double leaf effect cost more than triple in most situations.

[Soundman2020]

if TL is desired to be higher than possible with a given assembly for higher frequencies (greater than Fr), Multi-Leaf assemblies may be required.

I would really like to see such a case! Can you show us one? I mean, show us a scenario where a multileaf assembly gives better performance across the entire spectrum than a two-leaf MSM structure, all other factors being equal (cost, space, mass, thickness, etc).

Also, as Mr. Gervais I think stated already, real-world (usually economic) concerns sometimes prevent us from being able to get away from Triple-Leaf designs by removing an existing Leaf in an already finished structure -

But that's an entirely different case! You just switched sides on your own argument! Are you arguing for multi-leaf structures being better and desirable? Or are you arguing that sometimes you just have no choice? That's two entirely different things. Everyone agrees that sometimes there really is no choice, and that a 3-leaf is the only solution, but NOT because it is a BETTER solution acoustically, simply because there is another overriding factor that forces isolation to take a back seat. Examples are: existing structures that cannot be modified, code, time, cost, space, weight, etc.

In other words, make up your mind! If you are arguing the case that multi-leaf can be better than two-leaf, all other factors being equal, then go ahead and make that case. But don't try to then claim that the justification for that argument is that "sometimes you have no choice". That's an entirely different argument, and in fact using that argument automatically implies that multi-leaf is not the best solution, that there was a better solution acoustically (ie, 2-leaf), but that some OTHER factor moved it to second place.

You can't have it both ways! Either multi-leaf is always better acoustically, or it isn't better acoustically but sometimes you have no choice but to prefer it over the "better" solution, (which is always going to be two-leaf MSM).

for certain designs to be physically possible and structurally sound given commonly available materials, especially with structural retrofits, there might not be too many sensible ways to achieve very high TL's without using a multi-leaf system

Once again, you are arguing form the defeatist point of view: Your argument itself recognizes that multi-leaf is NOT the best solution acoustically, but that there are OTHER FACTORS that leave you with no other choice than to use it EVEN THOUGH it is not the best.

If one were unable to pour concrete into a stable wall, or use masonry products that made solid, flush (mechanically unified) leafs, this might be a case where it could become necessary.

Well, to be honest, I don't see anyone here saying that the best way to build a 2-leaf MSM wall is with masonry products that make solid, flush (mechanically unified) leafs! Rather, I see people using plain old drywall sheets nailed to plain old wooden studs. It's hard to envision a case where such a construction method is not possible. And one more time, your phrase "...might be a case where it could become necessary" admits defeat: you are arguing for compromise, for choosing multi-leaf for other reasons, even though it is not the best solution acoustically.

Also, as I struggle to understand the underlying concepts of the M-S-M concepts

Try not to think of it in terms of acoustics: try to think of it more familiar terms, such as trying to force a clock pendulum to swing at any rate other than its natural rate. Or better still, think of it in terms of electronics: an MSM wall is roughly equivalent to a tuned RC circuit. The spring is the capacitor, and the mass is the resistance. Or you can even think of it like a parametric equalizer. Acoustics is confusing, but real-world analogies are rather helpful. For me, at least.

is it not true that any single material might exhibit properties that are both Mass-like and Spring-like

Yes, but if you are going to use such materials then you need to consider them in the MSM equations, in which case you cannot use the simplified version, and you'd need to fall back on other more complex equations that take these into account. Or if you don't have any such equations then you'd have to test your hypothetical materials in an acoustic lab, to extract the equations empirically.

But once again, you are sliding the goalposts: Either mult-leaf is better per se, or it isn't. If you have to resort to exotic and really expensive materials, and more complex mathematics, just to get the same result, then you kind of defeated the purpose of the exercise, didn't you?

or is this strictly a case of trying to differentiate situations where a solid and a gas are compared?

The MSM equations do no speak of solids and gasses: they speak of masses and springs. Simple Newtonian mechanics. The masses are assumed to be rigid, or rather sufficiently rigid that their "springiness" is negligible, and the spring is assumed to be mass-less, or rather sufficiently low density that the mass is negligible. Yeah, if you really wanted to, you could consider the mass of the air as part of the equation, and you could also consider the springiness of the masses, but doing so would not change the results by enough to be of concern, for regular building materials and reasonable costs. Once again, if you have to resort to exotic materials in order to make your point, then you kind of defeated the purpose of the exercise.

For example, I postulate that a room made from a single leaf of uranium six inches thick will absolutely beat any conceivable multi-leaf structure you can come up with, but such a structure is rather impractical...

Specifically, are laminates of differing materials considered to be the Mass portion, regardless of differences in their densities

Exactly. From the point of view of the MSM equations, mass is mass. Exotic materials do not change the mass.

Think of it this way: if you take the pendulum off a grandfather clock and replace it with one made from laminates of MLV, carpet and egg crates, but having the same overall mass, will that make the clock run at a different speed? Obviously not: it won't change a thing. It is the mass that counts, not how you made the mass. And the higher then density, the better. Once you start resorting to things with low density, you start blurring the boundaries of the wall, thus invalidating the equations.

If the Inverse Square Law holds true for acoustics, shouldn't it be possible to design multi-leaf "laminates" whereby the differing leaf densities and distances between leaves would increase in such a way that the overall resonances would not coincide, thereby reducing the effect of unimodal low frequency transmission

No, not for any practical MSM wall. You seem to be talking about coincidence dip, which is an entirely different thing.

If you just stack up a whole bunch of differing materials, with differing acoustic impedances, all that you succeed in doing is changing the mass of the composite, from the MSM point of view. You might manage to change the path of some higher frequency sound waves through the wall, but you won't change the overall isolation provided by the wall by much. Once again, go back to the pendulum in the grandfather clock: Can you make it swing faster or slower by laminating a large number of exotic materials together but keeping the mass the same? Obviously, no you cannot. You can change the speed by changing the mass, period. Nothing else has any effect.

When it comes to MSM acoustic isolation, the number one law is this: Mass rules. (The number two law is: distance rules.)

There simply is no place in the equations that govern how an MSM wall works for the materials that go into it. If you change the materials, you change the mass, period. It doesn't matter how you made the mass, or how much you paid for it, or how much time you spent carefully laminating together your magical materials, in the end all that matters to the sound waves is the mass.

So, back to your original point: Can a multi-leaf wall be built that will isolate sound just as effectively as a two-leaf MSM wall? Absolutely it can! But it will cost a whole lot more, take up more space and be more complex to build. Which comes back to the basic point of the good old 2-leaf MSM wall: It is the best isolation you can get at reasonable cost and in a reasonable amount of space and using reasonable materials. You simply cannot build a multi-leaf wall that is both cheaper and better, or easier to build.


- Stuart -

[brainditch]

Drat, this BB posting function has twice wiped out a rather lengthy reply upon submittal.

Thanks for the curteous and rapid reply, Stuart. I appreciate your efforts to help one who is acoustically naive, such as myself. If I may return the favor-

Quote:
if TL is desired to be higher than possible with a given assembly for higher frequencies (greater than Fr), Multi-Leaf assemblies may be required.
I would really like to see such a case! Can you show us one? I mean, show us a scenario where a multileaf assembly gives better performance across the entire spectrum than a two-leaf MSM structure, all other factors being equal (cost, space, mass, etc).

I can't, because that's not how I qualified my statement- which pertains to higher frequencies only (1K & up).
Though not without caveats, the NRC IR-811 pdf file (pg. 73 od pdf, 61 of text) brings up a case comparison for ceiling joists. As Andre cited, it is an excellent comparison of three different Triple-Leaf systems, and two (proper) Double-Leaf systems. The baseline case is the classic Single Layer Double-Leaf, as a Floor-Joist-GB assembly. Just above this in the chart is the plot for a FL-J-GB-RC-GB config, Triple-Leaf system, which although far worse than the superlative Triple Layer Double-Leaf, does at least a little bit better than predicted by Mass Law (if I understand properly that Doubling Mass = 6dB frequency linear TL), but only in the high frequencies, and gets worse in the lows. Indeed, Double-Leaf systems dominate in general for low frequencies, but other examples on this chart suggest that in some cases, Triple-Leaf configs may equal or do better than Double-Leafs in the highs.

The fact that most of us here at this forum are more interested in low frequency stopping doesn't preclude this as a possible tool that might have to be utilized in the real world.

Quote:
Also, as Mr. Gervais I think stated already, real-world (usually economic) concerns sometimes prevent us from being able to get away from Triple-Leaf designs by removing an existing Leaf in an already finished structure -
But that's an entirely different case! You just switched sides on your own argument! Are you arguing for multi-leaf structures being better and desirable? Or are you arguing that sometimes you just have no choice? That's two entirely different things. Everyone agrees that sometimes there really is no choice, and that a 3-leaf is the only solution, but NOT because it is a BETTER solution acoustically, simply because there is another overriding factor that forces isolation to take a back seat. Examples are: existing structures that cannot be modified, code, time, cost, space, weight, etc.

In other words, make up your mind! If you are arguing the case that multi-leaf can be better than two-leaf, all other factors being equal, then go ahead and make that case. But don't try to then claim that the justification for that argument is that "sometimes you have no choice". That's an entirely different argument, and in fact using that argument automatically implies that multi-leaf is not the best solution, that there was a better solution acoustically (ie, 2-leaf), but that some OTHER factor moved it to second place.

Pardon the confusion, my point was not to waffle on the line of which is better (which is related to many factors, only one of which is to match the Acoustic Ideal), merely to suggest that they are different, and therefore may have unique utility in situ. And it's not an entirely different argument, just not so monolithic as you seem to require.

So Stuart, just so we're clear, I didn't post to champion Triple-Leaf over Double-Leaf for all cases. I'm not deluded that such superiority exists as an absolute, especially given all the overwhelming empirical evidence to the contrary, but I needed to suggest that there might be useful, unique properties with each.

Onve again, you are arguing form the defeatist point of view: Your argument itself recognizes that multi-leaf is NOT the best solution acousticaly, but that there are OTHER FACTORS that leave you with no other choice than to use it EVEN THOUGH it is not the best.

Beg pardon, but this is no Holy Joust, and taking a position which encourages open-mindedness is absolutely NOT "defeatist", sorry.

Quote:
If one were unable to pour concrete into a stable wall, or use masonry products that made solid, flush (mechanically unified) leafs, this might be a case where it could become necessary.
Well, to be honest, I don't see anyone here saying that the best way to build a 2-leaf MSM wall is with masonry products that made solid, flush (mechanically unified) leafs! Rather, I see people using plain old drywall sheets nailed to plain old wooden studs. It's hard to envision a case where such a construction method is not possible. And one more time, your phrase "...might be a case where it could become necessary" admits defeat: you are arguing for compromise, for choosing multi-leaf for other reasons, even though it is not the best solution acoustically.

How about the case above, wherein I suggest that masonry (and other structural extremes, like heavy steel I-Beam construction) might not be possible for some reason- would you prefer to have unsubstantially structurally supported super-thick Double-Leaf walls or a couple of well supported Triple-Leafs? Good Luck if you ever feel that headache rain down on you, which I sincerely hope will be never.

And I recognize that most of the time, the most common way of getting things done in the world will be with plain old vanilla stud and drywall construction. I'm currently a carpenter by trade, by the way.

Alright then, on to more fertile soil vis-a-vis salient facts and understanding of acoustics.
Now your next statement is very informative, thank you!

Also, as I struggle to understand the underlying concepts of the M-S-M concepts
Try not to think of it in terms of acoustics: try to think of it more familiar terms, such as trying to force a clock pendulum to swing at any rate other than its natural rate. Or better still, think of it in terms of electronics: an MSM wall is roughly equivalent to a tuned RC circuit. The spring is the capacitor, and the mass is the resistance. Or you can even think of it like a parametric equalizer. Acoustics is confusing, but real-world analogies are rather helpful. For me, at least.

So without being facetious, likening the MSM to a tuned electronic (RC) circuit (yes I spent ten years as an electronics tech) - won't the day be cool when we can tune a wall as easily as turning a dial? We might even see variable Q walls in our lifetime, if we keep our minds open to possibilities like the ones I'm trying to explore.

Quote:
is it not true that any single material might exhibit properties that are both Mass-like and Spring-like
Yes, but if you are going to use such materials then you need to consider them in the MSM equations, in which case you cannot use the simplified version, and you'd need to fall back on other more complex equations that take these into account, or if you don't have any such equations then you'd have to test your hypothetical materials in an acoustic lab, to extract the equations empirically.

But once again, you are sliding the goalposts: Either mult-leaf is better per se, or it isn't. If you have to resort to exotic and really expensive materials, and more complex mathematics, just to get the same result, then you kind of defeated the purpose of the exercise, didn't you?

Er, um, nope on "sliding the goalposts". I'm still trying to figure out what the white painted lines are for!
I guess my point here is really that we're still in a sort of infancy where the efficient implementation of acoustical science is concerned. Why, just a few decades ago mass alone was the only way we knew of achieving sound isolation, let alone understanding of the importance of coupling, absorption, damping, and their effects on resonance when dealing with common building materials.

Quote:
or is this strictly a case of trying to differentiate situations where a solid and a gas are compared?
The MSM equations do no speak of solids and gasses: they speak of masses and springs. Simple Newtonian mechanics. The masses are assumed to be rigid, or rather sufficiently rigid that their "springiness" is negligible, and the spring is assumed to be massless, or rather sufficiently low density that the mass is negligible. Yeah, if you really wanted to , you could consider the mass of the air as part of the equation, and you could also consider the springiness of the masses, but doing so would not change the results by enough to be of concern, for regular building materials and reasonable costs. Once again, if you have to resort to exotic materials in order to make your point, then you kind of defeated the purpose of the exercise. For example, I postulate that a room made from a single leaf of uranium six inches thick will absolutely beat any conceivable multi-leaf structure you can come up with, but such a structure is rather impractical...

Thanks for the illumination here. I don't know about uranium leafs, but I could swing down to Hanford and probably find some radioactive mud I could send ya
In all seriousness, building materials themselves are evolving. If I recall correctly elastomeric-compound CLD's like Green Glue have only been around a few years, so it's possible things won't need to be too exotic in order to achieve some of these goals. Often just a few simple ideas can change the way we do things, yes? If I recall correctly, you posted earlier in this thread about an impractical case of all steel construction, and I think your point was to explore hypothetical definitions of when an assembly could be considered all mass, and not subject to MSM - was this not your point?

Specifically, are laminates of differing materials considered to be the Mass portion, regardless of differences in their densities
Exactly. From the point of view of the MSM equations, mass is mass. Exotic materials do not change the mass.

Think of it this way: if you take the pendulum off a grandfather clock and replace it with one made from laminates of MLV, carpet and egg crates, but having the same overall mass, will that make the closk run at a different speed? Obviously not: it won't change a thing. It is the mass that counts, not how you made the mass. And the higher then density, the better. Once you start resorting to things with low density, you start blurring the boundaries of the wall, thus invalidating the equations.

Thanks for that assesment, and for further clarity on MSM. Although I think, a pendulum made of chicken feathers might make the clock run a little slow, if for no other reason than increased surface area

If the Inverse Square Law holds true for acoustics, shouldn't it be possible to design multi-leaf "laminates" whereby the differing leaf densities and distances between leaves would increase in such a way that the overall resonances would not coincide, thereby reducing the effect of unimodal low frequency transmission
No, not for any practical MSM wall. You seem to be talking about coincidence dip, which is an entirely different thing.

If you just stack up a whole bunch of differing materials, with differing acoustic impedances, all that you succeed in doing is changing the mass of the composite, from the MSM point of view. You might manage to change the path of some higher frequency sound waves through the wall, but you won't change the overall isolation provided by the wall. Once again, go back to the pendulum in the grandfather clock: Can you make it swing faster or slower by laminating a large number of exotic materials together but keeping the mass the same? Obviously, no you cannot. You can change the speed by changing the mass, period. Nothing else has any effect.

See chicken feather pendulum above.
OK, so I believe I've read that Coincidence Dip is a affected by / related to plate stiffness, whereas the Structural Resonance (usually <200 Hz) is described best by the MSM, which means of course mostly mass driven. If true then, apparently the most convenient variable to modify for MSM other than mass would be the "Spring". How much effect does insulation have on spring-like properties of the air within the cavity? Or am I overstating its importance for this attribute?

When it comes to acoustic isolation, the number one law is this: Mass rules. (The number two law is: distance rules.)

Although proper application of these two laws have yielded the relatively recent ability to isolate more sound energy with substantially less mass, ala proper Double-Leaf construction.

There simply is no place in the equations that govern how an MSM wall works for the materials that go into it. If you change the materials, you change the mass, period. IT doesn't matter how you made the mass, or how much you paid for it, or how much time you spent carefully laminating together your magical materials, in the end all that matters to the sound waves is the mass.

So back to your original point: Can a multi-leaf wall be built that will isolate sound just as effectively as a two-leaf MSM wall? Absolutely it can! But it will cost a whole lot more, take up more space and be more complex to build. Which comes back to the basic point of the good old 2-leaf MSM wall: It is the best isolation you can get at reasonable cost and in a reasonable amount of space and using reasonable materials. You simply cannot build a multi-leaf wall that is both cheaper and better, or easier to build.

I won't argue these points at all, the data so far is too compelling to support other wise, for a brand-new, unimpinged studio build. It is for cases that involve real-world compromises that I offered an alternate view, as I outlined above, that's all.

Thanks once again for your patience with my naivete, Stuart. I appreciate your help explaining some of the basic principles in easily understood terms and analogies.

Bill

[xSpace]

"but I needed to suggest that there might be useful, unique properties with each."


Said it myself.

I think the 3 leaf is a lot like STC which is a lot like a floating floor...they come at you begging to be noticed first and then you find more accurate ways with existing terminology, data, technology and literature to do what has to be done rather than sitting around and talking about how fast we can knock this thing out

[Soundman2020]

which pertains to higher frequencies only (1K & up).

Why would you want to isolate only half of the spectrum? While that might be an interesting mental experiment, I cannot, for the life of me, conceive of any conceivable studio situation where you'd only need to isolate half of the spectrum! I can't even think of any musical instruments where all the fundamentals fall entirely in the top half of the spectrum. What kind of studio are you imagining, and what kind of instruments, where no isolation is needed in the entire bottom half?

would you prefer to have unsubstantially structurally supported super-thick Double-Leaf walls or a couple of well supported Triple-Leafs?

You seem to be missing the point entirely. To get the same amount of isolation in the same physical space, the three-leaf system would have to be MORE massive than the two leaf, under all circumstances.

OK, so I believe I've read that Coincidence Dip is a affected by / related to plate stiffness, whereas the Structural Resonance (usually <200 Hz) is described best by the MSM, which means of course mostly mass driven.

since your hypothetical wall and hypothetical instruments only operate in the top 50% of the spectrum, I'd say that coincidence is going to be a major issue.

If true then, apparently the most convenient variable to modify for MSM other than mass would be the "Spring". How much effect does insulation have on spring-like properties of the air within the cavity? Or am I overstating its importance for this attribute?

The insulation is not the spring: the air is the spring. The insulation is the damper.


- Stuart -

[brainditch]

Why would you want to isolate only half of the spectrum? While that might be an interesting mental experiment, I cannot, for the life of me, conceive of any conceivable studio situation where you'd only need to isolate half of the spectrum! I can't even think of any musical instruments where all the fundamentals fall entirely in the top half of the spectrum. What kind of studio are you imagining, and what kind of instruments, where no isolation is needed in the entire bottom half?

Perhaps because the sound you are isolating is not generated inside the studio, but outside. Many high frequency annoyances can be transmitted to the inside of a studio if it is built in the same building as other noise sources, i.e. next to an industrial wood or metal shop, for example.

You seem to be missing the point entirely. To get the same amount of isolation in the same physical space, the three-leaf system would have to be MORE massive than the two leaf, under all circumstances.

I haven't missed any point you've made thus far, but I'm thinking of broader concerns now - for example:
If one were to require a wall massive enough, Double-Leaf requires point loading of the floor or other structural elements. Double-Leaf necessarily requires the load to be very concentrated (as in a point load) in the vertical plane if utilized in a single stud wall, for example. A Multi-Leaf assembly could be built that would spread the mass over a greater surface, relieving the point loading problem, obviously at the cost of increased floor space and materials. Under normally considered circumstances this is not a problem, I realize, but for special cases...

since your hypothetical wall and hypothetical instruments only operate in the top 50% of the spectrum, I'd say that coincidence is going to be a major issue.

OK, so you verified (through implication) that my understanding of Coincidence and MSM is generally correct. Thank you.
As for the hypothetical instruments, see above for “shop neighbors”. As for the wall’s Critical Frequency, I’m still learning about this attribute, and have much more study to do.

The insulation is not the spring: the air is the spring. The insulation is the damper.

This I understand, and as a damper, it is "robbing" energy from the spring, correct?
One thing I'm still unclear about is whether to a greater or lesser degree, the "absorber" may be acting as a sort of inefficient leaf, if I'm not misunderstanding the implications discussed below:
http://forum.studiotips.com/viewtopic.p ... 0&start=60

Bill

[AVare]

One thing I'm still unclear about is whether to a greater or lesser degree, the "absorber" may be acting as a sort of inefficient leaf, if I'm not misunderstanding the implications discussed below:
http://forum.studiotips.com/viewtopic.p ... 0&start=60

It may. IT all depends on the specifics.

ps: high loss above 1 kHz is easily done with almost completely normal construction methods.

Andre

[G-Sun]

This topic is just nailing my current question
Thanks!

[ndelonas]

From a practical approach it seems that the OP gives a good summary, but probably overestimates the double leaf properties he suggests (and blow-in is only possible when the cavity was still empty, but any absorption versus empty will have a significant impact).

Hi Eric,

What type of blow-in material would you recommend for situations where removal of the surface is not practical? I have a floor I'm trying to treat and while I can't get to the cavity from below, I could remove a few planks and blow in material between the joists from above. That'd be easy to do. If it would help much at all in lowering airborne sound transmission through the floor and the expense isn't too bad, then I could add that to the other treatment options I'm considering.

--Nick

[Ted White]

I'll offer a thought from the practical perspective, as we deal with this issue very regularly. Blowing in insulation can be a liability. First, in my experience most installers of blown-in believe that for acoustic purposes, you want MORE insulation. That is- denser. This is incorrect as compressed insulation can conduct vibration.

Secondly, it is almost unavoidable (it seems) that the blowing insulation get's caught on wires, pipes, nails and starts to congest and compact certain areas, while leaving other areas completely without insulation.

It's very common for us to get a call from someone who just had insulation blown in and now things are worse. Again, very common.

[ndelonas]

I'll offer a thought from the practical perspective, as we deal with this issue very regularly. Blowing in insulation can be a liability. First, in my experience most installers of blown-in believe that for acoustic purposes, you want MORE insulation. That is- denser. This is incorrect as compressed insulation can conduct vibration.

Secondly, it is almost unavoidable (it seems) that the blowing insulation get's caught on wires, pipes, nails and starts to congest and compact certain areas, while leaving other areas completely without insulation.

It's very common for us to get a call from someone who just had insulation blown in and now things are worse. Again, very common.

Ah, okay. I guess I'll stick with adding a bit of mass with green glue to the surface. Thanks Ted.

-- Nick

[Podgorny]

sometimes you have no choice but to prefer it over the "better" solution, (which is always going to be two-leaf MSM).

Stuart. It sounds like you are misinterpreting this "3rd leaf decreases isolation" rule.

If you have a typical MSM system, and bisect that system with a third leaf, you WILL decrease low end isolation. That is true... Except when it isn't. If the space is large enough that it can be halved in volume without moving the resonance into the audible range, you will improve isolation. But of course, in this case, we're not talking about a typical setup.
But let's be clear; If you have an MSM system and ADD a third leaf to the outside, you will NOT decrease isolation, as the resonance of the air space or the original mass has not changed.

Or I may have misinterpreted what you said.
Long story short, it is good advice to avoid MSMSM (with a caveat or two).

[Soundman2020]

But let's be clear; If you have an MSM system and ADD a third leaf to the outside, you will NOT decrease isolation,

Well, that's not strictly correct either: Unless your leaf is sufficiently massive, or at a sufficiently large distance, yes you could end up decreasing isolation. Since adding the third leaf creates a three-leaf system, you now have two fundamental resonant frequencies (f+ and f-) BOTH of which are higher than the single frequency for the two-leaf wall (f0). (OK, we are talking light weight panels and small gaps here to make that happen, but it is still possible).

I recall that Rod has mentioned this somewhere as a common problem he has seen in 2-leaf party-wall situations, where one of the neighbors doesn't like listening to the TV next door, and figures he can improve matters by adding an extra leaf to his side of the wall, so he tacks up a sheet of thin drywall on battens, then he can't understand why things got worse, not better ...

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...

OK, in reality this point is splitting hairs. The original issue was people making claims, then changing their claims as they were shown to be wrong, then changing them again when still shown to be wrong, until the eventually got it right, or stopped talking.

In any event, for practical studio builds this probably is not too much of a problem, since the situation where you would need to add a 3rd leaf outside of an existing MSM 2-leaf would seldom occur anyway, if the place is properly designed. So there's not much in talking about hypothetical situations the are very improbable in real life.

As you say: " it is good advice to avoid MSMSM". And if you do run into the situation where you have no choice, then it is good to know that it is possible to compensate by increasing the mass or the separation sufficiently (or both).

But of course, in this case, we're not talking about a typical setup.

Exactly! I'm only talking about realistic, common situations. It would be VERY unlikely for a home studio builder to run into the situation where his two-leaf wall has such a large gap!


- Stuart -

[Podgorny]

I recall that Rod has mentioned this somewhere as a common problem he has seen in 2-leaf party-wall situations, where one of the neighbors doesn't like listening to the TV next door, and figures he can improve matters by adding an extra leaf to his side of the wall, so he tacks up a sheet of thin drywall on battens, then he can't understand why things got worse, not better ...

I was with you until this part.

Adding an additional space and mass to the OUTSIDE of an MSM system does not change the mass or resonance of the original system. Since the third leaf is mechanically disconnected from the first system by the second space, in order to make things worse, it would have to literally create energy, which of course it cannot do. Common sense tells us this.

The issue with MSMSM systems is the resonance of the spaces. If you can add another leaf without changing the resonance of the first system, it WILL improve isolation. Case in point, plug your ears - You're essentially adding another barrier to an existing system - but you don't start hearing MORE low end, because you're not appreciably changing the size of the air space. But again, in typical MSM systems where we're talking about small gaps between mass, (as you have said) it would require a great deal of effort to get a third leaf to negate the loss of isolation caused by halving the size of the air space.

[Soundman2020]

Adding an additional space and mass to the OUTSIDE of an MSM system does not change the mass or resonance of the original system.

Yes it does. It must, since it changes the system from being MSM to being MSMSM. Most people don't realize that walls are tuned systems, and adding anything to them changes the tuning. Moving from a 2-leaf MSM system to a 3-leaf MSMSM system implies a different system.

You use different equations to solve for the resonant frequency of a three-leaf system, since it does not behave the same as a two leaf system. Adding an extra leaf to a two-leaf system makes it into a three-leaf, no matter where you put it. Inside or out, the third leaf is still a third leaf, and does, indeed, modify the entire system.

Since the third leaf is mechanically disconnected from the first system by the second space,

No it is not. There is no mechanical disconnection. In reality, all parts of the system are interconnected, and they all act together as a whole. The air gap does not disconnect the leaves: on the contrary, it ties them together. That's why it is considered as a "spring". That's why the system is referred to as a mass-SPRING-mass system: Air is a really, really good spring, from the point of view of sound waves... The air gaps in an 2-leaf or 3-leaf wall do not disconnect the leaves from each other: rather, they connect them in the exact same way as the spring on your car's suspension connects the wheels to the chassis.

in order to make things worse, it would have to literally create energy, which of course it cannot do. Common sense tells us this.

Actually, it doesn't have to "create" energy: it just has to resonate. Resonance is a powerful effect: have you ever seen that famous video of the Tacoma narrows bridge tearing itself to pieces at resonance when the wind was just right? The bridge did not need to "create" any energy to do that! All that was necessary was the resonant conditions set up by the wind. It just needed to absorb a little bit more energy from the wind on each oscillation than it did on the last. Just like a child going higher and higher in a swing, from a tiny extra push at the end of each cycle. It is the exact same principle.

Have you ever heard the way a certain bass note can "build up" in a room, to a level much louder than the instrument playing it? Same effect. Standing waves (room modes) are another example.

Same with the wall situation: At resonance, the wall can, in fact, amplify sounds at that specific frequency. In fact, an MSM wall does exactly that: at resonance it is effectively transparent, and can amplify the sound. Unity gain is only achieved at about 1.41 * f0, so the wall does not even start isolating until that point. Between f0 and 1.41 * f0, amplification can happen due to the resonance itself. On each oscillation of the wall, it takes on a bit more energy from the sound wave that it is causing the resonance, so the vibration can become louder than the note that is causing it. That's the power of resonance, and is the reason why engineers work so hard to eliminate resonance in machinery and equipment. Unchecked, resonance can easily rise to levels that cause damage to equipment.

Hence the rule of thumb that you should tune an MSM wall to half the lowest frequency that you need to isolate, such that you are well into positive isolation territory at that frequency.

What keeps resonance under control is damping: an un-damped MSM system will resonate wonderfully: Which is why it is so important to put plenty if insulation in the cavity. Insulation acts as the damper on the air spring, in exactly the same way as the shock absorbers on your car damp the resonance of your suspension. If you had no shock absorbers, your suspension could be torn apart if you happened to drive over a corrugated road at the right speed.

In any event, maybe this graph will help to understand the issue:

2-leaf-vs-3-leaf-700pix.jpg

Adding that third leaf does not need to "create" energy: it just needs to move the resonant frequency up the scale enough that the "transparent" frequency is now in the audible range, when it wasn't before. So before putting the third leaf in place, our well-meaning neighbor could maybe only hear muffled low frequencies, but now he has moved the resonance up the scale and he can also hear voices. Not because the extra panel is creating energy, but rather because the entire system is now re-tuned higher up the scale, and more of the audible spectrum now falls within the band of frequencies that the wall passes. In addition, that "band" is no wider than it was: with a two-leaf wall, there is only one resonant frequency, f0. With a three leaf wall, there are two: f+ and f-.

The issue with MSMSM systems is the resonance of the spaces.

Actually, no, that isn't correct. It is the resonance of the entire system that matters. It is NOT the space between the leaves that oscillates! It is the leaves themselves. The space acts as the spring, and the leaves are the mass. In a resonant system, it is the mass that oscillates. The spring moves two, but what keeps it moving is the inertia of the mass.

If you can add another leaf without changing the resonance of the first system,

That's impossible! The simple fact of adding the third leaf re-tunes the entire system to a different frequency, in exactly the same way as adding an additional capacitor and resistor to a tuned electronic circuit will re-tune the entire circuit. You cannot add a new leaf without affecting the resonance of the existing leaves. You should not view a resonant system as several individual parts that act on their own: it must be viewed as a SYSTEM of parts that act together. The whole is greater than the sum of its parts.

Think of it this way: if you have a weight hanging from a spring, then it will bounce up and down at a certain frequency. This is the exactly analogous to an 2-leaf wall Mass-Spring-Mass. Now, if you hang a second spring and weight from the bottom of the first spring and weight, you change everything: and now you have an exact analogy for an 3-leaf wall system: Mass-Spring-Mass-Spring-Mass. It is obvious that the additional weight and spring that you just added MUST have an effect on the weight and spring that were there before. It it impossible that you could add the extra weight and spring without affecting the original weight and spring. Think about it.... so your argument breaks down right there, since it is based on false assumptions.


- Stuart -

[Podgorny]

"A Comparison of the Transmission Loss Provided by
Double and Triple Panel Constructions of Equal
Total Mass and Overall Thickness."

And I quote for emphasis...
CONSTRUCTIONS OF EQUAL TOTAL MASS AND OVERALL THICKNESS

ONE: Equal mass.
Each leaf is of lighter weight in the triple-panel construction, than those in the double-panel.

TWO: Equal thickness.
This is illustrating that decreasing the size of the space has an adverse affect on low end isolation (which is true, except in cases of very large spaces).


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).


Now obviously, the third leaf will pass sound at its resonant frequency, just like any mass (which is why it is beneficial to use differing materials on each side of an MSM system), and in this case will STILL attenuate all frequencies not harmonic to the resonant frequency.