Practice studio construction guidance

[GeorgeG]

A proper two leaf M-S-M system forms a low pass filter through the mechanics of mass-sealed air-mass. The resonance is lower by increasing leaf mass and/or increasing the sealed air gap.

Is it an air volume thing regardless of air space shape (total air moved by the leaf surface area) or is it a separation of leafs thing (a wavelength component) or both. In other words I see rules of thumb like an 8" air gap for two parallel leafs which will yield a constant air volume to leaf surface area but does an irregular air gap shape impact performance even if it has equal to or greater than the same air volume for a given leaf size?

Example is a pitched roof and ceiling where the two leafs are anywhere from a few inches to many feet apart.

Thanks,

[Soundman2020]

My design presently has an 8" air gap between the 2 wall leafs (of 3X 16mm drywall each). Should I increase it to 12" if I have the room? In what way is 8" ideal in your earlier post vs the 12" gap discussed here?

12" will get you better isolation than 8", if you can afford the space. More mass on the leaves will also get you more isolation.

It varies from a few inches away near the perimeter of the building to 6 feet above the ceiling in the middle. Can I also ignore the roof and just depend on the 2 leaf system below? This one is even harder to model because of the 6/12 roof pitch.

Yeah. you can pretty much ignore the roof issue here: Sure, at the lowest end of the roof the gap is just a few inches, so theoretically, you would have a higher MSM frequency and the lowest isolation there, but if you have enough mass on the other two leaves, you should be fine. More mass is your friend, here. And as the roof height increases (getting further away from the other two leaves) it just gets better and better.

Is it an air volume thing regardless of air space shape (total air moved by the leaf surface area) or is it a separation of leafs thing (a wavelength component) or both.

The two main factors are depth of the air gap and the mass on the two leaves. The shape isn't important. It is a simple one-degree-of-freedom resonant system, where the mass oscillates at the end of a spring. The spring in this case is the air-gap-plus-the-insulation. Increasing the air gap is equivalent to increasing the "mushiness" of the spring (don't you just love my highly accurate technical term ).

In other words I see rules of thumb like an 8" air gap for two parallel leafs which will yield a constant air volume to leaf surface area but does an irregular air gap shape impact performance even if it has equal to or greater than the same air volume for a given leaf size?

Small irregularities won't make much difference. Theoretically, the wall is only as good as the point that has the smallest air gap and the point that has the lowest mass, so if you angle a leaf then the "worst" part of that wall will be where the two leaves are closest together. Same for the roof: The worst part will be the point where the roof is closest to the other leaves. Once again, mass is your friend: If you have no choice but to make a 3 leaf system, and no choice but to have a small air gap at some point, then the solution is to put more mass on at least one of the leaves.

- Stuart -

[GeorgeG]

Thanks Stuart

Where can I find the formulas to calculate the resonance for given leaf mass and air gap?

Thanks,

[Soundman2020]

For a 2-leaf wall, the simple form of the equation is:

f = 60 / √md

where
m=the mass per unit area of the leaves (kg/m2)
d=distance between the leaves (meters)

For a 3-leaf wall, such as yours, there are actually two overlapping frequencies, f+ and f-. Here are the two equations, in the more complete form which includes air density and speed of sound:

f+ = (1/2π)√((3.6 ρ c^2)/(m d))

f- = f+/√2

where
ρ = density of air
c = speed of sound in air
m1, m2, m3 = mass per unit area of the three leaves, and m = m1 = m3 = 1/2 m2
d = the separation between m1 and m2, and also m2 to m3 (both equal)

If the masses are different, or the air gaps are different, then things get a bit more complex...


- Stuart -

[GeorgeG]

Trying to understand the basic formula to help calculate wall characteristics that make sense:

5/8" drywall is 105 lbs per 4' X 12' sheet = 2.2 lbs/sq ft = 10.8 kg/m2 X 6 sheets (both sides) = 64.8 kg per m2 total

12" = 0.30 meters

f = 60/√(64.8 X 0.30) = 60/4.41 = 13.6 hz

I can't get to 10hz with 3 layers of 5/8" on each side and 12", looks like you need 22" or more mass of course. Do I have this right or is it that 14hz is close enough?

Thanks,

[Soundman2020]

What instrument are you recording that you need to isolate down to 28 Hz? About the only thing I can think of off hand that goes down that low is a full pipe organ! You're gonna put a pipe organ in your studio?

Anyway, are you allowing for insulation? The constant of "60" is for a cavity with no insulation. It is more like 43 if the cavity is filled with insulation. Plus your drywall figure seems a bit light: good USGS drywall should be more like 12 kg/m3.

3 layers of 5/8 on each side of an insulation-filled 12" air gap should get you down around 9-and-a-bit Hz. That wall will start isolating at around 13 Hz, and isolates quite well at 20 Hz.

In any event, even at 13Hz you are doing pretty well, since there just aren't many musical things that put out appreciable energy at 26 Hz, and not too many sound systems that can reproduce it anyway. Plus the human ear is not very sensitive at all down that low.


- Stuart -

[GeorgeG]

One problem is that I was not accounting for insulation which in this case will be 5.5" batts or half of the airspace so I will assume a constant of 52.

USG technical support gave me the 105 lbs per 4' X 12' X 5/8" board which translated to 10.8kg/m2 but maybe there is an opportunity to find denser drywall and help even further.

I am now at essentially 12hz "f" or isolation at 24hz.

What "f" do you suggest in this case as the minimum? If 12hz is overkill, maybe I can go back to an 8" airspace. That would give me 14hz/28hz.

Application is a rock band practice studio (assume 120db), 50db external measured volume maximum, neighbor separation is 90 meters.

Thanks,

[Soundman2020]

If your nearest "problem" is 90 meters away, then that is good news! 50 dB just outside your walls, a couple of meters away, is going to be totally inaudible long before it gets to your 90-meter-neighbor! It will be lost way down in the ambient noise, so you might just be over-killing this thing. Consider that 65 db is very roughly normal conversation level: can you hear your neighbor talking / radio playing / phone ringing from the position of the studio? If not, then I reckon you are doing some overkill here.

Anyway, assuming that you really do want 50 dB outside and you are producing 120 inside (that's REALLY loud!), then you are looking for about 70 db of isolation. I'd say that you are well in the ball park for that, with your current plan. The walls are not going to be your weak point: it will be the doors, windows and HVAC ducting.

Anyway, rock bands don't have a lot of stuff in them that goes down much below 40 Hz, certainly not below 30. Some keyboard stuff, maybe, and low bass perhaps, but unlikely. So MSM resonance even up at 15 Hz would probably be OK, so if you are getting theoretical numbers of around 12, that's great. Of course, reality won't match theory exactly, but you are at least in the right place to start with.

So, if you build to your current plan, your manic rock band won't be audible outside your walls more than a few meters away, for sure.

I'd be concentrating on how you are going to get the same level of isolation form your doors, windows, and HVAC as you will from that wall! Think: "seals". Lots of them. Good ones. And "mass". Lots of it.


- Stuart -

[xSpace]

The difference in your sheetrock weights, George, is most likely the difference between typical 5/8 rock and fire rated (commonly called X rated) sheetrock.

Fire rated is recommended since it is the more dense of the two.

[GeorgeG]

Thanks for the fire rated sheet rock tip

[GeorgeG]

Well the project is complete. We were asked to turn a CMU outbuilding into a "bomb proof" (bombs going off inside) practice room for this metal band in a very ritzy neighborhood. Thanks to Stuart and others for your help. We were shooting for 65-70 db of isolation (well I was, nobody else even cares what that means) because they needed Live at Leeds db levels inside to yield whisper quiet levels at 50 ft. I interpreted that to the above targets. They are not technical clients and wont even make the time for isolation measurements to determine the outcome but they are extremely happy. Chaos inside and everyone says amazingly quiet outside. The approach:

Single rectangular room, no focus on ratios.
Common monolithic slab floor.
Sealed external windows with poured concrete.
Inner room with 10" air space to block wall, 12" air space to original ceiling, everything filled with fiberglass insulation.
2x4 wood stud walls, 2x10 wood ceiling joists.
Inside of exterior wall painted twice.
Original ceiling cladded in one layer of OSB and 2 layers or 5/8" drywall.
Inner ceiling and walls all 3 layers of 5/8" drywall, staggered and sealed, all 2 leaf.
HVAC isolated with a flex duct.
Solid wood doors with good exterior seals. They did not follow the recomendation to add additional MDF to the doors for mass and extra seals.
Bamboo engineered flooring floated over a foam membrane for moisture.
Total spent around $50K US.

Fought conventional construction techniques the whole way. Wanted to add drywall on all sides (3/4 leafs). Wanted to add foam board and drywall to the inside of the outer wall. Said it was too cheap as designed. Did not want to seal at each drywall layer. Connected the leafs at the doors with solid wood (made them tear that out). Never did add mass to the doors. If you do this for a living it must be like hearding cats. I felt like Copernicus trying to convince people that the earth revolves around the sun. It almost all got done right and everyone is happy so on to my project (seperate posts). There will be a lot of personal involvement when the next one gets built.

Thanks again to all who helped.

[Soundman2020]

Not sure if you are still around, George, but I was going through old threads to find "finished" and "in progress" rooms, and I found your thread again. So I added yours to the list of "finished" places (here: http://www.johnlsayers.com/phpBB2/viewt ... =10&t=5842 )

So I was just wondering if you ever did any final tests on this room, to see how much isolation you ended up with, versus how much you wanted originally?

Also, it would be great if you could add some "before" and "after" photos, and maybe some "in progress" photos too!


- Stuart -