When does the triple leaf effect come into play?

[timsouthorn]

Hi, this is my first post so please let me know if I need to address anything in particular…

I'm looking to build two separate writing rooms/production suites. They will be used mainly for song writing, electronic music production and occasional vocal tracking. I don't believe the details are that important to my question at this point, though I will certainly be asking more questions with more detail regarding use case and construction in the future.

What I've been struggling with is, when does the triple/quadruple leaf effect come into play?
Does it only apply if the air gaps are sealed?

Say I were to build two free standing isolated rooms, booth room within a room construction, that were placed next to each other, both free standing so the air gap would be open on three edges (as in fig a).
As the middle air gap between the two rooms is not sealed, would it still contribute to the quadruple leaf effect?
Would it make a difference if that air gap was say 4" compared to 12"?

Would it be better to build two inner rooms with a single outer room (as in fig b), with two leaves and an air gap equal to the total equivalent depth of the four leaves. In this scenario, would an air gap that large even be necessary?
It certainly seems like the cheaper and least labour intensive option, though that is not my driving force at this point. I'm after isolation above all else, though maximising useable space is a definite bonus.

Also, what about the scenario in fig c? Would it be better to use the existing outer walls or to isolate completely from them? I believe the outer walls are constructed from either dense or aerated concrete blocks, and there is a potentially noisy neighbour on on side. Same situation applies regarding the air gap not being sealed.

Please note the sketches are for illustrative purposes only and not indicative of any scale, etc.

Many thanks for any help anyone may be able to offer,

Tim

fig a.jpg

fig b.jpg

fig c.jpg

[Soundman2020]

Hi Tim, and Welcome!

Say I were to build two free standing isolated rooms, booth room within a room construction, that were placed next to each other, both free standing so the air gap would be open on three edges (as in fig a). As the middle air gap between the two rooms is not sealed, would it still contribute to the quadruple leaf effect?

Yes it would, but to a lesser extent than if the gap were sealed. The air in the gap is still a spring, just not such a good one. It's all about resonance. Think of it this way: A kick drum with heads on both sides rings loud and long, but if you cut a hole in one head (so it is no longer sealed), it still rings pretty darn well... just slightly less. And if you take off one head completely, it STILL rings: You still get a nice satisfying "boom", in addition to just the "clack" of the beater hitting the head. There's still resonance going in inside the shell of the drum itself.

Building two rooms like your "a" would not be a good idea. A waste of materials.

Would it make a difference if that air gap was say 4" compared to 12"?

Yes it would: the frequency would be higher, and the isolation would be lower.

Would it be better to build two inner rooms with a single outer room (as in fig b), with two leaves and an air gap

That is, indeed, the correct way to build it. That's the way studios are normally built. 2-leaf MSM, as you show there, is the best way to get good isolation for the lowest cost, least materials, and thinnest profile. Any other system requires more materials, more money, and more depth.

...with two leaves and an air gap equal to the total equivalent depth of the four leaves.

You would actually need LESS air gap than the 4-leaf scenario, to get the SAME isolation. If you left a large gap, similar to the total for the 4 leaf, then you would get BETTER isolation, with a LOWER MSM resonance. Its the size of the air gap between any two leaves that sets the resonant frequency for that leaf pair. The smaller the gap, the higher the frequency, and thus the worse the isolation will be.

It certainly seems like the cheaper and least labour intensive option, though that is not my driving force at this point. I'm after isolation above all else,

Proper fully decoupled two-leaf MSM, which is what you are showing in "B", is indeed the cheapest, simplest, lowest cost, and gives you the best isolation, all other factors being equal.

Also, what about the scenario in fig c?

That would be a 3-leaf situation on two sides, and a two-leaf on the other two. In that case, it would be better to remove the middle leaf on those two "3-leaf" sides, and continue the outer leaf from the other two sides all the way to the outer-leaf wall. Once again, that would get you back to a 2-leaf system: less materials, less cost, simpler faster construction, etc.

The diagram below might help you to get a better understanding of the various possible leaf arrangements. All three have the exact same total thickness, and the same mass (actually, the on in the middle has LESS mass than the one on the left, but still isolates better...

2-leaf-3-leaf-4-leaf-STC-diagram--classic-enh.gif

- Stuart -

[timsouthorn]

Hi Stuart, thank you for taking the time to reply, and so promptly.

I had seen the diagram you posted and others similar to it, my confusion was that it was unclear in any of the diagrams i had seen whether that central air gap in the quadruple leaf assembly was sealed or not, and whether that would affect performance.
Thank you for helping to clear that up.

Out of interest (and without sounding like i'm not accepting your advice!), from what you're saying it wouldn't make a difference even if the central air gap was completely open to the elements?

Say you had two structures as in my original 'fig b', positioned opposite each other with an adjoining corridor as in my diagram below, would the quadruple leaf effect still be worth taking into consideration?
Note that the two pairs of rooms would be free-standing with no shared roof, so the corridor would be open at the top (ie. built inside a warehouse with 16m high ceilings)

fig d.jpg

Once again, thanks for your insight.

Tim

[Soundman2020]

In your hypothetical situation, it wouldn't matter at all: the corridor is presumably something like a meter or so wide (+/- 36"), so any MSM resonance would be at such a low frequency as to be irrelevant. It would not affect the isolation of any of the rooms.

What you probably need to do, is to look into the theory of how MSM systems work. Here's the basic equation for calculating the resonant frequency of such a structure:

Fc=c[(m1+m2)/(m1m2d)]^.5
c=constant
m1=mass of first leaf (surface density)
m2 mass of second leaf (surface density)
d=depth of cavity (spacing between leaves)
(For imperial units: C=60 for empty cavity, 43 for cavity filled with insulation)

That gives you the resonant frequency: A that frequency, the system does not isolate at all, and can actually amplify. At 1.414 times that frequency and above, it isolates. Isolation increases at rough 18 dB/octave in theory.... but only for part of the spectrum! It's more like 12-15 dB/octave in real life

- Stuart -