MS or M

Just a general construction question here. Consider the following wall construction from outside-in: 120mm Brickwall, 100mm airspace (with about 40-50mm loose glasswool batting affixed to the drywall) 2 layers of 16mm drywall, 2x4 wooden framing. Basically a typical inside out isolation wall construction. Now, before the wall is constructed, it is suggested an extra layer of 16mm drywall be used, thus making 3 layers of drywall in the above structure. Due to concerns (let's say) about room-space, or existing construction, the walls cannot be moved any further inwards. This means that the third drywall layer will eat into the 100mm airspace. It is said that about 4" or 100mm is about the minimum spacing for an MSM constuct. Which is more important, mass or airspace? Would the consequent reduction in airspace be so disadventageous as to make the added mass layer worthless? As the space is reduced the RF increases just as the RF will be lower for an increase in mass. Is there a ratio or something involved here?

The wool is also part of your "spring" (the S in M-S-M) so your cavity would be 100mm+50mm=150mm. I'd tighten the airspace. sure.

Is it really simply additive? Theoretically then, I could increase the insulation to 65mm and would have practically the same "S" as before !?

yup!

Which is more important, mass or airspace?

The answer is: "Yes"! :) In other words, they are both equally important, very roughly. Rule of thumb: if you cut the mass in half, then doubling the airspace will compensate, approximately. The relationship is not that exact, and is NOT linear, but it gives you a rough idea. Once you get much below 4" or above 12" for your gap then it stops being a useful guideline. So, in your case, you are increasing your mass by 50%, and losing about 15% of your gap. Not really a problem, even though you are going slightly less that 4" on your gap. I wouldn't sweat it too much.

This means that the third drywall layer will eat into the 100mm airspace.

Not necessarily! You could use the "beefing up the wall between the studs" concept, and add the extra drywall to the room side, carefully cutting strips of drywall to fit in the spaces between the studs. Cleat and caulk. Done deal! That way you get the best of both worlds: you increase your mass by 50% without reducing your air gap.

Theoretically then, I could increase the insulation to 65mm and would have practically the same "S" as before !?

And you can improve it even more by filling the entire cavity (assuming that your local building code allows that). Theoretically, the difference between an empty cavity and a full cavity can be as much as 16dB of isolation (depending on many factors), but more insulation is always better for isolation, provided that you don't pack it in tightly: just enough to fill is great. So if you can get all 100mm of cavity depth with wool, plus the extra layer of drywall between the studs, then you will ave a really good improvement in isolation. And if you REALLY want to go overboard, put Green Glue between the layers of drywall. If you want the actual numbers: Theoretically, 3 layers of drywall over a 100mm cavity without insulation gives an MSM resonance of 22 Hz., so your wall starts isolating at 44 Hz, and isolates well at 66 Hz. Add the insulation and the MSM resonance drops to 16 Hz, so your wall isolates at 32 Hz, and isolates well at 48 Hz. In other words, adding the insulation means that your wall will isolate well for nearly another half octave on the bottom end of the spectrum. OK, now the same calculations for the three layers over an air gap of 84mm (100mm less the extra layer of drywall): No insulation MSM resonance = 24.5 Hz, wall isolates at 49 Hz, isolates well at 73.5 Hz. With insulation, MSM resonance = 17.5 Hz, wall isolates at 33 Hz, isolates well at 52.5 Hz. And finally, to compare that with the original plan of only 2 layers over 100mm: With no insulation, MSM resonance = 27.5 Hz, wall isolates at 55 Hz, isolates well at 82.5 Hz. With insulation, MSM resonance = 20 Hz, wall isolates at 40 Hz, isolates well at 60 Hz. Conclusion: Adding the third layer inside the cavity (reducing air depth, but with insulation in both cases) improves the MSM resonance from 20 to 17.5 Hz. So even though you lost air cavity depth, you still gained overall isolation due to the extra mass. But adding that third layer between the studs improves things even more, from 20 Hz. to 16 Hz. That doesn't seem too much, until you figure the frequency at which the wall starts isolating well: 3rd layer in cavity=52.5 Hz, 3rd layer between studs=48 Hz. But either way, that's a big improvement over the original 60 Hz! So there are your numbers: now you can figure out what makes the most sense for you! - Stuart -

Thanks Stuart. Another very informative answer. My original question was prompted more out of curiosity than my actual build. In my build the spacing of the walls is indeed critical - can't really afford to lose too much width, so this information will indeed help. As for the "Beefing up" method, I'll have to keep that in mind, but I think I'm going to have a major issue with the acoustics i.e. will need a lot of absorption. So I want to keep as much of the space - depth between the studs for absorption and trapping as possible. Green Glue I might add is really unknown here. Ask for it and you get Scotch Green glue which is just a glue. I am still sourcing materials here - you wouldn't believe how difficult it is to find 2x4 lumber (50x100mm or even 45 x 90) it's nearly unheard of here it seems, whereas practically every other place in the world it's so common! I know it can be sourced because they used it (exactly 50x100) in wall construction in our attic, so I've got the number now for the supplier from our architect, have to see what the pricing is like. In regard to the drywall, I am thinking 2 layers of 18mm, again I'm waiting for some pricing and availability info. Could you show me the formula you used to calculate the resonances so I could apply it to the aforesaid 18mm construction. By the way Stuart, feel free to comment on my design thread, viewtopic.php?f=1&t=15635&start=30 there is an open question regarding ventilation I think Glenn is on hiatus (well deserved).

As for the "Beefing up" method, I'll have to keep that in mind, but I think I'm going to have a major issue with the acoustics i.e. will need a lot of absorption. So I want to keep as much of the space - depth between the studs for absorption and trapping as possible.

OK, I'll comment on that on your build thread.

you wouldn't believe how difficult it is to find 2x4 lumber

Can you get larger dimension? 2x6 for example? or 2x8? Or is it just hard to get wood in general) If you can get larger stuff, with a table saw you can get it down to size real quick.... or just leave it large, if it will fit: oversize lumber is stiffer and stronger, both of which are good for isolation. The other possibility is to use metal framing, instead of wood.

In regard to the drywall, I am thinking 2 layers of 18mm, again I'm waiting for some pricing and availability info.

Can you ask about the density of that stuff? You need to know that for the calculations. Either true density or surface density is fine.

Could you show me the formula you used to calculate the resonances so I could apply it to the aforesaid 18mm construction.

For your case, for a drywall leaf in front of a block wall, that would be: f= 60 / SQRT(m*d) Where: m = the mass of the leaf (surface density) in kg/m2 d = the size of the air gap (distance between block wall and drywall) in meters - Stuart -