How do small woofers produce large bass?

@bartsw wrote:

I would't disagree with the possibly of using HT speakers in this application. But I disagree with people using the term physics and science as if it's a complete equation.

Physics are a prerequisite that's typically left out - that's the problem. That's not to say it's all about displacement area, but it sets the stage for priorities that should be covered as a primary concern and what this means for the design implications. 

A 12-15" HT driver can be room overload for many homes above 80Hz. Thus to get the most clean and beautiful sound for mid-range and music with the lease room mode, smaller drivers could be more appropriate.

When I said I don't consider drivers below 12-15" to be woofers from the perspective of the physics involved, it's also implying that midrange drivers should be somewhat larger than your typical 4 to 6.5" units (which again has design implications). Above the Schroeder frequency what exacerbates the reflective nature of emitted sound waves is a wider dispersive field from a smaller cone area, whereas a larger driver diameter and/or horn will narrow the dispersive field and thus heighthen the ratio of direct vs. reflected sound for less room interaction - an important aspect, if you ask me.

In addition a greater surface area from the upper bass into the lower to central midrange lends a much needed sense of physicality, commanding presence and ease in this region, but for drivers to be suitable for this it typically means woofer/midrange designs with higher efficiency crossed over to horns in the 500-1kHz range. 

So, physics here is also about accommodating radiation pattern control and uniformity and how this affects the sound we perceive. Unfortunately many seem to be focusing on loudness and overpowering a listening space when larger speakers designs are discussed, while leaving out above mentioned.

If you have a well-designed speaker system of higher efficiency with prodigious air radiation area and where the driver sections sum at the listening position, while factoring in the above re: dispersive nature, I see a far more capable speaker outset than what would be achievable from a smaller, low efficiency package where mentioned parameters are harder, not to say impossible to come by. 

As others have noted, one can get deeper and stronger bass by increasing excursion and this might compensate for the smaller cone area vis-a-vis another driver with a larger cone.  But in audio, as is the case with almost anything else, there are tradeoffs involved.  My favorite drivers are low excursion drivers meaning that I don't go for extremely deep bass.  My speakers utilize twin 12" drivers in a Jensen-Onken cabinet and they can go as deep as 35 hz.  While this does seem a bit modest, this low excursion driver is very fast and clean and blends well with the horn/compression midrange driver of my system. 

A local builder uses 18" drivers, sometimes in twin driver arrays and he says it is good to 30 hz or so.  He will soon be building with 31.5" woofers that are rated to 28 hz; I've heard the prototype and it sounds great.  It is not just the amount or depth of bass that matters; large driver/speakers deliver a sense of weight, large scale and authority (with no feeling of strain) that smaller systems cannot match.  My own system, which is two feet wide by three feet all and about 18" deep is on the tiny side for a horn system and does not have the weight and scale of the systems with larger woofers and much larger horns.

Several factors come into play when discussing the abilities of woofer drivers. Given the materials used to produce the cone, type of compliance, spider stiffness, the resonant frequency of the driver, all affect performance. There is science behind it, but the case design matched to the charactistics if the woofer create the desired sound. 

As far as woofer size, the effective radiated area of 2 six inch woofers will be about the same as a 12" woofer. In the right cabinet design, they can perform impressively.  My experience is that a larger woofer will give more slam, hit, kick, in a 12" woofer vs two 6". However, the two 6" will likely respond more quickly in music dynamics because there is less mass to control.

Both will get low frequencies equally well.

They don't.