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

this will get you started to understand this somewhat complex subject

A ' driver ' has electro - mechanical - acoustic properties ( TS Parameters ) and the volume relates to ' efficiency ' in a ' system ' ( loudspeaker ) as well as other relational properties.

Physics

It's a shame manufacturers went the way of small thin cabinets and tiny woofers. They all sound like giant tweeters these days....

 My understanding is that a larger cabinet will support a lower frequency response in the bass. The shape of that frequency response is also shaped by the design of the cabinet, i.e., whether it be sealed box or bass reflex (let's leave out the other designs for the sake of keeping this simple).

  As many of you already know, the sealed box design will make a slower slope in the bass response (although not as deep) than the bass reflex, which goes lower in frequency, yet at a higher slope than the sealed design. Given this, bass response is altered by the physical size of the cabinet. A smaller cabinet simply cannot load the woofer for lower frequencies. Of course, these factors much match the T/S parameters of the driver to begin with to make a reasonable bass response in the first place. A bigger cabinet allows for lower and possibly flatter response in general than trying to make a small woofer and cabinet do what it cannot. A popular trick used for smaller cabinet/woofer sizes is to make use of a bump usually at 100hz. It gives the likeness of more bass, a thump, if you will, but it is not ideal for my tastes. 

   This is the case for passive speakers, but active speakers can use EQ in the signal to try and offset the limitations of the cabinet and driver. In the end, physics will rule up to the limits of the final product.

Hofmann's Iron Law

three parameters that cannot all be had at the same time. They are low-bass reproduction, small (enclosure) size, and high (output) sensitivity." Hofmann stated that designers could pick two of these three parameters, but in doing so, it would compromise the third parameter.

Speakers dont live alone in life...

They are married to a room...

I use the room to mitigate the effect  or improve on the Hofmann law...

Acoustic is queen...

mahgister,

  Yes, the room acoustics are fascinating to me even as a child. So, maybe understanding the room first, and then 'marry' a speaker to it?

mahgister,

Yes, the room acoustics are fascinating to me even as a child. So, maybe understanding the room first, and then ’marry’ a speaker to it?

You must use a speakers pair to understand the room throught them...

You cannot understand a room out of his dialogue with a specific speakers pair...

It is the room that will reveal the beauty of your speakers, and it is your speakers that will ask for the room response first ...After a balanced material acoustic treatment, if you have a dedicated room, explore active mechanical control with Helmholtz devices...

After that you can use psycho-acoustic basic to adapt speaker A and B to ear A and B...but this is more complicate, if you go there i will give you some advice at this time...

If you have a small room it is easier to do... Under 15 feet... my room is 13 feet square... I dont have experience with big room...They will ask for other experiments... there is no universal recipe for a small room...The acoustic content, the audio system ask for specific installation.. . A great hall is another completely different matter... Science know much about big hall acoustic than about small room acoustic, because it is a new phenomema for few decades...

In acoustic listening experiments dictate all choices....Recipe are for acoustic sellers panels to simplify their life... 😁😊

If i had used simplistic acoustic recipe instead of experimenting, no way i will had enjoy a so great improvement... But my room with hundred of devices is a dedicated room and not a living room...Acoustic ask for an audio room...Living room are OK but you cannot transform it enough to serve the speaker and your own head and listening location... It is not the gear price the audiophile luxury it is a dedicated room...

All room is in individual content , you adapt , there is no great value in general recipe for ALL ROOMS ...

Nothing is more fun than exploring acoustic...if you chose well designed basic gear, upgrading is a waste of money by people unsatisfied who cannot change their acoustic than they change the gear...

I cannot even imagine i will upgrade because it will be costly for minor improvements... And even if this would be more major improvement i did not even think about this because i am too much happy already...

Nothing can beat acoustic experiments fun...

In simple physics terms, the woofer can woof more when the cabinet is bigger or is ported or a passive radiator is used.

Are you guys saying that a woofer can extrude further into the room and therefore play louder in a larger cabinet?  Is that because the air pressure is lower in a larger cabinet, so it pulls less on the woofer as it moves foward?

Well, it is a marriage between the driver and its abilities, and the cabinet made for it. You play to that particular drivers' strengths. In general, the bigger the woofer the bigger the cabinet. Again, this is applying to sealed and bass reflex/ported designs.

 It isn't a matter of the woofer being able to play louder any more than the woofer is supported by the cabinet's extension of resonance that aids in the woofer's lower octave response.

  You want big low bass, you will be the most successful with a larger cabinet and driver, given a proper design. And then you will move air.

You have to brace the heck out a large cabinet though, or else it will vibrate too much and the bass will be crap. A lot of smaller subs with strong cabinets can yield some amazing results.

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

By the way, that was a very good question OP!👍

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. 

@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.