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Resonant Frequency, why so high? Dynamics Processors (HW)
Old 4 weeks ago
  #1
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thechrisl's Avatar
 

Resonant Frequency, why so high?

So, I've been looking at the formula for resonant frequency of a Mass-Air-Mass system. I'll provide the details below. My understanding is that "default" soundproofing for most situations where decoupled walls are used consists of 2 layers of fire rated drywall in each leaf, with some damping and an air gap of about 8-10 inches. If you have very close neighbors you can add extra mass to improve on this and/or increase your air gap.

Another assumption is that you want the resonant frequency of the system as low as possible. Ideally below the range of human hearing, or under 20Hz. This is because the wall is sonically transparent at that frequency and starts to get effective a bit higher, maybe 25Hz.

So far so good, right? And we'll assume floor and ceiling are treated in similar fashion.

But after running some numbers, it really seems like 2 or even 3 layers of drywall is not nearly enough to achieve this. Again I'm talking about the typical situation where you want to keep full range music IN (i.e. Bass and Kick) while keeping environmental sounds (road noise, aircraft) OUT. So the lower the better!

If that's the case, why isn't it common knowledge that you really need 4 or 5 layers to get full range isolation? With that much mass, you need to be much more concerned about the frame/floor/slab's ability to hold everything up.

IOW, you'd almost always need a structural engineer to analyze your building for safety reasons & possibly beef it up, re-pour the slab, etc, etc.

OR it's possible that my calculations are wrong. Here's what I'm using:


I found it easier to keep everything metric for the calculation, but refer to inches of air gap later on:

At 25deg C:

c = 343 m/s (speed of sound in air)
p = 1.2 kg/m3 (density of air)
5/8 fire rated drywall = 11 kg/m2 (maybe a bit more but I rounded down)
1/2pi = .159

So, for example, 2 layers w/ a 2in air gap (.051m), I get:

pc^2/d = 2,781,072

.159 * Square Root((2,781,072*(1/22 + 1/22)) = 80Hz

So even with 2+2 layers, the air gap is way too small! I must be missing something, like the change in constants due to insulation or the use of Green Glue, etc.

I know you guys who do this a lot have charts so if my calculations are way off, let me know.

In any case, I ran these numbers through a spreadsheet and, even with 3+3 layers and a 12in air gap, the frequency is still high (though much better than 80Hz).

Here's my little chart. Any comments or suggestions on what I may be missing? Bottom line it seems to me that everyone is doing it wrong unless they are using way more mass than what is usually bandied about in discussion forums!

Old 4 weeks ago
  #2
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If you insulate the gap this will lower the resonant frequency. Need to find the spreadsheet I have, but from what I remember yes something like 2 layers and 4" is insufficient if you need 20 Hz isolation.
Old 4 weeks ago
  #3
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You are 100% correct. Isolation is tricky. Its all about TL (trasmsission loss) at a desired frequencies. To acheive 80db TL @ 20hz would be damned near impossible for almost anyone. Double layers of drywall with a decupled MSM system will give you an STC rating of 65ish i believe, which is considered good for home studios, but STC is based on speech, not music. You would most likely only get 35db reduction in LF. Theres lots of great info on the following thread.

Please check my garden studio plan - work has just started!
Old 4 weeks ago
  #4
Gear Nut
 

You can also build walls of stone.
That will give you a lot more sound isolation.

And remember isolation is starting from SQRT2 * fs.
So when fs = 80Hz your isolation starts at 113 Hz.
Old 4 weeks ago
  #5
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While it's true that a lot of LF isolation is tough, there are a couple things working in our favor.

One is that the threshold of audibility is pretty high down there. If you look a Fletcher Munson chart that's usually the lowest one. You can see that at 80hz it takes 50dB to be able to hear it, and even more as you go down.

Of course a mic doesn't have a threshold of audibility like that, but we do have high pass filters and for most instruments you aren't recording a whole lot of LF information...
Old 4 weeks ago
  #6
Gear Nut
 

These are the corrections for sound with a popmusic spectrum

63 Hz - -27 dB
125 - -14
250 - -9
500 - -6
1000 - -5
2000 - -6
4000 - -10

So at 60 Hz you get 27 dB isolation for free.
I can assure you you gonna need it if you work with lightweight constructions

IR-761 shows it is hard to get more than R = 30 [email protected] Hz.
So the sound level of a drummer or band at 110 dB(A) will be reduced to 110 - 30 - 27 = 53dB(A).
Over here depending on the time of day inside 15-25 dB(A) is allowed, outside on the facade 30-40 dB(A).

Last edited by bert stoltenborg; 4 weeks ago at 07:20 PM..
Old 4 weeks ago
  #7
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thechrisl's Avatar
 

Quote:
Originally Posted by bert stoltenborg View Post
You can also build walls of stone.
That will give you a lot more sound isolation.

And remember isolation is starting from SQRT2 * fs.
So when fs = 80Hz your isolation starts at 113 Hz.
I would love to do that but I'm working in an existing room with limited space. I also have to consider that the slab everything rests on was built to nominal residential specs.

If I was building from scratch I could see the benefit of an outer leaf made of concrete, stone or brick (if it could be well sealed) an an inner leaf of studs and drywall that can flex a bit.
Old 4 weeks ago
  #8
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Thanks, I'll read the linked threads and the threads linked in those threads.

Also, yes it would help to understand the effects of insulation on the resonant frequency. I'm lucky in that I don't have to worry about my noise bothering others, but I have to deal with environmental noises (low flying single engine planes, helicopters, gunshots, etc.). I live in the sometimes quiet country.

I seriously doubt I will achieve a level of isolation that would keep out the low freqs from a chinook flying directly overhead at 100ft off the deck -- but that's an event that happens maybe every other week. If I can keep most of the noise to a barely perceptible roar, I'll be more or less satisfied. And I know fletcher-munson curves help.

This was a helo fly-by in my untreated room. I'd say it's my worst case scenario.


I think part of my confusion is in differentiating the importance of mass law with resonant frequency. The IR-761 charts help with that -- I was just having second thoughts after trying to run some numbers and coming up with such high resonance.

In fact, I think the curved line in the chart represents hearing threshold, so if I can get the 30+ TL at 63dB as shown in TL-93-283, I may still hear it, but barely. Unfortunately IR-761 doesn't show much lower than ~50Hz so that lowest octave may still be a problem on occasion.

At some point it's a game of diminishing returns, I'm sure.
Old 4 weeks ago
  #9
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Jason Foi's Avatar
 

Quote:
Originally Posted by bert stoltenborg View Post
These are the corrections for sound with a popmusic spectrum

63 Hz - -27 dB
125 - -14
250 - -9
500 - -6
1000 - -5
2000 - -6
4000 - -10

So at 60 Hz you get 27 dB isolation for free.
I can assure you you gonna need it if you work with lightweight constructions

IR-761 shows it is hard to get more than R = 30 [email protected] Hz.
So the sound level of a drummer or band at 110 dB(A) will be reduced to 110 - 30 - 27 = 53dB(A).
Over here depending on the time of day inside 15-25 dB(A) is allowed, outside on the facade 30-40 dB(A).
I thought most noise ordinences were 65db(a) at the property line. 30db is QUIET.
Old 4 weeks ago
  #11
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[QUOTE=thechrisl;13690280] I also have to consider that the slab everything rests on was built to nominal residential specs.
/QUOTE]

Unless it's crumbling or something a standard slab on grade can support 1500 lb per square inch. Even if there was a reason you wanted to derate that to half or something that is a hell of a lot of drywall.
Old 4 weeks ago
  #12
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Quote:
Originally Posted by bert stoltenborg View Post
These are the corrections for sound with a popmusic spectrum

63 Hz - -27 dB
125 - -14
250 - -9
500 - -6
1000 - -5
2000 - -6
4000 - -10
I'm not following that...why would the threshold of hearing be different for pop music?

I just tried putting on a 63hz sine @27dB using C weighting and there is no way anyone is hearing that- I had to go to about 45 to where I could, but the room isn't that quiet so I guess the noise floor masks it at the lowest levels. This is a bit of crude test because my living room isn't anechoic and the noise floor in here is around 30dB, but it seems to line up with Fletcher Munson ballpark at least.

Where I live the noise ordinance is 55dB dB(A) 7am-10pm and 50dB(A) 10pm to 7am for music played inside (yes they actually have a separate level for lawn mowers). I've done a handful of consulting jobs with noise ordinance violations and stood there with the code officer while he took measurements and followed that up at the hearings. He uses the slowest averaging on his meter.

The truth is that 50dB(A) in a city is an impossible standard if the property is anywhere near a road with regular traffic. In the last case I was a part of the code officer pegged the ambient noise of the area (downtown) at 68dB(a) and would hold that as the adjusted standard at the hearing. Of course the idiot who owned this night club was bringing in 20kW systems to a 5000sf place with a glass curtain wall and doing 110dB(a) at the property line. He wouldn't listen to me or anyone else and got shut down.

In any case 30dB(A) would be quite difficult to enforce I would think...on some level they have to prove it's you over the ambient noise in the area.
Old 4 weeks ago
  #13
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Quote:
Originally Posted by thechrisl View Post
In fact, I think the curved line in the chart represents hearing threshold, so if I can get the 30+ TL at 63dB as shown in TL-93-283, I may still hear it, but barely. Unfortunately IR-761 doesn't show much lower than ~50Hz so that lowest octave may still be a problem on occasion.
You're concerned that you will hear it while mixing?

If you consider the original purpose of dB(A) which is to eq the spectrum to more closely match Fletcher Munson, keep in mind that this also applies to your overall noise floor. So let's say you are able to get a noise floor that measures around 15-20dB on an SPL meter with A weighting, if you look at the FM chart that is going to be somewhere around the 3rd line from the bottom (2nd blue one). If you follow that up for the bass, that is your comparable (to 20dB-A) noise floor at LF. And keep in mind that we are looking at the difference between audibility and the FM curve where between 3-5k audibility goes below 0dB. So 70dB of 30Hz rumble is comparable to about 20 dB of 3-5k noise from HVAC, computers etc.

Maybe if you are concerned about getting a low noise recording of a contrabass flute or something we start to have to be concerned, but in real life day to day studio activity I think this is going to be less problematic that you are thinking...

That said do keep in mind on your RTA there that you want to look at peaks (the red ones) and those will be audible over the smoothed blue measurements...
Attached Thumbnails
Resonant Frequency, why so high?-puhtk.png  
Old 4 weeks ago
  #14
Gear Nut
 

Quote:
Originally Posted by RyanC View Post
I'm not following that...why would the threshold of hearing be different for pop music?

I just tried putting on a 63hz sine @27dB using C weighting and there is no way anyone is hearing that- I had to go to about 45 to where I could, but the room isn't that quiet so I guess the noise floor masks it at the lowest levels. This is a bit of crude test because my living room isn't anechoic and the noise floor in here is around 30dB, but it seems to line up with Fletcher Munson ballpark at least.

Where I live the noise ordinance is 55dB dB(A) 7am-10pm and 50dB(A) 10pm to 7am for music played inside (yes they actually have a separate level for lawn mowers). I've done a handful of consulting jobs with noise ordinance violations and stood there with the code officer while he took measurements and followed that up at the hearings. He uses the slowest averaging on his meter.

The truth is that 50dB(A) in a city is an impossible standard if the property is anywhere near a road with regular traffic. In the last case I was a part of the code officer pegged the ambient noise of the area (downtown) at 68dB(a) and would hold that as the adjusted standard at the hearing. Of course the idiot who owned this night club was bringing in 20kW systems to a 5000sf place with a glass curtain wall and doing 110dB(a) at the property line. He wouldn't listen to me or anyone else and got shut down.

In any case 30dB(A) would be quite difficult to enforce I would think...on some level they have to prove it's you over the ambient noise in the area.
It's not about the treshold of hearing but about the spectrum of the sound. STC is an one number average not counting in low frequencies, spectrum popmusic is a one number quantity for that kind of noise. We also have spectra for other kinds of sound, I posted them a couple of days ago.
So if you have f.e. a band this spectrum is a tool to calculate the sound levels in dB(A) but as the standard is in octave bands also makes it possible to calculate the isolation of constructions when the R-values in 1.3 or 1/1 octaves are known.

When over here in the Netherlands, Germany, Belgium houses are exposed to soundlevels exeeding f.e. 40 dB(A) measures have to be taken like barriers blocking the noise, roads being shut down for heavy traffic, roads with speed limits, noise proof glazing and ventilation, etc.
If measuring is difficult because of the environmental circumstances there are standards to calculate with. A bar with mechanical music is supposed to keep soundlevels under 80 dB(A), a disco or live event is limited to 105 dB()A with a spectrum popmusic, for EDM they have even more severe spectra.
It's not always very easy but they really maintain these standards by law.
Old 4 weeks ago
  #15
Gear Nut
 

It's in dutch but if you look at the graphs and mumbers it should be clear.
Attached Files
Old 4 weeks ago
  #16
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Quote:
Originally Posted by bert stoltenborg View Post
It's in dutch but if you look at the graphs and mumbers it should be clear.
I see, it's basically various weightings that take averaged source curves into account relative to what an SPL meter would read? So if a source is more scooped it would read a lower dB(A) even though it has more bass.

Makes sense, especially for a law that applies broadly...That being said I think in the OP's case he can use the actual measured isolation requirements against the fletcher munson curves. That basically enables him to do the same thing but with the specific noise sources he is concerned about instead of an averaged analysis of various genres etc.
Old 4 weeks ago
  #17
Gear Nut
 

Quote:
Originally Posted by RyanC View Post
I see, it's basically various weightings that take averaged source curves into account relative to what an SPL meter would read? So if a source is more scooped it would read a lower dB(A) even though it has more bass.

Makes sense, especially for a law that applies broadly...That being said I think in the OP's case he can use the actual measured isolation requirements against the fletcher munson curves. That basically enables him to do the same thing but with the specific noise sources he is concerned about instead of an averaged analysis of various genres etc.
There are of course also weightings for sources like traffic, heavy traffic, air traffic, etc.
A lot of laboratories here measure data on constructions and also calculate the sound attenuation for all these sources making it easier for layman to get a grip on what they need concerning isolation.
Old 4 weeks ago
  #18
Gear Maniac
 
thechrisl's Avatar
 

Quote:
Originally Posted by RyanC View Post
You're concerned that you will hear it while mixing?

If you consider the original purpose of dB(A) which is to eq the spectrum to more closely match Fletcher Munson, keep in mind that this also applies to your overall noise floor. So let's say you are able to get a noise floor that measures around 15-20dB on an SPL meter with A weighting, if you look at the FM chart that is going to be somewhere around the 3rd line from the bottom (2nd blue one). If you follow that up for the bass, that is your comparable (to 20dB-A) noise floor at LF. And keep in mind that we are looking at the difference between audibility and the FM curve where between 3-5k audibility goes below 0dB. So 70dB of 30Hz rumble is comparable to about 20 dB of 3-5k noise from HVAC, computers etc.

Maybe if you are concerned about getting a low noise recording of a contrabass flute or something we start to have to be concerned, but in real life day to day studio activity I think this is going to be less problematic that you are thinking...

That said do keep in mind on your RTA there that you want to look at peaks (the red ones) and those will be audible over the smoothed blue measurements...
Yes I'm concerned about hearing outside noise while mixing but more with tracking say, acoustic guitar. Or something like a kick drum where I'd typically avoid lo-cut filters.

I think I get what you're saying about A-weighing. I've been doing all my measurements unweighted since low freqs are the hardest to control and where most of the concern lies. Then (afterwards) taking into account the hearing thresholds -- which is a little more complicated but makes me more confident that I'm not missing something important.

The screenshot above is from the Studio Six app which is pretty well regarded (and I use it with an external measurement mic). The dark blue curve is supposed to represent hearing threshold but it's quite a bit different from the curves you posted. For example, mine shows about 35dB at 63Hz while yours is more like 47dB. Why is that?
Old 4 weeks ago
  #19
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Quote:
Originally Posted by thechrisl View Post
Yes I'm concerned about hearing outside noise while mixing but more with tracking say, acoustic guitar. Or something like a kick drum where I'd typically avoid lo-cut filters.

I think I get what you're saying about A-weighing. I've been doing all my measurements unweighted since low freqs are the hardest to control and where most of the concern lies. Then (afterwards) taking into account the hearing thresholds -- which is a little more complicated but makes me more confident that I'm not missing something important.

The screenshot above is from the Studio Six app which is pretty well regarded (and I use it with an external measurement mic). The dark blue curve is supposed to represent hearing threshold but it's quite a bit different from the curves you posted. For example, mine shows about 35dB at 63Hz while yours is more like 47dB. Why is that?
The lowest note on a guitar is 82.41 Hz, and kick drums are loud...I'm not sure why there is a difference, maybe the app airs on the safe side? Do you have a sub in there now? Mess with it and see what you hear, of course subs typically have pretty high THD, but it should still give you an idea.

Don't get me wrong, the lowest possible amount of background noise is the best- but the point where the wall assembly isn't the weakest link in the chain comes on pretty fast. What is your HVAC plan? Machine room? (double) Doors? It's going to take a significant investment before these are matching let alone outperforming a room-in-a-room with 3 and 2 layers of 5/8 with a ~9" air gap.
Old 3 weeks ago
  #20
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I'm not sure if I understood the first part of your response. I just chose 63Hz at random to compare the two curves supposedly showing hearing threshold. The dark blue curve in my screenshot is just a reference. The RTA graph being shown is from a helicopter flying by before any treatment in the room.

I think maybe this graph explains the discrepancy. It looks like your curve was Fletcher-Munson while mine (which I though was the same) is Equal Loudness. They are about 10dB different at ~60Hz. I thought they were the same thing.


But the point was that I want to keep low freqs out while recording other low freqs that can interfere (and obviously when mixing). I'm feeling reasonably good about the 2+2 isolated wall plan now (with insulation, air gap and Green Glue on one shell). I think it will handle most noise issues but I'm skeptical about the low flying aircraft, especially helos. Fortunately it's not all that frequent.

I plan to have a solid core door on each leaf, with mass at least as much as the wall + seals.

I already built an adjacent equipment room which I will probably house the HVAC system in, similar to a setup described in Rod's book. Or I may just get the quietest split system I can find -- though I know fresh air is needed as well.

To be honest I'm trying to just get the outer shell beefed up for now. I don't have a complete plan fleshed out. I was working with someone on another site (i.e. a down payment was made) but I'm not sure whether the relationship is going to work out. He's gone pretty much silent, with me at least. This is upsetting as he is well regarded here and elsewhere.

Assuming that doesn't pan out, I am looking for help on the overall design. In fact I planned to start a thread here asking for a list of pros who typically work with DIYers like myself with a budget well under six figures. The only ones I know of for sure are J. Brandt and the person I thought I would be working with.
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