Double bass array

A double bass array (DBA) is a specific layout of subwoofers within a rectangular listening space. It removes unwanted room related resonances (modes) over a wide listening area.
Preface.
A DBA requires at least two subwoofers (preferably same make and model) that are placed at opposing walls in a specific layout. The subwoofer array on the back wall is inverted and delayed based on the distance to the frontal subwoofer array. This will actively "absorb" any reflected sound.
Design.
Array layout.
Modes between side walls, floor and ceiling are suppressed by arranging the subwoofer in a specific grid:
formula_1
formula_2
formula_3: Wall width
formula_4: Wall height
formula_5: Horizontal distance from wall (formula_6 for n=0 in picture)
formula_7: Vertical distance from wall (formula_8 for n=0 in picture)
formula_9: Number of subwoofers horizontally
formula_10: Number of subwoofers vertically
Counter formula_11
With this specific grid layout reflections from the walls act as mirror sources. Interference of the subwoofers and mirror sources create a plane wave up to a certain frequency. The more sources the higher the frequency. This cutoff frequency formula_12 can be calculated for each dimension as follows:
formula_13
formula_14: Speed of sound
formula_15: Distance between subwoofers
Example: A 2 × 2 array on a wall measuring 4 × 3 m would work up to 86Hz horizontally formula_16 and up to 114Hz vertically formula_17.
Active Absorption.
Due to the specific grid layout of the subwoofer array most modal effects are suppressed. The length modes on the other hand get fully excited. The array on the back wall will emit a polarity inverted wave at the very same moment the wave from the front wall hits the back wall. Reflection and inverted wave will interfere with each other destructively so the reflection is canceled. This is also known as "active absorption".
The necessary delay formula_18 of the back array is based on the length formula_19 of the room:
formula_20
formula_14: Speed of sound
The necessary delay required for a DBA is available in most digital equalizers or digital crossovers. Polarity of the back array can easily be achieved by inverting the signal coming from the amps or by swapping the cables going to the driver. Most active subwoofers also offer a polarity switch.
Notes.
A DBA just requires two opposing walls, so it is possible to have one array on the floor and the other on the ceiling, or one on the left wall and the other on the right. However, low frequencies become localizable at a specific frequency, so in most cases it's probably a good idea to use the walls with the lower distance of separation.
The effectiveness of DBA largely depends on the room's physical characteristics.