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

I asked this exact question to Richard Vandersteen a few days ago.  I own his 5A's, and he literally has a section on his website called, "Ask Richard."  So i went ahead and asked him.  This was his response:

There are 100s of books and unlimited resources available online that will explain speaker design in detail for you.  I’m very busy and don’t have that kind of time.  RV

I managed to actually piss off Richard Vandersteen! Oops!

@djones51 --

"Newer designs like the Devialet Phantoms manipulate Hoffman’s Iron Law using DSP and crazy amounts of power to get bass in small enclosures."

Hofmann's Iron Law still applies, as the crazy amount of power is necessitated due to low efficiency and to get the small cone (in a small enclosure volume) moving enough to generate low frequencies at an intended, respectable SPL to make the low frequencies reproduced worthwhile - at least in sheer volume. 

Again, the "manipulative" aspect here is one that has no impact on named law itself, but is merely a compensatory measure in an effort to generate more SPL through added power capacity and handling. You easily end up chasing your own tail though, as the design choices leading to added power handling in a driver has a tendency to reduce efficiency, even though such designs can be made to mesh well with smaller enclosure volumes and thus may need less EQ in the lower octaves. 

In the end though small size comes at a price: smaller drivers, or even bigger ones in small enclosures has to work harder in generating more excursion, and ultimately this comes off as a "huffing and puffing" imprinting of the bass that simply cannot be ignored as something sounding too distinct. Many may not know the difference though, as few have likely heard how bass can sound from much larger systems with large (or horn-loaded) cones that move only a fraction by comparison. 

Regarding larger enclosures vibrating too much (unless extensively braced and weighing several hundred kg's), I've never encountered this to be any hindrance with the large sub designs I've heard, most of which have been well constructed birch plywood boxes "naturally" braced via their design specifics as horns and/or bandpass iterations, and therefore with rather complex enclosure innards with horn paths and such. Vibration control as it's argued to be of extreme importance to me is a bad excuse to avoid large size. 

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.