Subwoofer Array Spacing & Cardioid Delay Calculator
Calculate physical driver spacing, end-fire delay offsets, and quarter-wavelength cancellation boundaries for cardioid subwoofer arrays and broadside ground stacks.
Acoustic Subwoofer Geometry Calculator
QUARTER-WAVE PHYSICSQuarter-Wave Spacing (λ/4)
Acoustic Delay Offset (Δt)
Max Spacing Limit (λ/2)
Speed of Sound (c)
surround_sound How Cardioid Subwoofer Cancellation Cleans Up Live Stages
Because low frequencies (30 Hz to 100 Hz) have long acoustic wavelengths (spanning 3 to 11 meters), individual subwoofer enclosures radiate sound omnidirectionally—sending just as much low-end energy backward onto the stage as forward into the crowd. This stage bleed washes out vocal clarity, triggers low-frequency feedback through open stage mics, and overwhelms musicians on stage.
In an End-Fire Array or Inverted Cardioid Stack, subwoofers are positioned with deliberate physical front-to-back spacing (typically one-quarter wavelength of the target frequency) and delayed electronically. Moving toward the audience, the physical travel time and electronic delay sync up perfectly, producing powerful forward summation (+3 to +6 dB). Toward the rear stage, the arrivals meet 180 degrees out of phase, creating deep cancellation (-15 to -25 dB rejection) and leaving the stage quiet and punchy.
Accurate physical placement is critical: even a few inches of placement error on stage will shift the phase cancellation notch, degrading rear rejection and spilling muddy bass back onto your performers.
warning Real-World Venue Realities & Manufacturer Presets
While mathematical calculations provide the essential spatial baseline, real-world cardioid arrays are affected by enclosure acoustics:
- Cabinet Depth & Port Phase Shifts: Bass-reflex ports exhibit steep phase wrap around their tuning frequency, meaning sound does not emerge instantaneously from the front baffle.
- Manufacturer Calibration: Major touring brands (d&b audiotechnik, L-Acoustics, Meyer Sound) utilize proprietary all-pass filters in their factory presets to linearize phase. SoundEngg provides the geometric spacing calculation so you can physically place cabinets correctly before fine-tuning with RTA.