The easiest way to visualize what’s going on in those boxes is to imagine them as working like a coil (inductor), as opposed to all other loudspeaker cabinets which act more like a condenser (capacitor).
Under “d.c.” acoustic conditions, the bass unit reaches it’s maximum excursion boundary and sits there. Pressure (the applied signal) equalizes through the system and the acoustic resistance (flow of air) falls (stops), although an acoustic potential (‘back-EMF’) remains. When the d.c. condition is removed, the acoustic potential discharges in the opposite direction to the force that was previously applied, producing a classic cosine waveform.
This is the very definition of an acoustic inductor.
Under “a.c.” acoustic conditions, the bass unit must dissipate the acoustic back-EMF in the cabinet before it can change direction and complete the next part of the waveform. Fortunately, the direction of collapse for this wave function is the direction that the bass unit is now required to travel in. However, as the internal pressures cannot equalize in time (requires 5 to 10 % of a second, which reflects the value of acoustic inductance measured in Carrolls), the acoustic potential remains integrated with the applied signal with a small phase shift (CIVIL- for all you non-electrical engineers out there, C. I. V. I. L. refers to the electrical behaviours of Capacitors [C] and Inductors [L], and breaks down to mean; “CIV- in capacitive systems, current leads voltage. VIL- voltage leads current in inductive systems”).
In practice, this effectively prevents the bass cone moving, though it is still propagating energy prolifically. The tiny amount of residual motion is indicative of a very low acoustic power-factor loss (ie, the bass unit has maximum traction on the room-air load; no ‘slip’).
The process repeats and the bass unit is then caught between the two opposing collapsing waveforms which it re-energizes constantly, while being clamped firmly between them.
It could be viewed as similar to how horn-loaded loudspeaker-drivers (eg, Lowthers) work with an excursion of less than 1mm; because they are optimised as pressure-transducers. They expect to be at the throat of a horn, which matches the high pressure low amplitude at the throat, to low pressure high amplitude at the mouth of the horn. The horn acts as an acoustic transformer. In our case, it works without the phase inversions that plague horn loudspeakers because instead of being a multiply-coupled system, ours just runs as a single pure acoustic induction element.