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PostPosted: Sun Jan 13, 2013 11:37 pm 
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Basically, this graphic has exactly nothing to do with what we're talking about (adding a third leaf to the outside of an existing MSM system).
Actually, it has everything to do with what we are talking about. Take a closer look... There is an area where the resonant frequency for the 3-leaf system is much higher for the same total mass and total wall thickness (air gap). Therefore, logically, there is an also an area where the frequency is STILL higher for a wall with greater mass and greater air gap.

Think about it.... Increasing or decreasing the air gap in either system will move the relevant curve slightly left or right on the graph. But you need to move that 3-leaf curve a lot over to the left to make it better than 2-leaf for all frequencies. In other words, there needs to be a substantial change in mass or air gap to get that curve further over than the 2-leaf curve. Implying that there is STILL a zone where the three-leaf curve is WORSE than the two leaf curve for low frequencies. That's the zone were adding a third leaf to the outside of a two-leaf system makes it a worse isolator for low frequencies.

That's what the graph is illustrating.

That's also the entire issue here, and the reason why people do, indeed, have problems with reduced low frequency isolation after adding a third leaf to the outside of what was formerly a two leaf system. Just like you, they have not understood that adding the extra leaf changes the rules of the game: they don't get that they are now playing a different game entirely: They are not playing the game of "2-leaves plus something else", since no such game can exist in the world of physics. Rather, they are now playing the game of "3-leaf", which has different rules. Until they recognize that they changed games, they'll never understand what happened, nor how to fix it. If they try to keep on thinking in terms of individual panels vibrating at their own resonant frequencies, then they'll never understand that panel resonance is simply irrelevant to what is happening in the MSM region.

Quote:
This is illustrating that decreasing the size of the space has an adverse affect on low end isolation
No it isn't: Rather, it is demonstrating that a totally different set of rules is in play when you have a three leaf system, as compared to a two leaf system. This is actually pretty obvious, when you look at the graph: Clearly, there are two entirely different curves, demonstrating entirely differently phenomena. Above resonance (or rather, between resonance and coincidence) the law changes from 18 dB/octave to more like 24 dB/octave. That's an entirely different law at work, not related to the law that governs 2-leaf systems. It is a different game, a different set of rules, that governs the MSM region of the isolation curve.

Quote:
Now obviously, the third leaf will pass sound at its resonant frequency,
One more time: the third leaf does NOT act on its own, and it does NOT "pass sound at it's resonant frequency". The resonant frequency of that panel by itself is irrelevant to the resonant frequency of the wall. Rather, the entire wall, as a system, passes sound at its resonant frequency, and that frequency is now HIGHER than it was, due to the third leaf, EVEN THOUGH the total wall thickness and total wall mass may have gone up. That's what the graph shows.

I know that this is not an easy thing to grasp: it takes a while to get your head around the concept that this is not related at all to panel resonance. MSM resonance of walls is something entirely different. To make matters worse, some early texts simply got it wrong, before the phenomena was understood, and those are still in circulation. Unfortunately, there are still a lot of web sites that continue to repeat that wrong information, which makes it hard to find the truth among the clutter on the Internet.

If you hope to understand this phenomena you need to stop thinking about the leaves and air gaps as separate disjointed parts that act on their own; they are not. Rather, you have to realize that the wall acts as a system, where all of the parts interact and change the behavior of the entire wall. So you can't say that "the third leaf passes sound at its resonant frequency" since the third leaf does nothing at all on its own in the MSM region: it must act in conjunction with BOTH of the other leaves AND the two resonant cavities AND the damping in both of them. The third leaf does not have a resonant frequency all of its own, when talking about MSM: rather, it has the same resonant frequency as that of the entire wall, which is very different from the resonant frequencies of each of the parts, and different again from the resonant frequency of a two leaf wall of the same mass and total thickness, or even of a slightly lesser mass and thickness.

Perhaps the best document that you can learn from to get you head around this, is the famous Wyle Report WR 73-5, from way back in 1973. If you work through that, the concepts become very clear.

Quote:
just like any mass (which is why it is beneficial to use differing materials on each side of an MSM system)
Actually, that isn't true either. If you look at the Wyle report, you'll find that optimum isolation in MSM systems is achieved when the masses on both sides are equal (for a two leaf system), or sum to the same total as the mass of the middle leaf (in the case of a three-leaf wall). Empirical testing proves this to be true, despite claims to the contrary in some older texts. In other words, for 2 leaf, when m1 = m2 you get the best performance. And for three leaf that happens when m1 = m3 = 1/2 m2, and also d1 = d2. For all other combinations, the resonant frequency is higher and overall low frequency isolation is reduced.

Once again, this has nothing at all to do with the natural resonance of the leaf on each side of the wall: that's just irrelevant to what is happening here, with MSM resonance. So choosing materials that have different resonant characteristics for each leaf has zero effect on the overall low frequency isolation, and indeed individual panel resonance does not even come into the equations! There are no variables in the equation for MSM resonance that relate to the resonant frequencies of the individual leaves. Rather, there is a direct relationship between the sum of their masses and the product of their masses, but no factor at all related to the individual resonances. Take a look at the MSM equation yourself, and see if you can find any place where individual panel resonance is taken into account.

In fact, the resonance of the individual panels only becomes an issue at coincidence, where bending waves in the panels start to have an effect, but it has no effect at all on the MSM resonance. Until you can let go of this concept of the two sides behaving separately, rather than as a system, you won't be able to grasp what is really happening here. This is a case of not being able to see the forest because the trees are getting in the way! Step back, stop looking at the individual trees, and start looking at the entire forest.

Just to make it crystal clear: this has nothing at all to do with PANEL resonance, which is a totally different thing, and simple does not come into play for MSM calculations.


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PostPosted: Mon Jan 14, 2013 3:21 am 
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It is possible to do some simple calculations of resonance frequency of double leaf partitions and triple leaf partitions. Equations here:
Attachment:
double-triple f0.jpg


m1,m2,m3 - mass per unit area (kg/m2)
c0 - speed of sound 343 m/s
ro0 - air density 1,18 kg/m3

Example: Lets take a double leaf partition: 2xplasterboard (tot. thickness 24mm) - air gap (d1=100mm) - 3xplasterboard(tot. thickness 36mm). Resonant frequency f0 would be around 70 Hz (it depends on density of plasterboard, sound speed, air density). I assumed plasterboard density of 0,88 kg/m2/mm.

Now assume that we want to improve isolation and add another leaf of 2xplasterboard (24mm) spaced d2=100mm from existing partition. This system will have 2 resonant frequency: fa=77 and fb=110 Hz (around). This whole system would give better isolation for frequencies above 4*f0 but worse for f0<f<4f0 and better for f<f0.

But there is some limit distance d2 when resonance frequency would be the same for double and triple leaf. It is around d2=1,375*d1. If we add third leaf to double leaf wall in distance greater than limit distance it will have lower resonance frequency and it could give better isolation. Number I gave (1,375) is accurate to only this case because it also depends on masses of leaves but it is simple to calculate for different start conditions.

So for the double leaf partition from example limit distance is 0,14m. Another leaf spaced more by 0,14m will give better isolation than double leaf partition. I'm not sure of freq range fa<f<fb. But above fb the transmission loss increases at a rate of 30dB/octave when double leaf above f0 with 18dB/octave.

Of course it will be very thick wall but it will work.

One more point here: I can't agree that triple leaf wall is always a bad idea. It is a bad idea when it has to isolate music where bass is the main concern but what if it is intended to isolate speech? It would work better than double leaf partition. What is more triple leaf partitions are more forgiving of poor construction practice such as improperly isolated electrical boxes, outlets etc.

Everything depends on the application of a wall. Correct me if I'm wrong..

--
Mathew


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Last edited by acuspace on Mon Jan 14, 2013 5:06 am, edited 1 time in total.

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PostPosted: Mon Jan 14, 2013 5:06 am 
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This whole system would give better isolation for frequencies above 4*f0 but worse for f0<f<4f0 and better for f<f0.
Exactly. And that is precisely the point I've been trying to make. And exactly what happens in real-world situations where third-leaves are added without understanding the issues, and the results are worse isolation in the low end. This is what Rod has spoken about before: it does, in fact, happen in real life, exactly as theory predicts.

Quote:
But there is some limit distance d2 when resonance frequency would be the same for double and triple leaf. It is around d2=1,375*d1. If we add third leaf to double leaf wall in distance greater than limit distance it will have lower resonance frequency and it could give better isolation.
Correct. Like I said in my previous post, there is a range of masses and air gap sizes where the 3-leaf curve will always be to the right of the 2-leaf curve, thus producing the problem with worse isolation in low frequencies. And that range of masses / air gaps just happens to fall in the range that are commonly found available for home studio builders.

QED.

Quote:
It is a bad idea when it has to isolate music where bass is the main concern
Well,that kind of is what we are talking about here! Most studio builders do, in fact, want to isolate music where bass is the main concern. About the only exception I can think of would be a studio that is meant exclusively for voice-overs, or perhaps radio announcers or other purely voice related recordings, where the low end of whatever is recorded can simply be eliminated with EQ. There haven't been too many of those on the forum, that I recall... :)

So, getting back to the original point about 2-leaf vs- 3-leaf, I guess I would summarize it like this: Trying to isolate a recording studio by using triple leaf walls is a bad idea on many fronts, considering that you need a thicker, more massive, more expensive, and more complex wall, in both design and construction, in order to compensate for the deficiencies caused by the third leaf, which happen to occur in the area of the spectrum that is of most interest to studio builders, and is the hardest to isolate in any event. Sometimes you have no choice, and have to have a 3-leaf system, but that should be avoided wherever possible, since it is not the most effective arrangement.


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PostPosted: Fri Oct 14, 2016 8:54 am 
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In any event, you do not need to demolish the entire wall: careful removal of the sheet rock from the side of the wall that will face the cavity, is all that is required. Said "carefully-removed-sheetrock" can then be used to beef up the other side of that wall, from within, between the studs.


Thinking about this for a situation where I don't really have access to my neighbor's side of the wall. How do you attach the sheetrock? You can't screw it into other sheetrock right? Adhesive? Blocking on each piece?

Thanks!

Alex

Sorry for dredging up a post from 2009...


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PostPosted: Sat Oct 15, 2016 12:42 am 
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I don't really have access to my neighbor's side of the wall. How do you attach the sheetrock? You can't screw it into other sheetrock right? Adhesive? Blocking on each piece?
You don't need to attach it to the other side, directly! You just push it into place against the drywall on the far side, then caulk around the edges to get a good seal and mass continuity, then you nail small cleats sideways, into the studs, and pressed up against the "beef" panels, to hold them in place.

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PostPosted: Fri Apr 06, 2018 8:15 am 
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Soundman2020 wrote:
Quote:

Also, it isn't just MSM vs MSMSM that we are talking about: below the MSM region, stiffness rules, and adding a third leaf does not change the stiffness of the wall. So, if the resonant frequency is higher, stiffness now governs a larger chunk of the spectrum... And drywall isn't know for its rigidity...


Just to be clear for those still paying attention, the bolded part of Soundman2020's post statement above needs to be clarified- here's why: the overall assembly of the wall as a Structural System is made stiffer (which equals stronger, but more so for forces exerted along certain planes) by the addition of the third leaf, even if the individual plates (drywall sheets, for example) for each leaf are not made substantially stiffer. Just as in the MSM case and all its variants (MSMSM, MSMSMSM, etc.) a Structural System is created by a third-leaf addition which need to be judged as a new or different system as soon as there is any modification of the original form.

The example I will provide that most will understand easily is that of a corrugated cardboard Structural System. All real mathematics have been spared, as the rigorously examined Structural System calculations are absolutely non-trivial; indeed more than a few doctoral dissertations have been written on the exact science of corrugated cardboard configuration strengths. Simple text character illustration follows, with "fake" numbers employed for demonstration purposes (too many real variables exist for them to be in any way accurate):

I
(single sheet of card stock- "bending strength" or stiffness equals 1X)

II
(two sheets of card stock sheets glued together- "bending strength" or stiffness equals 2X)

III
(three sheets of card stock glued together- "bending strength" or stiffness equals 3X)

I~
(most simple single-faced corrugation- "bending strength" or stiffness equals 3X)

I~I
(simple double-faced corrugation, a.k.a. Single Wall- "bending strength" or stiffness equals 6X)

I~I~I
(heavy-duty triple sheet corrugation, a.k.a. Double Wall- "bending strength" or stiffness equals 12X)

Now, in the case of our triple-leaf construction, the overall assembly may have gained substantial improvement of stiffness as load-bearing members in the direction of gravity (resistance to compressive forces, as well as torsional stiffness (resistance to twisting forces), lateral stiffness (resistance to sideways forces), etc. What it would not improve subtantially is the Plate Stiffness, which is the kind of stiffness that takes over for Mass Law in the lowest frequency ranges for our typical wall assemblies.

To accomplish an improvement in Plate Stiffness, something similar to the corrugation example above would have to be employed, triangular interconnections ("webs" in Structural Theory) in-between the plates, which in effect would negate the fully decoupled isolation advantages of independent leafs.

To be complete in this assessment, the air gap between each leaf in our wall assemblies does provide some very small increase in stiffness, but because air is a compressible medium, it is negligible compared to what the solid materials provide.

In the heat of discussion it can be difficult to be as carefully provisional as possible to avoid misunderstandings without getting too wordy. In the case of Internet Discourse, where future generations may be hinging their understandings on the use of every word by an individual who is being vital to the discussion, some care must be taken both by the reader and the statement writer as to the implications.

As a "newbie" student in the field of acoustics, I've often made incorrect assumptions based on examples which weren't fully qualified by others in the immediacy of the moment. Hence the reluctance by Avare, and others to be completely exhaustive in their answers or statements- this world of Acoustics (like many real sciences) is incredibly complex, and often counter-intuitive!


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