Physics Question: Why does cabinet volume matter so much to bass response?

Yes, manipulate wasn't a good way of putting it. I've heard very good bass, at least in my subjective opinion, from active monitors. My room isn't huge either which helps. 

@marined -

     As rego mentioned: how a driver responds in an enclosure, depends largely on T/S parameters.

     I didn’t notice anyone else providing further info, but- I HATE to type, so:

          https://audiojudgement.com/thiele-small-parameters-explained/

@djones51 --

"... I’ve heard very good bass, at least in my subjective opinion, from active monitors. My room isn’t huge either which helps."

The same have I, actively configured monitors not least, not that they’re bending any laws of physics here, but because removing passive components between the amp and the woofer is a rather significant advantage, I (and many others, obviously) find. And a listening room not too large nor heavily damped will only help where limited displacement is at play, sure.

My issue is the relatively small cube-sized subs with very long excursion, larger sized woofers and quite heavy cones + voice coils crawling into the infrasonic territory. The ones I’ve heard are fiendishly difficult to integrate properly with regard to music reproduction, not to say nigh on impossible, but crossed low enough (<40-50Hz) may prove less of a hassle here. For home theater duties though they’re usually very good providing weight and the eerie-feeling "shudder" effects to below 20Hz. Perhaps this is the main reason audiophiles at large prefer REL subs for augmentation, because the driver choice for these is more about the >20Hz range.

I’m sure you’ve seen the pics or videos of stacked, larger REL subs, oftentimes with 3 or 4 of them per channel stack. Many balk at these constellations, finding them way overkill and for the über-bass heads only, but to me it makes perfect sense; they’re not tuned too low per above, and there’s prodigious displacement and better coupling to the acoustics for that effortless, clean and powerful-when-needed presentation that’s really all about what audiophiles should aspire to here. My only contention with the REL approach is price; there are cheaper ways to achieve this, not least with DIY offerings, but if you have the dough - go for it.

I used to own an SVS SB16-Ultra. For its size and right use it was an impressive sub - indeed a beastly little cube. My current pair of subs are over 4 times the volume (per cab) compared to the SVS, and yet the SVS went between 5-10Hz deeper. Noodling a bit with Hofmann’s law above you can figure out what that’s about. Many an audiophile would assume the SVS sub to be the "audiophile" choice, but it’s actually the other way ’round; a pair of 20cf. per cab tapped horn subs just sound so much more integrated, smooth and enveloping, but I guess most would have to hear it to believe it. To boot, when these things unload, they truly unload. 

Used the Fostex 31.5" woofer I have designed many bass systems inc sum used in military simulators. I also have designed many monitors. Small is just small if your going small in loudspeakers you are compromising performance so you can have a small speaker. Think about the wavelength sizes your trying to replicate. Are real-life musical performances the size of a loaf of bread?

I am surprised that the OP read Richard Vandersteen's response as "pissed off." Every time I have corresponded with Richard, he has been helpful.  I believe his response is related to the complexity of the question, as indicated by all the other responses.  I know Richard is busy and considers answering customer questions quickly a high priority, as he mentioned once when I attended a Vandersteen seminar.  By the way, I have Quatro CTs after many years of passive bass. And I am glad I made a move.