I haven't done system for years now. Things get forgotten.. Might I ask what's the reason to the quarter wavelength?
If doing a normal cardioid stack, I remember one simple solution was to invert the rear facing, but delay it to the ms which would equal to the depth of the cab? If my memory doesn't trick me? (or more precise, the travel distance from front to back, measured from center of a dual cab)
Your memory is fine, it's just that there are two different ways to create cardioid subwoofer arrays: "end-fire" and "gradient" (to borrow Bob McCarthy's term). Tim described a gradient array (i.e. delay the front sub to the back sub and add a polarity inversion), you're describing an end-fire array (i.e. delay the back sub to the front sub with no polarity inversion). End-fire produces full-range, full-power summation out front and a fairly narrow frequency band of cancellation in the back, while gradient arrays produce full-range cancellation behind them and a (relatively-broad) band-limited audience-facing output (that is also—technically—content-dependent because of the polarity inversion), as well as a small loss of overall efficiency vs. end-fire (or non-cardioid) options.
The "quarter wavelength" is important because both designs are frequency-specific: in end-fire arrays the distance between the subs is used to tune the frequency of rear null, while in gradient arrays the distance is used to tune the centre of the audience-facing output band. In practice, though, the distance used
is often just the depth of the box (which for touring-grade subwoofers is, not coincidentally, typically the quarter wavelength of some useful frequency like 60 or 70 Hz).
-Russ
