Here is a drawing I created in attempt to capture the differences.
Either 1 or 2 is fine. Definitely not 3. Personally I prefer #2 but renumbering the layers, so your layer 2 is first, then your layer 1, then your layer 4, then your layer 3. If you do it in that order, then the drywall on the wall gives you a small "ledge" to rest the ceiling drywall while you are maneuvering it into place.
However, I'm curious about this:
Drywall-corner-transition-leaf-not-decoupled.jpg
What's going in there? What's the light grey and dark grey, and the black channel-thingy? To me it looks like your inner-leaf is coupled to your outer leaf there.
to the outer layer of a decoupled soffit frame;
How is it decoupled? That's not clear from the image. Indeed, from the image it looks like it is coupled!
Should one leave the small air gaps (white spaces) which may occur,
There should be no air spaces. If you push the backer rod in deep enough, then caulk well, there would only be very minor air spaces in there between the round backer rod and the flat drywall faces. That's not a problem at all.
Is the 1/4" gap just to allow insertion of sealant,
What '1/4" gap'? I don't see that marked on your diagram.
Is there a good way to build without the gap, corners tight, without need for backer rod at all?
No. Because that would not allow for good sealing. If you cannot get backer rod where you live, then you can do two layers of caulk instead, with the first layer replacing the backer rod. Wait until that is dry before you do the second one.
A lot of illustrations and instructions online seem to show no gap, just a tight fit of the panels at all corners.
That might be the case, but that's probably just for clarity, not actual construction practice. In the studio designs that I do for paying customers, I don't show those gaps, since it's a lot of extra work to model them. I just mention them in the notes or explanations. Just like I don't show where to put every single nail or screw: some things are taken for granted in construction, and there's no need to detail them on the plans or 3D model.
Rod Gervais and others mentioned otherwise that this is not a good method since it relies on just tape for seal.
Right!
Are there any links to info on the relative isolation provided by 3 layers of sheetrock/drywall/gypsum instead of 2? I seem to recall that it becomes a matter of diminishing returns, but can't find the source.
Here's your answer: Don't guess! do the math to make sure that you really will get the correct MSM resonance frequency, and the amount of isolation that you need, at the frequencies where you need it. Here's what you need to know:
The equations for calculating total isolation of a two-leaf wall are simple:
First, for each single-leaf barrier individually you need the Mass Law equation:
TL = 14.5 log (M * 0.205) + 23 dB
Where: M = Surface density in kg/m2
For a two-leaf wall, you need to calculate the above for EACH leaf separately (call the results "R1" and "R2").
Then you need to know the resonant frequency of the system, using the MSM resonance equation:
f0 = C [ (m1 + m2) / (m1 x m2 x d)]^0.5
Where:
C=constant (60 if the cavity is empty, 43 if you fill it with suitable insulation)
m1=mass of first leaf (kg/m^2)
m2 mass of second leaf (kg/m^2)
d=depth of cavity (m)
Then you use the following three equations to determine the isolation that your wall will provide for each of the three frequency ranges:
R = 20log(f (m1 + m2)) - 47 ...[for the region where f < f0]
R = R1 + R2 + 20log(f x d) - 29 ...[for the region where f0 < f < f1]
R = R1 + R2 + 6 ...[for the region where f > f1]
Where:
f0 is the resonant frequency from the MSM resonant equation,
f1 is 55/d Hz
R1 and R2 are the transmission loss numbers you calculated first, using the mass law equation
And that's it! Nothing complex. Any high school student can do that. It's just simple addition, subtraction, multiplication, division, square roots, and logarithms.
One thing I've not been clear on is whether or not it is necessary to tape and float joints on the inner layer(s)? Can you just caulk the inside layers or do you also have to tape and float those as well?
That's about aesthetics, not acoustics: If the wall will be seen inside the room, as part of the final finished surface, then yes, I would very much suggest "mud and tape" before you paint. In that case, do not caulk all the way to the surface: leave a small gap so there's space for the mud. But if the wall won't ever be seen (eg, if you do an inside-out wall, or if it will be completely covered with other treatment), then it isn't necessary to mud-and-tape it, since it won't ever be seen.
- Stuart -