Wall Resonance Calculations

[ngcost]

My first post, so please excuse any 'missteps', and thanks in advance. I searched and searched but could not find the answers I was looking for on this topic (but did find so much other great information, thanks everyone who has shared and contributed).

Brief background: New construction basement space 22'7" W x 12'8" D x 10' H shell (excluding 'soundproofing'), multi-use for home recording and rehearsal space. I'd like to minimize the low frequencies - weighing the associated benefit of air gap and dropping resonance frequency vs cost of eating up room square footage - I hope answers to my questions below will help guide weighting my decision either direction.

Using the Fc=c[(m1+m2)/(m1m2d)]^.5 simplified resonance equation for double leaf MSM cited in multiple other posts, I calculated:

~29Hz = 5/8 gypsum + GG + 5/8 gypsum + ~8" insulated gap (2 x 6 framing + RC/RC clip with grommet) + 5/8 gypsum + GG + 5/8 gypsum.

(GG - green glue, RC - resilient channel)

Several threads have stated you want the wall resonance to be 1/2 of your lowest dominant Hz, which for me will be the low E on an electric bass (41Hz). Getting to ~20Hz takes quite a bit more air gap and/or a 3rd layer of gypsum on each wall per my calculations.

Questions:

1) How does the use of Greenglue affect this MSM calculation if at all? Does the combined mass unit (5/8+5/8) no longer functions as a single mass unit with the GG interposed between layers? I also think I remember reading that if you use different density/thickness materials separated by GG (e.g 5/8 and 1/2" gypsum, or 5/8" gypsum and MDF) this also can help ?broaden the resonance 'dip' so the affect of resonance is somewhat mitigated...?

2) How do resilient channel clips (e.g. RSIC-1, Genieclip, etc) affect this calculation - I have read that it may adversely affect (? increase) your resonance frequency.

3) What is the added value of the more expensive resilient channel clips vs a standard metal on frame clip - is it mostly marketing, double cost with minimal gain, or will it truly help and where (e.g. low frequency transmission, or overall STC)? The dB loss vs Hz curve I've seen from testing (not using double layer with GG) seem to have minimal additional impact using the rubber grommet on the clip, and haven't seen testing when you're already using two layers of drywall with GG with the more expensive rubber grommet clips. Minimal value add?

4) One of my walls will be an acoustic double glass sliding door partition (5/8" and 3/8"), whose spacing using the MSM equation I'll be at ~ 41 Hz at 6 inches and at ~31Hz at 10 inches space between glass panels. Should I assume that at the 31Hz (in relation to the 41Hz Bass guitar low E) will be reasonably separated, albeit not 'ideal', but enough to not want to sacrifice additional room depth. I figure if I did the 6 inch air gap at 41Hz, the low E will be pretty transparent through the glass... ouch...?

5) Limp mass, e.g. draped MLV with insulation and air gap between leafs - seen some specs for bass trap design for acoustic treatment, but is there any benefit for low frequency dB attenuation within walls? I've read somewhere about the analogy of throwing a ball against a blanket vs a rigid wall, absorbing rather than reflecting the energy. I am making the assumption sound absorption from a limp mass barrier with dissipation of the sound energy may have some benefit beyond acoustics, or really negligible... ?

6) Higher density insulation e.g. Roxul (vs fiberglass) no significant affect on dB attenuation between double leaf decoupled wall assembly (slightly off topic, thought I'd through it in there).

Thanks again.

[Soundman2020]

Hi there "ngcost", and Welcome to the forum!

Clearly, you've been doing your homework on this! And doing it rather well. That's refreshing, since way too many new members don't bother.

OK, first, things first:

Using the Fc=c[(m1+m2)/(m1m2d)]^.5 simplified resonance equation for double leaf MSM cited in multiple other posts, I calculated:

What constant are you using for "C" in that equation, and are you taking into account insulation?

For the record, the full equation details goes like this:

Fc=c[(m1+m2)/(m1m2d)]^.5

where:

Fc=resonance frequency (Hz)
c=constant (60 for empty gaps and 43 for with insulation)
m1=mass of first leaf (kg/m^2)
m2 mass of second leaf (kg/m^2)
d=interleaf spacing (m)

For imperial units the constants are 170 and 120.

The reason for two different constants is that no insulation, the air acts adiabatically. With insulation it acts isothermally. If you only fill the cavity partially, then the air inside the insulation acts adiabatically while the "free" air in the rest of the gap acts isothermally, so you have to choose a constant somewhere in between the two, but always biased towards the higher number.

So check that you are using the correct constant there.

(2 x 6 framing + RC/RC clip with grommet)

Why 2x6 framing?

And why "framing plus RC"? You would be better off (more isolation) by building a second frame that is totally decoupled from the first.

8" insulated gap (2 x 6 framing + RC/RC clip

Your math doesn't work out here: 2x6 framing plus RC will not give you 8" of depth. 2x6 framing is only 5-1/2" deep, and adding RC to that only increases it by about 1/2", so your air cavity would be 6" deep, not 8" deep.

Also, why would you want to put RC on an isolation clip? That would be unsafe, and would offer no benefits anyway. You should never use construction materials in ways that the manufacturer has not approved, and as far as I know, no manufacturer of RC would approve using their product in isolation clips.

Several threads have stated you want the wall resonance to be 1/2 of your lowest dominant Hz,

Correct. Or even lower, if you can get it.

1) How does the use of Greenglue affect this MSM calculation if at all?

It improves isolation by several points, across the spectrum. However, I'm not aware of any equation that you can use to calculate that. You might want to contact Green Glue Company and see if they have such an equation, or maybe at least a rule of thumb.

Does the combined mass unit (5/8+5/8) no longer functions as a single mass unit with the GG interposed between layers?

Yes and no. For the purposes of basic MSM calculations, it is still a single mass, because MSM calculations do not have any place for plugging in the characteristics of the constrained layer damping effect that the GG provides. To be accurate, you could add in the extra mass that the GG provides, but that won't make much of a difference. You would need to come up with an entirely new equation that does take that into account.

However, there's an interesting "rule of thumb" floating around, and I'm not sure of it's source so take it with a grain of salt, but many acousticians will tell you that you can get roughly the same effect as adding GG between two layers of drywall, by just adding a third layer of drywall. So you could use that in your equations, to get a very rough estimate of the improvement that you'd get from using GG.

I also think I remember reading that if you use different density/thickness materials separated by GG (e.g 5/8 and 1/2" gypsum, or 5/8" gypsum and MDF) this also can help ?broaden the resonance 'dip' so the affect of resonance is somewhat mitigated...?

You are confusing your dips! Using different densities does not change the MSM resonance dip at all, since that doesn't depend on waves traveling through the leaf: it depends on the motion of the leaf as a whole, which is defined by stiffness, as well as the mass. The wavelengths are just way too long for that to have much effect. However, up at the frequency of the coincidence dip, there's a very marked effect from having materials of different densities, since they also have different critical frequencies. So using two different materials will broaden and flatten the coincidence dip (reduce the Q, technically).

That said, for most MSM walls in studios, by the time you get up to the coincidence dip you already have Pretty Darn Good isolation, so it won't make a huge difference to total perceived sound transmission.

That's why the general recommendation here is to not bother about that. It would be better to make both layers out of the heavier material to get better performance in the low end. There might be other reasons why you'd want two different materials (for example, using OSB or plywood as the first layer gives you a nailing surface around the entire room, that you would not have from drywall alone), but there's not much reason to do it in the hope that it would improve isolation.

2) How do resilient channel clips (e.g. RSIC-1, Genieclip, etc) affect this calculation -

You seem to be confusing yourself here: those are not resilient channel clips. They are hat channel clips.

I have read that it may adversely affect (? increase) your resonance frequency.

You have read wrong! When used properly, clips + channel can improve overall isolation for several reasons. First, they decouple the drywall on one side of the frame from the drywall on the other side of the frame, which already makes a huge difference, and secondly they increase the depth of the cavity by the thickness of the clip, which can also help. Both of those help to drive down the resonant frequency.

3) What is the added value of the more expensive resilient channel clips vs a standard metal on frame clip -

I'm not sure what you mean here: please elaborate. What "resilient channel clips" are you referring to? I', not aware of any isolation clips that can be used with RC. I'm also not sure what you mean by "standard metal on frame clip". Proper isolation clips are not "metal on frame". There is always a resilient buffer of some type, often neoprene-based, to provide the resilience.

4) One of my walls will be an acoustic double glass sliding door partition (5/8" and 3/8"), whose spacing using the MSM equation I'll be at ~ 41 Hz at 6 inches and at ~31Hz at 10 inches space between glass panels. Should I assume that at the 31Hz (in relation to the 41Hz Bass guitar low E) will be reasonably separated, albeit not 'ideal', but enough to not want to sacrifice additional room depth.

You do not seem to be allowing for the edge absorption around the cavity. It's not a lot, but will lower your F0 a little. I'd estimate around 5% for the 6" gap and maybe 10% , so your two F0s would be around 36Hz and 27Hz, respectively. That implies good isolation above 75 Hz 55 Hz, respectively.

I figure if I did the 6 inch air gap at 41Hz, the low E will be pretty transparent through the glass... ouch...?

In theory, yes, but there could be other factors at play that would improve that. For example, a higher area of edge damping, or if you use laminated glass for your doors with the thicker 0.060 acoustic PVB interlayer, or if the glass is decoupled from the frames, or if one door is splayed with respect to the other... All of that, and more, can make a difference.

5) Limp mass, e.g. draped MLV with insulation and air gap between leafs -

Careful there! If you hang limp mass inside your wall cavity, then it become both a three-leaf wall and a resonant membrane trap... And if you sandwich it between your layers of drywall, then it is no longer "limp" mass: it is just "mass". And very, very expensive mass!

6) Higher density insulation e.g. Roxul (vs fiberglass) no significant affect on dB attenuation between double leaf decoupled wall assembly (slightly off topic, thought I'd through it in there).

Yes it does have an effect on isolation: it REDUCES the isolation. Increasing the density of the insulation reduces low frequency absorption. There is an optimum density for each type of insulation, and higher densities are worse for low frequency absorption (but better for high frequency absorption.

In reality, it isn't about the density

per se

, but rather about the gas flow resistivity of the insulation. It turns out that 15,000 MKS rayls is about right for this application. Fortunately, there's a very rough connection between gas flow resistivity and density, that varies for each type of insulation but remains more or less vaguely linear within that class of insulation. For fiberglass, the optimum density that gets you the right gas flow resistivity is around 30 kg/m3, and for mineral wool it is around 50 kg/m3. If you go too high with the density in either case, you lose isolation in the low frequencies. The higher you go, the worse it gets. If you have to choose, go a little lower in density, not higher. For example, if you have a choice of 25 kg/m3 fiberglass or 35 kg/m3 fiberglass, go with the 25 mg/m3 stuff.

- Stuart -

[ngcost]

Thank you so much for the thoughtful comments Stuart, so helpful.

What constant are you using for "C" in that equation, and are you taking into account insulation?

I converted from imperial to metric and used the 60 constant for the door and 43 for the walls with insulation, so I think we're good there. I think now that I'm better understanding the MSM resonance equation with your feedback and knowledge, and how the non included variables (hat channels, channel clips, GG) play into it, I'll get into my more specific calculations (hence some of the depth estimates, apologize for my inaccuracy on some of those distances).

Quote:
2) How do resilient channel clips (e.g. RSIC-1, Genieclip, etc) affect this calculation -
You seem to be confusing yourself here: those are not resilient channel clips. They are hat channel clips.

OK, so my 'misstep' I guess is nomenclature I've been learning, trying to describe 1) hat channel clip with rubber grommet = resilient channel clip e.g. RSIC-1 or genie clip, vs a basic hat channel clip. I'll just refer to them now as 'sound isolation clips' and 2) hat channel = resilient channel. I've read these clips described as resilient system clips, etc., so let me take a step back and hopefully clarify:

Question:
How do soundproofing clips (e.g. RSIC-1, Genieclip, etc) with a 7/8" hat channel affect this calculation, and is that rubber grommet on the soundproofing clips actually worth anything for these systems ,or is it just marketing hype over a basic clip (e.g. RSIC-V or IB-1).

Quote:
(2 x 6 framing + RC/RC clip with grommet)

Why 2x6 framing?

And why "framing plus RC"? You would be better off (more isolation) by building a second frame that is totally decoupled from the first.

To clarify what I meant, 2 x 6 framing rather than 2 x 4 to increase the air gap, and then a sound isolation clip + hat channel rather than framing out a full second decoupled wall to save on the square footage. It sounds like you think I should bite the bullet and build the second decoupled wall...?

Overall, I hope to post my preliminary design in the near future for the forum to poke holes and offer advice, but want to do my homework and try and understand all the components well before throwing anything out there.

Thanks again Stuart, tremendous help!

Nick

[Soundman2020]

trying to describe 1) hat channel clip with rubber grommet = resilient channel clip e.g. RSIC-1 or genie clip, vs a basic hat channel clip. I'll just refer to them now as 'sound isolation clips' and 2) hat channel = resilient channel.

Nope! Hat channel is not resilient channel. They are very different things, and confusing them would be a big, big mistake. Sort of like filling your diesel car with gasoline, thinking they are both "fuel"...

Hat channel is the normal metal channel stuff that you often see used for drywall all over the place. It does NOT isolate at all. It does not decouple. It creates a hard, solid, mechanical connection between the drywall and the studs or joists. Hat channel is also called "hat rack" and "metal furring channel" and a few other things.

Resilient channel, on the other hand, really does isolate: It is designed to create a flexible, "resilient" connect between the drywall and the studs or joists. It looks a bit similar to hat channel, but it is very different. Resilient channel is also called "resilient bar" and a few other things

Isolation clips are a different thing entirely: you use them with hat channel, but never with resilient channel. They are designed to work with plain old ordinary hat channel by decoupling it from the studs/joists, but in an entirely different fashion from the way resilient channel ("RC") works. Isolation clips come in several different types, but they all have one thing in common: they use some type of resilient "spring" (usually rubber) to decouple the hat channel from the stud/joist. Some of them grip the hat channel firmly but have a resilient base that goes on the stud/joist. Others are screwed directly to the stud/joist and have a resilient holder for the hat channel. The principle is the same, but the implementation is different.

But you can't use resilient channel with isolation clips. You can only use hat channel with isolation clips, or you can use resilient channel all by itself. One system or the other, but not both.

RC is OK for reasonable isolation, but clips+hat channel is much better, and there is much less chance of short-circuiting it with a badly placed screw.

And better than both of those, is a completely separate frame for the inner-leaf, fully decoupled from the outer-leaf. That's the best of the lot. And if you do that, then you don't need clips, you don't need hat channel, and you don't need resilient channel.

Question:
How do soundproofing clips (e.g. RSIC-1, Genieclip, etc) with a 7/8" hat channel affect this calculation,

They don't! It's a different set of calculations you'll need to do there, because the 2-leaf MSM equation is for that, and that alone: fully-decoupled two-leaf systems. RC helps to decouple somewhat, but does not decouple completely. Different types of RC provide different levels of isolation that are only vaguely related to the equation. Clips + hat channel is better, and provides improved decoupling, but still not as good as a fully-decoupled separate frame. So the equation would still not be accurate for predicting how a clip+hat channel wall will isolate.

and is that rubber grommet on the soundproofing clips actually worth anything for these systems ,

Oh yes, very much so. They work very well. However, don't assume that all clips are equal: they aren't. Check the actual technical data provided by the manufacturer, and look for full test reports from the independent acoustic lab where the tests were done, not just the manufacturer's claims. If the manufacturer can't (or won't!) provide those reports, and only wants to talk about their claims and in-house testing, then walk away and find another manufacturer.

To clarify what I meant, 2 x 6 framing rather than 2 x 4 to increase the air gap,

If you are thinking of 2x6 framing, then it would be better to go with "staggered studs": using a 2x6 sole plate and 2x6 top plates, but with 2x4 studs connecting them, with alternate studs set up on alternate edges of the plates. In other words, studs #1, 3, 5, 7, 9 etc are slid over flush with the left edge of the plates and hold the outer leaf drywall, while studs #2, 4, 6, 8 etc are flush with the right edge of the plates and hold the inner leaf drywall. That's an improvement over a simple 2x6 frame, and decouples much better... except at the plates. Those are still fully coupled.

It sounds like you think I should bite the bullet and build the second decoupled wall...?

Yep! If you want high isolation at low frequencies...

Besides, you actually don't save much space at all with a 2x6 wall vs a pair of 2x4 walls! Do the math:

For the 2x6 wall (using RSIC clips and hat channel):
2x5/8" drywall + 5-1/2" (stud) + 1-5/8" (clip with hat channel) + 2x5/8" drywall = 9-5/8" total thickness

For the dual 2x4 wall:
2x5/8" drywall + 3-1/2" (stud) + 1/4" gap + 3-1/2" (stud) + 2x5/8" drywall = 9-3/4"

So you'd save exactly one eighth of an inch with your plan, vs. my plan, and your isolation would not be as good as mine... Mine really is fully-decoupled, and has a deeper air gap as well!

Hmmmm.... food for thought.... !!!

Also, do the math on materials costs. Yes, my plan needs more studs, but they are cheaper. more common 2x4's not the expensive 2x6's that you need (which are also heavier and harder to work with ans slower to cut...), and my plan does not need isolation clips, which cost several dollars each, nor does it need hat channel, which also costs money... add, subtract, multiply, divide... my wall is likely less expensive than your wall, too!

I'd say that's a no-brainer....

Overall, I hope to post my preliminary design in the near future for the forum to poke holes and offer advice,

Cool! I'm looking forward to seeing that!


- Stuart -

[ngcost]

Thank you for all your clarification Stuart.

To be continued....!