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

The simplest answer is that the air in the cabinet forms part of the suspension.

Before box speakers everything was pretty much close to open air/open baffle designs.

  Never knew much about them, but I remember seeing a driver that was mounted in a closet door. This was back in the 50's.

  I agree that the volume of the cabinet will dictate the amount of air suspension that the woofer is given. It is also important to know that the cabinet volume will determine the resonance of the cabinet itself. Think of different sized bottles and the sound that they make when blown over.

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.