Array layout

Modes between side walls, floor and ceiling are suppressed by arranging the subwoofer in a specific grid:

${\displaystyle p_{x}{=}{\frac {(2\cdot n+1)\cdot w_{x}}{2\cdot a_{x}}}}$

${\displaystyle p_{y}{=}{\frac {(2\cdot n+1)\cdot w_{y}}{2\cdot a_{y}}}}$

${\displaystyle w_{x}}$: Wall width

${\displaystyle w_{y}}$: Wall height

${\displaystyle p_{x}}$: Horizontal distance from wall (${\displaystyle d_{x}/2}$ for n=0 in picture)

${\displaystyle p_{y}}$: Vertical distance from wall (${\displaystyle d_{y}/2}$ for n=0 in picture)

${\displaystyle a_{x}}$: Number of subwoofers horizontally

${\displaystyle a_{y}}$: Number of subwoofers vertically

Counter ${\displaystyle n={0,1,2,3,...,(a-1)}}$

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 ${\displaystyle f_{c}}$ can be calculated for each dimension as follows:

${\displaystyle f_{c}{=}{\frac {c}{2\cdot d}}}$

${\displaystyle c}$: Speed of sound

${\displaystyle d}$: Distance between subwoofers

Example: A 2 × 2 array on a wall measuring 4 × 3 m would work up to 86Hz horizontally ${\displaystyle f_{c}{=}{\frac {343m/s}{2\cdot 2m}}}$ and up to 114Hz vertically ${\displaystyle f_{c}{=}{\frac {343m/s}{2\cdot 1.5m}}}$.

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 ${\displaystyle t_{d}}$ of the back array is based on the length ${\displaystyle l}$ of the room:

${\displaystyle t_{d}{=}{\frac {l}{c}}}$

${\displaystyle c}$: 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.