or more boxes turned to face the rear. The rear-facing box is polarity inverted and delayed so that behind the stack it cancels the forward boxes' rear output, while in front its contribution adds to the main output.
- The forward-to-reversed ratio depends on how much the cabinet radiates rearwards; set it from measurement.
- Delay is set from the front-to-back distance between acoustic centres.
- Some energy is spent on cancellation, so forward output per box falls slightly.
- It fits a normal stage footprint.
Some manufacturers build cardioid behaviour into a single cabinet with rear or side-firing drivers. The principle is the same.
| Layout | Footprint | Rear reduction | Suits |
|---|---|---|---|
| Centre cluster | Small | None | Even coverage, simple setup |
| Left/right stacks | Small | None | Narrow rooms; power alley risk on wide stages |
| End-fire | Deep | Strongest near design frequency | Outdoor events with depth to spare |
| Cardioid gradient | Compact | Across a useful band | Stages, live mics, quieter backstage |
Setting it up
- Identical cabinets and drivers throughout. Different boxes have different phase and make cancellation unreliable.
- Check every box for polarity first.
- Measure between acoustic centres, not box edges.
- Set delays in the DSP and verify with a measurement mic in front and behind.
- Re-align the tops to the array after any change. See crossover basics.
Arrays need box count. Planning that: how many subs do you need.
Sound systems and arrays
Traditional reggae and dub sound systems stack scoops or horns in one coupled wall, built for weight rather than steering. Arrays are a tool for events with noise limits or stage problems. Both depend on matched bass boxes: for scoops and folded horns, the WM18X451 (115 mm copper coil, double spider, 1800 W RMS, £345), or the WM1850/8 (1800 W AES, 12 mm Xmax, £275).
Safety
End-fire rows and stacked arrays mean heavy cabinets and high stacks. Two-person lifts, stable stacking, and follow loading and stacking safely.
Questions
What is a cardioid subwoofer array?
A group of subs where at least one box faces the rear, polarity inverted and delayed, so that bass behind the array cancels while output in front is kept.
What is the difference between end-fire and cardioid subs?
End-fire puts all subs facing forward in a front-to-back line, each delayed by its spacing divided by the speed of sound, and needs floor depth. Cardioid uses a compact stack with a reversed, inverted and delayed box.
How far apart should subwoofers be?
For even coverage keep centres closer than half a wavelength at the highest frequency they play: about 1.7 m at 100 Hz. A tight cluster is the most predictable layout.
What is power alley?
A strip of extra-loud bass down the centre between two separated sub stacks, with cancellation zones either side, caused by their outputs arriving in and out of phase at different positions.