John Sayers' Recording Studio Design Forum Archive

Hi, i have had a go with a formular that i found but to be honest, not being the best at that sort of thing im not sure if im doing it right.

basically i was wondering what was the resonant frequency of this wall design:

1st leaf - standard uk residential red brick.
against that would be a stud frame filled with insulation.
2nd leaf - would be 3 layers of plasterboard 12.5mm thick each, isolated from stud frame with resillient channel strips.

1st leaf thickness - 102.5mm
2nd leaf thickness - 37.5mm plus thin layer of plaster (not sure what thickness its usually done too).
air gap - 101.7mm based of a resillient channel depth of 12.7mm (looked online so im not sure how accurate it is).

oh and what do people think the rough isolation db would be?

Its just an idea in my head at the moment so its all hypothetical.
thanks in advance

The density of brick is highly variable, between around 2000 to 3000 kg/m3. So let's split the difference, and call it 2500 in your case. Your brick is 102 mm thick, meaning that you have a surface density of roughly 250 kg/m2 on that leaf.

Drywall density is also variable, between maybe 600 and 800 kg/m3, but 650 is a good guess. Yours will be 40 mm (assuming a thin layer of plaster), meaning surface density on that leaf is about 28 kg/m2.

Your air gap is about 102mm.

Therefore, in theory...:

There are two ways of calculating this: The simple equation considers only one leaf, and assumes that the other is infinitely massive, which is a somewhat valid assumption in your case, given the large difference in mass.

According to this "simplified" equation, the resonant frequency of that wall is 35.5 Hz. Therefore, the wall will not isolate below that, not up t 1.4 times that. So it will start isolating at 49.7 Hz. It will isolate well starting at 71 Hz, and very well above 106 Hz.

The long form of the equation considers the density of both leaves, and is more accurate. Using this version, your wall resonates at 37.4 Hz, does not isolate until at 52.4 Hz, isolates well at 74.9, and very well at 112 Hz. As you can see, the difference between the two is not that much, since the brick wall is quite massive, as compared to the drywall.

In both cases you can improve the isolation considerably by filling the cavity with insulation. In that case, the numbers (for the second equation) are:

Resonance: 26.7 Hz. Does not isolate until: 37.5 Hz. Isolates well: 53.5 Hz. Very well: 80.2 Hz.

However, It would not be a good idea to use 12.5mm drywall: it is too thin, too flexible, high resonant frequency, low mass, etc. It would be better to use two layers of 16mm drywall, rather than three layers of 12.5. Despite the slightly reduced thickness, the overall effect will be better.

Also, if you have a separate stud frame then you do not also need resilient channel. If the frame only rests on the floor and does not touch the ceiling or any other part of the existing outer leaf, then that's all you need. Adding RC is pointless. RC decouples. The separate stud frame decouples. Decoupling twice does not help at all. Decoupled is decoupled.

oh and what do people think the rough isolation db would be?

That's a bit tougher! That depends on many factors, including the quality of the seals and workmanship, degree of decoupling, infill percentage/type/density, as well as things like windows, doors, HVAC, electrical, etc. But at a very rough guess, best case would be in the mid to high 50's.

Of course, all of the above is theoretical. Practice might be different. Your actual millage may vary. Void where prohibited by law. Murphy rules! Etc.

Does all of the above agree with the equation that you found?

- Stuart -

Hey Stuart...I've been searching the forum for a more detailed explanation of how to use these equations...it's proving hard to find the equations first of all, let alone how to apply them to my own MSM isolating structure.

Where can I look to find this stuff?? I couldn't even track it down in the MHoA but I would bet I'm just overlooking it...

Thanks
Trevor

Where can I look to find this stuff??

The place I learned it originally is in the legendary Wyle report of 1973. It gets a bit complex, but the basis is there, and fairly well explained.

The report is Wyle WR 73-5. You should be able to find it online somewhere. Fascinating reading!

- Stuart -

Great! Thanks Stuart!

this is good info...thanks

A great exchange of information.

Interesting thread. I'm considering a a similar wall construction for my studio build:

http://www.johnlsayers.com/phpBB2/viewt ... =1&t=20085

Useful info here, thanks!

A great exchange of information.