I think I've tried to ask this kind of question before, but have never seen a definitive answer. I am building a room within a room where one of the outside leaf walls is a glass facade (glass curtain wall). Its an office and the facade is either 8.38mm or 10.38mm. The inside leaf walls will be a total of 44mm particle board, which is 33kg/m2 in density. The gap between this inner wall and the existing glass facade needs to be a minimum of 150mm.

Right, so I want some windows in my inner leaf, so I'll need glass for this window to be at least 15mm to match the wall's density. But the thing isI have a ton of 10.38 office partition glass leftover from the decommissioning of the previous office fitout, and I'd really like to use them. Now single pane 10mm is only 25kg/m2, so I'd need to double up on the 10mm panes. I thought maybe just place them back to back, but apparently there would be vibration and/or condensation issues. So a window frame maker suggests a double pane window for the inner leaf.

I explained to him that this would cause a 3 leaf effect, where a 100mm gap between these 2 panes would cause resonance at 38hz,effectively being useless at stopping frequencies lower than 54hz. Now, because I need to keep low frequencies from drums and bass from getting through the floor below me, this kind of spacing may create a problem. Or will it? After all, there is the outer leaf glass wall a further 150mm away. Beyond that a low frequency then needs to pass through the 125mm concrete slab to the floor below (my only noise sensitive neighbours).

You can see why I'd love to know how to calculate this 3 leaf effect in this instance. It's hard to know if the 100mm gap will perform worse than a 1mm gap, at least as far as LF is concerned (I don't really care about frequencies over 250hz as they should get attenuated sufficiently through the glass facade and slab below). For example, a tiny 1mm gap (if that's even possible! ) still creates a resonance dip between 250hz and 540hz (centred around 340hz).
Presumably this should attenuate frequencies below 250hz better than the 100mm gap!

Can anyone offer the best solution, with the attendant math? Cheers!

Assuming you can live with th fmam at 340 Hz the double 10.38 will give better lf isolation than the single 15.

Cheers. Do you agree that a 1mm gap will suit my needs better than the 100mm gap?

No. Where is the extra 99 mm coming from? It would be better to locate the double layer 100 mm away from the facade. With 100 mm already there it would not make much of a difference. Less than 2 dB but the fmam would be closer to your desired rejection range.

The outer leaf would be 150mm away from the double inner leaf with 100mm gap. If the double pane had only a 1mm gap, then add up to 99mm to the original 150mm gap. So, which is best for LF attenuation (sub 250hz)?

The 1mm gap is better for LF attenuation.

Thanks! That's what I thought. That along with what would probably end up being a 200mm gap between the double pane and the existing outer leaf glass should be OK, I hope. Actually, I think my frame maker said the smallest gap would be 1.6mm, but that it would need to be tested to see if vibration causes the 2m x 1m panes to touch. Maybe a couple of well positioned small, shallow rubber pads between the panes might stop that?

http://forum.studiotips.com/viewtopic.php?f=1&t=3930

Very on point ! Interesting that with the double pane, the expected fmam would be around 136hz (if I'm using my calculator correctly). Yet, perhaps because of the rest of the system may absorb this resonance, it hardly makes a difference.

From this, I'm wondering if I might as well have a 12mm gap in my double pane instead of just 1.6mm. Less problematic, but also ideal thermally, I'm led to believe...?

Edit: BTW, how do you explain the dip the 80hz TL dip? My calculator predicts the fmam for the 200mm gap should be closer to 40 hz...

Measurements and calculations are different worlds sometime. You often don't know what size the measured samples are, what size the rooms are etc....
I saw measurements on the same materials in labs with different sized rooms that deviated considerably, and the round robbins where different labs measure the same samples also differ to an amount you have to shake your head.
But I'll look into it.

For the explanation of the construction you could replace the mass-spring-mass-spring-mass by coils, capacitors and resistors (f.e. see Beranek Acoustics or Olson Acoustical Engeneering). In such filters you'll see that a large cap is so dominant that a small cap hardly matters.

So, I'm still left wondering how the 3 leaves can be best placed. If we refer to the above described requirements, if I have a total of 250mm to play with, how do I divide that in a way that best attenuates low frequencies through the floor outside of the outer leaf?

Dividing the 250mm equally? ie

glass / 125mm / glass / 125mm / glass ?

glass / 249mm / glass / 1.0 mm / glass ?


or something in between? At what point does the 2nd gap cause problems? As shown in the earlier posts, if the main gap is much larger than the second gap, then the 3 leaf effect is negligible.What is the largest the second gap can be ?

30mm? 50mm? 80mm? Surely this would have been tested??

Triple leaf isolation becomes very complex with all the potential variables, There are a couple of sections in LONG Architectural Acoustics covering it.

What are you asking for? Was post 6 not clear enough? The 1 mm gap is better.

It causes problem when the fmams coincide with the desired isolation range.

It is shifted to where it less harm.

The largest is what space you can afford to devote to it.

Sure, 1mm may be better, but 20 or 40 mm may be better still. 80mm or 100mm might be where it starts to make this worse, I don't know...

Is there some magic ratio between gaps that safely avoids problems?

10:1 ? 100:1 ? Just looking for the optimum solution...

For what we are referring to the smaller the second gap the better.

There is no magic ratio.

As an example of the complexity of triple leafs attached is a master's thesis.