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.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).
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.
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.This is illustrating that decreasing the size of the space has an adverse affect on low end isolation
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.Now obviously, the third leaf will pass sound at its resonant frequency,
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.
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.just like any mass (which is why it is beneficial to use differing materials on each side of an MSM system)
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.
- Stuart -