Resonant frequency formula sanity check

Hi All, So by putting what I believe are the correct data into the formula I get a resonant frequency of 29.3Hz This is the formula Fc=c[(m1+m2)/(m1m2d)]^.5 (taken from other threads here) My isolation system will be as follows: inner leaf of 6"x 2" wood frame filled with insulation (pink fiberglass or rockwool, not sure yet) with a double layer of plasterboard, -> air gap of 100 mm -> exterior cavity wall of double 4" concrete blocks with a 5" air gap inside. My data is as follows: c 43 m1 24 (double layer of plasterboard) m2 200 (weight of 4" block/m2 taken from here: http://www.spanman.net/Members/Technical/Weight-Of-Building-Materials) d 0.1 (100mm gap between existing wall and wood frame) I have done the calculation in excel and I think I'm right.... but I am only adding the mass on one half of the cavity wall... QUESTION: How do I calculate the whole system with both leaves of the cavity wall? Is that a triple leaf? Thanks,

but I am only adding the mass on one half of the cavity wall...

Then add the other half too! :)

QUESTION: How do I calculate the whole system with both leaves of the cavity wall? Is that a triple leaf?

Technically, your existing concrete block cavity wall is a coupled two-leafed system. Even though there's a cavity in there, I'd bet good money that the two walls are are not decoupled: Very likely there are metal ties across it, there are possible also blobs of mortar creating bridges, and in any event there flanking paths at the top, bottom and both ends. So basically it acts as a single leaf... mostly! (sort of). For your calculations, it's is probably fine to consider it as a single leaf. I doubt the air cavity is going to make a lot of difference. You could do a check as if it were a 3-leaf system, but my guess is that the difference will be minimal.

inner leaf of 6"x 2" wood frame filled with insulation (pink fiberglass or rockwool, not sure yet) with a double layer of plasterboard,

That implies you are building your inner-leaf "inside out". Correct? IN other words, you are building your inner-leaf wall with the plasterboard (drywall) facing the wall cavity, and the studs facing the room. Is that correct? - Stuart -

Soundman2020 wrote:

but I am only adding the mass on one half of the cavity wall...

Then add the other half too! :)

Unfortunately the outside of the walls is in neighbours' gardens either side! Also, I probably mis-spoke (or mis-typed!) I am leaving an air gap of 100mm so in fact my inner wall will not be adding mass to the cavity wall at all :-)

QUESTION: How do I calculate the whole system with both leaves of the cavity wall? Is that a triple leaf?

Technically, your existing concrete block cavity wall is a coupled two-leafed system. Even though there's a cavity in there, I'd bet good money that the two walls are are not decoupled: Very likely there are metal ties across it, there are possible also blobs of mortar creating bridges, and in any event there flanking paths at the top, bottom and both ends. So basically it acts as a single leaf... mostly! (sort of). For your calculations, it's is probably fine to consider it as a single leaf. I doubt the air cavity is going to make a lot of difference. You could do a check as if it were a 3-leaf system, but my guess is that the difference will be minimal.

OK. Thanks for clarifying. With a mass of 200 kg/m2 for 4" block, there is not much difference in the resonant frequency if I double it to 400, because the inner wall is only 24 kg/m2, being double layer plasterboard.

inner leaf of 6"x 2" wood frame filled with insulation (pink fiberglass or rockwool, not sure yet) with a double layer of plasterboard,

That implies you are building your inner-leaf "inside out". Correct? IN other words, you are building your inner-leaf wall with the plasterboard (drywall) facing the wall cavity, and the studs facing the room. Is that correct?

That is correct yes. I am going for a room-in-a-room with an inside out style. Thanks, Stuart. With those clarifications, I now realize that I was putting the air gap in to the formula as 100 mm ... however that is the gap between the wall and the wood frame. If I use 6" x 2" wood for the frame, then the actual distance between the existing wall and the first of the two plasterboard layers is in fact 252 mm. If I input that into the formula I get a resonant frequency of 18.8 Hz ... much better! So if I understand the principles correctly I will get poor isolation at 18 Hz, better at 36 Hz, much better at 72 Hz and so on. So while not brilliant, it's not a disaster.

If I input that into the formula I get a resonant frequency of 18.8 Hz ... much better! So if I understand the principles correctly I will get poor isolation at 18 Hz, better at 36 Hz, much better at 72 Hz and so on. So while not brilliant, it's not a disaster.

It's very, very good, actually! Most studio builders do not manage to get their MSM resonance down as low as that. You should be fine. - Stuart -