I would (and always do) use 2" rockwool; in the ceiling speakers I alluded to in the other thread I did cut the 2" sheet in half however that was because the enclosure was too shallow to fit both the 2" rockwool and the activated charcoal. actually the magnet on the ceiling speakers was 'bottoming out' on the back wall also; I cut out another 1/2" of rockwool behind the magnet so everything would fit well... basically I would actually recommend rockwool lining every wall, 2" thick since high frequency noise is more of what you are trying to reduce...
to get a better feeling of the reduction that each material provides you can take a speaker... like a 'mid' bookshelf speaker or something, not a sub... (preferably do this in a large garage or something) and play it loud at an angle facing towards a sheet of mdf board or plywood. you should be listening where the secondary reflection travels (so say you have a 10 ft line, from you to the speaker, the speaker is aimed at the mdf which is between you and the speaker but also offset so that it is not directly between you. then have someone move various materials in front of the mdf so they are adsorbing the reflection; this can help you compare/test materials.
your last post seems to have an attitude of trying to 'get away with' something other than rockwool. there are specially engineered materials (I have been told of something called "Black Hole 5") that will also work; so here is 'the deal' rockwool will be the cheapest broad spectrum/general purpose absorber you will find (at least in my experience). Other materials will probably work, though they will not work *as well* as rockwool. So really it is up to you, the Black Hole 5 is pretty expensive stuff (a 12x18" sheet is $27.50 USD in a quick price check, there may be better deals out there).
There are 3 main 'categories' of noise reduction/filling when building speakers:
-reducing structure borne noise (eg. stiff materials/thick walls, and also using heavy *dense* materials such as the padded rubber). You are trying to keep the box from flexing due to pressure/vacuum inside it, and also if there is any flexing, you try to make the resonant frequency a very low one (every octave down (in frequency), you need 4x the excursion (distance traveled by the transducer) to produce the same intensity of sound, so if you consider every wall of the enclosure to be its own transducer (driven by the pressure differences created by the actual speaker/sub), cutting the resonant frequency in half will mean that the panel resonances (at the resonant frequency) should be 6 db less for a given input power, not to mention that if you can get the resonant frequency very different from what frequency you are playing (trying to push something resonant at 20 hz with a 30 hz tone) will also give a reduction in transmission, so if you can get the resonant frequency very low (say 10 hz) you may actually have a 12 or 15 db reduction in the energy produced by the panels of the box. If you have noticed by visually looking at your passive radiators (depending on your tuning frequency), or by feeling the amount of airflow through a port on a ported speaker, the port/passive radiator is tuned to a resonant frequency, so there will be very little motion/airflow unless the speaker is trying to play a frequency at or near the resonant frequency of the port/passive radiator. Basically in making the panels more dense, you are trying to push the resonant frequency out of the range the speaker will be producing so the box does not add (or subtract) from the sound. Also, adding a different kind of mass (say thick rubber adhered to mdf), you will also be helping reduce the 'resonant modes' of the panels; basically, depending on the speed of sound in the material you are working with, a certain shaped piece of material will have a certain resonant frequency, however anything over that frequency may or may not be a resonant mode, typically a multiple of the f0, the initail resonant frequency (and create a 'standing wave') in the material, so there would actually be a standing wave *inside* the board of mdf causing it to flex at high frequencies. Using a more dense material and adhering it to the mdf will help to reduce the standing waves of the box because you are using the same principle of 'driving' (pushing) something at a frequency that is not resonant; the idea is that the resonant frequency (and subsequent modes) of the rubber will be different than those of the mdf, so when the mdf resonates, the rubber will be being 'driven' by the mdf, however since the rubber does not have the same resonances, it will help dampen (adsorb) the energy.
-reducing internal reflections; here is where rockwool/ is useful. rockwool has very good adsorption characteristics for 'incident sounds', it also should be noted that rockwool has a very low resonant frequency due to its relatively high density and 'floppiness'. If you were to do the experiment I mentioned with the speaker, sheet of plywood and you (listening to the reflections off the board and then seeing how various materials differed when placed in front of the board), you would probably notice that rockwool adsorbs almost all of the sound, the difference really will be night and day. The reason rockwool (and other adsorbing materials) do what they do are due to two primary modes of action, rockwool since it is flat yet adsorbs so much sound works because of its porosity, so there is not really a definite change from air to rockwool when the sound wave hits it, the 'deeper' into the surface of the rockwool the sound travels, the more sound is adsorbed, the energy is adsorbed both by resistance to motion (due to the rockwool's density or 'heft') and also because it thermodynamically adsorbs 'evens out' the very small temperature swings caused by pressure variations (compressing a gas concentrates energy (heat), letting a gas 'expand' (eg. compressed air) will mean that the energy that was in x volume now is distributed over a larger area, which reduces the heat concentration (making cold...)), another common use for rockwool is for insulation (it has a higher "r" value than fiberglass insulation), its ability to keep the temperature swings from happening as the sound wave travels into the material help to stop the sound wave also. The degree to which different materials do the two things I just described will in large, determine their 'airborne' sound adsorbing properties. One thing to notice about egg-crate foam is that typically the larger the wedges you get, the better the noise reduction coefficients you get, this is because egg-crate foam scatters and traps sound as well as providing decent adsrobption (relative to rockwool), so the larger the 'egg-crates' or pyramid shapes, the more surface area (the more surface area, the more area you have to reduce and divide up the sound pressure wave), the better the adsorbption. Also, another function of the shape is that the reflections will 1) be scattered in many directions (diffusion) and 2) some of the primary reflections that are not adsorbed will end up reflecting into a nearby part of the foam, so you may have two or more subsequent reflections (and reductions) before the sound is coming back at you, if each reflection knocks off 5 db of intensity, and you have 3 reflections, you get -15 db
granted, that is only part of the wave that is going to be getting that many reflections, some points may get more some may get less; on average though it works pretty well. The best combination I know of is to cut relatively 'high' wedges of rockwool to adsorb sound since you will then be getting the 'multiple reflection effect' also. I know that anechoic chambers use that method; I saw a photo of one at klipsch which appeared to be rockwool wedges... Granted, the box is also going to have its own reduction in signal travel, the adsorption inside a box, as mentioned in other posts, is more to reduce mechanical noise or any speaker/sub cone breakup modes that are playing inside of the box, the idea is that you don't want the mechanical noise to reflect off of the back wall and be reflect back into (through) what is typically a relatively thin speaker cone to be heard outside the speaker. For a midrange speaker it will adsorb the high frequencies playing off the back side of the cone also (I mentioned breakup modes since you are talking more about a subwoofer)...
-Lastly (I know it's been a lot of info) there is the method you mentioned of making the box 'appear' larger to the speaker. This is accomplished in two ways (that I know of), 1) by using poly-fill as a thermal mass to even out the temperature swings caused by the pressure waves; by having the entire volume of air 'mixed' with a substance that will adsorb the temperature swings (keeping a more constant temperature), you will be able to put that much (a little bit) more compression/rarefaction (vacuum) on the air in the box. Also, the mass of the material will help slow down the speed at which pressure waves travel through the material, lowering the tuning frequency a bit; you won't remove the standing waves, you will be shifting the frequencies at which they occur. In the past I have mentioned using activated charcoal in my speakers; this is an idea I came across that is used in some speakers made by the KEF company. The activated charcoal (as KEF explains and I understand) literally adsorbs and releases some of the air molecules, due to Van der Walls forces; basically activated charcoal has a HUGE surface area due to all of the microscopic tunnels inside its structure (a gram has over 500 m^2, up to 1500 m^2 of surface area), the material is very similar in consistency to 'medium/large' sand particles. This makes it great as a temperature swing equalizer, in addition to the key property of literally "sucking up" ('removing a volume of gas from the system' when under pressure) air when pressurized. Activated carbon is used in industry in devices that separate gases; you know 'continuous flow' oxygen units (oxygen concentrators) for the elderly, they use activated carbon in a process called "pressure swing adsorption" which first pressurizes air (adsorbs it into the activated carbon) then releases the pressure, at certain pressure points, different ratios of gases are released, ex, more oxygen may be released first, then more nitrogen at a lower pressure so if you want oxygen, you would take the 'product' when you release the high pressure to go to medium pressure, then you release the 'waste' nitrogen into the atmosphere (when going to 'normal pressure', so the end result is a 'feed' of gas with a higher oxygen concentration. When researching about activated charcoal for my sub, I found (based on extrapolating some of the numbers KEF gives in their specs) that activated charcoal should give a 2.6:1 ratio of volume, so if you have 1 cubic foot of activated charcoal, you are getting a 'free' 1.6 cubic feet of box volume. It should be noted that this effect is frequency dependent, so at ~80-100 hz, the ratio drops off, however it is the really low frequencies that typically need the larger volume anyways... I should probably start a thread to disseminate the activated charcoal info, I did all that stuff in 2005... Anyways, you do need to get the *right kind* of activated charcoal, because different kinds have different surface areas, and also there are different pore sizes from different initial materials/manufacturing methods, so you do need to consider a few things before just 'throwing some carbon in there'
Well... Phew, that is what I consider to be a pretty good (but lengthy) explanation of how and a big part of the why you would use various filling, damping, adsorption, for different purposes. Hopefully someone read it all ;p questions or comments, let me know!
