RACK/ARRAYS & PHASE

\theta_{null}

Power Alley Mapper

L/R sub interference map: central summation and off-axis null lanes.

MOD-07•2D HORIZONTAL INTERFERENCE & LOBING BENCH

L/R Subwoofer Power Alley & Null Lane Mapper

Visualize the central $+6\text{ dB}$ Power Alley and destructive off-axis cancellation valleys ( $\theta_{\text{null}}$ ) created when Left and Right subwoofer stacks are physically separated across a stage.

Stage Width Presets

FIRST OFF-AXIS NULL ANGLE

\theta_{\text{null},1}

±9.8deg

Total Null Lanes: 6 valleysW / λ = 2.94 wavelengths

FIRST NULL OFFSET @ FOH (28m)

y_{\text{null}}

±4.8m

Distance from Center Power Alleyλ @ 63Hz = 5.45 m

MAX COUPLING SPACING (λ / 2)

d_{\max} \le \lambda/2

2.72m

Max Sub Center-to-Center for 0 Nulls8.9 ft

STAGE L/R SPACING & FREQUENCY PARAMETERS

Left-to-Right Sub Stack Separation

W_{\text{LR}}

1 m36 m

Subwoofer Evaluation Frequency

f_{\text{sub}}

32 Hz120 Hz

Audience Floor Depth

D_{\text{aud}}

15 m80 m

Right Sub Stack Delay Steering

\Delta t_R

-8 ms8 ms

2D PLAN-VIEW ACOUSTIC PRESSURE INTERFERENCE HEATMAP

HOW IT WORKS: ELECTRO-ACOUSTIC PHYSICS & MATHEMATICAL DERIVATION

The Physics of L/R Subwoofer Lobing & The Center Power Alley

When subwoofer stacks are split Left and Right on either side of a stage separated by distance $W_{\text{LR}}$ , any listener standing along the exact geometric centerline ( $0^\circ$ ) is equidistant from both stacks ( $\Delta d = 0$ ). Both low-frequency waves arrive identically in phase at every frequency, summing constructively by $+6\text{ dB}$ along a narrow central corridor known as the Power Alley.

However, moving just a few meters off-center introduces a path-length difference $\Delta d = W_{\text{LR}} \sin\theta$ . Whenever $\Delta d$ equals an odd half-wavelength $(2k-1)\frac{\lambda}{2}$ , the Left and Right subwoofers arrive $180^\circ$ out of phase and cancel each other out, carving deep dead zones through the audience area.

Off-Axis Destructive Null Angles for Separated L/R SourcesEQ-01

\theta_{\text{null},k} = \arcsin\!\left( \frac{(2k - 1)\,\lambda}{2\,W_{\text{LR}}} \right), \qquad k = 1, 2, 3, \dots

Maximum Inter-Sub Spacing for Seamless Horizontal CouplingEQ-02

s_{\max} \le \frac{\lambda_{\min}}{2} = \frac{c}{2 f_{\text{upper}}}

To eliminate off-axis cancellation lanes up to

80\text{ Hz}

(

\lambda = 4.29\text{ m}

), distribute subwoofers horizontally across the front of the stage with center-to-center spacing

s \le 2.14\text{ m}

(

\le 7\text{ ft}

Nomenclature & Physical Variables

$W_{\text{LR}}$
Center-to-center horizontal distance between Left and Right sub stacks
Unit: m
$\lambda$
Acoustic wavelength at subwoofer frequency ( $c / f_{\text{sub}}$ )
Unit: m
$\theta_{\text{null},k}$
Azimuth angle of the $k$ -th destructive cancellation valley
Unit: deg

FOH & System Tech Field Application Notes

If FOH mix position is located dead-center in the Power Alley of a wide L/R sub deployment, the engineer hears $+6\text{ dB}$ more bass than $75\%$ of the audience and will instinctively mix the show bass-light!
Whenever stage architecture permits, replace wide L/R sub stacks with a center mono cluster or a horizontally distributed broadside sub array spaced at $\le \lambda/2$ ( $1.8\text{ m}$ to $2.2\text{ m}$ centers).