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So what exactly is "MSM"?
MSM stands for "Mass-Spring-Mass", and that refers to a very simple principle in Physics. In studio design, you also sometimes see this referred to as "MAM" for "Mass-Air-Mass", but that's somewhat misleading, so I prefer the more accurate "MSM".
OK, let me try to explain: If you are building a home studio as a "room-in-a-room", then you will probably start out with the empty shell of an unfinished garage, basement, or something like that, then within that shell you build stud frame walls, then put ceiling joists across the top of that, and put two layers of drywall on just one side of that framing, sealing everything carefully, etc.... then you have a well isolated room.
In technical jargon, you have created a proper "fully decoupled two-leaf MSM system",
Let's break that down again, similar to what I did in the other article:
"Fully decoupled" means that no part of your new structure touches any part of the original structure (except the floor, of course, but that's usually a massive concrete slab sitting directly on planet earth, so that is already doing a good job of isolating).
"Two-leaf" means that you have an "outer leaf" (the original walls and ceiling of the basement or garage), and you have an "inner-leaf" (the new walls and ceiling that you just built. A "leaf" just means a continuous, massive surface that encloses something. Your inner leaf in this case would be the "two layers of drywall on the stud frame". But those two layers MUST go on the SAME side of the studs, ie, one layer right on top of the other layer. If you put one layer on each side of the studs, then you would have a three-leaf system, which is bad (not intuitive, but we'll get to that in a minute). So you have two-leaves around your room: One is the original walls / ceiling, and the other is the "double-drywall-on-one-side-of-the-studs" that actually encloses the room.
"MSM System", as I mentions above, means "Mass-Spring-Mass", which refers to the principle of physics on which this isolation works. This is a bit harder to explain, but it is the key to why this isolation method works. If you hang a weight from a spring, and give it a nudge, it will bounce up and down for a looooong time, at a fixed rate that does not change:
- MSM-Animated-mass-bouncing-spring-animated.gif (341.32 KiB) Viewed 64353 times
- MSM-Animated-mass-bouncing-spring-animated.gif (341.32 KiB) Viewed 64353 times
It doesn't matter how hard or how gently you pull down on that weight before releasing it, the rate of the bounce will ALWAYS be the same, at "X bounces per minute". It is a tuned system that is resonating at its natural resonant frequency. If you wanted to make it bounce faster or slower, then you would have to make the weight heavier or lighter, or you would have to change the spring for another one that has different "resilience" (in other words, a harder or softer spring). There's no other way you can make it bounce differently, because the mass and the spring act together to "tune" the system to a specific frequency. This is the basis of the "Mass-Spring-Mass" principle.
Another example: Have you ever pushed a child on a swing?
- child-on-swing-pushing-animated-2.gif (161.51 KiB) Viewed 64353 times
- child-on-swing-pushing-animated-2.gif (161.51 KiB) Viewed 64353 times
Notice that the swing only ever goes at one rate, no matter how hard or soft you push? For each child, the swing will always complete full cycles in exactly the same time period: "X per minute". To make it go faster or slower, you have to put in a lighter or heavier child, or change the length of the ropes. This too is an "MSM" system.
Another example: A grandfather-clock pendulum,
- grandfather-clock-animated..gif (797.02 KiB) Viewed 64353 times
- grandfather-clock-animated..gif (797.02 KiB) Viewed 64353 times
These three are all examples of tuned "mass-spring" resonant systems. In the case of the swing and the pendulum, its not so easy to see where the "spring" is, but basically it is gravity.... think about it.
So, going back to the kid on the swing: what would happen if you tried to force that swing with the child to go at a DIFFERENT rate? Let's say that you want it to go 50% faster: how do you do that (without changing the child or the ropes)? Answer: you cannot do it easily, since the mass and the spring (rope/gravity) are resisting all changes to the resonance of that system. You would have to physically force the swing through the entire cycle, using all your strength at each point to make it go at a different speed. You'd have to put a lot of effort into doing that, but as soon as you release the swing, it will immediately go back to swinging at its natural rate, effortlessly.
OK, your studio wall does the exact same thing. The only difference is that there are two masses connected by a spring, but the concept is the same. The two leaves (outer-leaf and inner-leaf) are the two masses, and the air in between them is the spring. The wall is a tuned MSM system. It wants to resonate at only one natural frequency, and it does not want to resonate at all other frequencies. There is one frequency where it will vibrate and resonate and sing like crazy, directly and effortlessly passing all the energy from one side to the other. So what good is that to you? Well, if you tune it so low that the resonant frequency is BELOW the threshold of human hearing, then it will naturally resist passing all other frequencies! We have a word for that: isolation.
So if you tune your walls such that the resonant frequency is below 20 Hz (generally considered to be the lowest frequency that we humans can hear), then it will isolate across the entire audible spectrum.
The way you "tune" the walls is the same way you "tune" the kid in the swing: either you change the mass (get a fatter kid, or skinnier kid), or you change the length of the rope. In the same way with your wall, you can change the mass on each leaf, or the distance between them (the spring). More mass = lower frequency. More gap = lower frequency. So you simply select the amount of mass and the size of the air gap such that the resonant frequency is lower than the lowest frequency you want to isolate. Easy!
That's how you isolate studios!
OK, so this is where most people think: "Well, if a one-leaf wall by itself is bad, and a 2-leaf wall is good, then a 3-leaf wall must be fantastic!" Wrong. Not intuitive, but a 3-leaf wall is actually WORSE than a 2-leaf wall, all other factors being equal. In other words, if instead of putting those two layers of drywall on top of each on the same side of the studs, you decided to put one layer on each side, well that wall would not isolate very well at all in the low frequencies. Same mass, same total air gap (just split in two), same total wall thickness, but worse isolation. Sounds wrong, but it works like this: if you change anything in that wall, then you re-tune it to a different frequency. Remember that I said that the way you tune a wall is with the size of the air gap and the mass? Well, now you have TWO air gaps, and they are both much smaller than the original big one, so the resonant frequency of each is much higher. And you have also split the mass, so the mass on each of these two leaves is now much lower, so the resonant frequency went up again! It turns out that your wall is now tuned to resonate well within the audible spectrum, and therefore does a lousy job of isolating low frequency sounds. Things like kick drums, snares, toms, bass guitars, keyboards, and anything else that plays low notes, will simply not be isolated. In fact, mathematically a 3-leaf wall has two additional resonant frequencies, called "F+" and "F-", both of which are much higher than the F0 frequency for the equivalent 2-leaf wall.
Here's an image that should make it very clear:
- 2-leaf-3-leaf-4-leaf-STC-diagram--classic-enh.gif (26.56 KiB) Viewed 64164 times
- 2-leaf-3-leaf-4-leaf-STC-diagram--classic-enh.gif (26.56 KiB) Viewed 64164 times
Now, if you take one of the leaves out of that from the middle of the wall, look what happens (the center illustration above): You get STC-53 isolation! In other words, even though you removed a quarter of the mass from that wall, you increased the isolation by 9 points, which is pretty darn good! So the wall has LESS mass, but isolates MORE! Sounds non-intuitive, but it is very true. The reason is simple: you only have two resonant air cavities now, instead of three, and one of them is much bigger. So the resonant frequency is now lower, and thus the isolation is better.
And for the right hand illustration above, the other internal leaf has also been removed, then both of those removed panels have now been placed on the outsides, on top of the existing drywall: the STC rating went up again, by ten points this time. This is a two-leaf wall, with two layers of drywall on each of those leaves. This wall has the exact same materials, total mass, and thickness as the one on the left, but it isolates about one hundred times better (it stops about 100 times more sound), and the subjective level on the other side would be about one quarter as loud (a drop of 10 dB sounds like roughly half as loud, so a drop of 20 dB is half of a half). The main reason for the large increase in isolation, is because there is now only one air cavity inside the wall, and the depth of that air cavity is now much greater. So there is only one resonance, and it is at a much lower frequency.
There are equations for figuring all this stuff out, but as a general rule you need two layers of 5/8" drywall on each side of an 8" gap to get full coverage of the entire spectrum. Consider that normal 2x4 studs are actually 3 1/2" wide, and you have two stud-framed leaves in most home studios, that's already 7": so if you have a 1" gap between the original outer-leaf frame, and your new inner-leaf frame, then you have an 8" gap! That's what the illustration on the right of the above image shows: two frames with a gap, and 2 sheets of drywall on only the outer sides of that.
Andre once explained the difference between 2-leaf and 3-leaf in a very simple way: "The frequency of the space is based upon the square root of the mass of walls and the space in between. The isolation of walls is based upon the the depth and mass. You put a leaf in between and you making two smaller mass-air-mass systems inter-connected and raising the frequency of resonance by half an octave.". I kept that comment, as I thought it was an excellent simplification of a confusing issue.
Back to the kid on the swing. If you really want to interfere with the resonance of that swing, then you could do something to add some drag on the system. For example, set it up over a deep puddle of water, so that the kid has to drag his legs through the water on every cycle. Now you have drastically increase the damping factor, and it just won't swing very well at all! (I mean "damping" not in the sense of "wetness" here, but in the sense of drag, viscosity). The resonant frequency is still the same: same kid, same rope, same gravity. But now the swing hardly moves, because the motion is damped by the viscosity of the water.
Well, you can't fill your walls with water, but you CAN fill them with fiberglass insulation! It turns out that plain old fiberglass or mineral wool insulation does a great job of "damping" the resonance of the wall, thus making it isolate even better. In fact, acoustically, the gap now seems bigger from the point of view of the sound waves, so you get a double effect from the fluffy stuff: It makes the sound waves take a path through the wall that is an average of about 1.4 times the actual distance, which lowers the resonant frequency even more. Good stuff!
OK, so the whole MSM thing is actually a bit more complex than that, and I'll update this article with more information in the future, but that simple explanation above should help you get your head around this principle behind acoustic isolation.
"Fully-decoupled 2-leaf MSM" is the absolute best way to isolate a room at low cost.
If you really want to figure out all of this mathematically, here's how you would do it:
There's a set of equations that you need for estimating overall isolation of a two-leaf wall in the various regions of the spectrum. All of the equations are fairly simple:
First, for a single-leaf barrier you need the Mass Law equation:
TL = 14.5 log (M * 0.205) + 23 dB
Where: M = Surface density in kg/m2
For the complete two-leaf wall, you need to calculate the above for EACH leaf separately (call the results "R1" and "R2").
Then you need to know the resonant frequency of the system, using the MSM resonance equation:
f0 = C [ (m1 + m2) / (m1 x m2 x d)]^0.5
Where:
C=constant (60 if the cavity is empty, 43 if you fill it with suitable insulation)
m1=mass of first leaf (kg/m^2 or lbs/ft2)
m2 mass of second leaf (kg/m^2 or lbs/ft2)
d=depth of cavity (m or ft)
(NOTE: C=60 for imperial empty cavity, 2650 metric empty cavity, 43 for imperial full, 1900 for metric full)
Then you use the following three equations to determine the isolation that your wall will provide for each of the three frequency ranges:
R = 20log(f * (m1 + m2) ) - 47 ...[for the region where f < f0]
R = (R1 + R2) + 20log(f * d) - 29 ...[for the region where f0 < f < f1] ***
R = R1 + R2 + 6 ...[for the region where f > f1]
Where:
m1 and m2 are still the surface densities of leaf 1 and leaf 2, respectively
f0 is the resonant frequency from the MSM resonant equation,
f1 is 55/d Hz
R1 and R2 are the transmission loss numbers you calculated first, using the mass law equation for each leaf
And that's it! Nothing complex. High school math. It's just simple addition, subtraction, multiplication, division, square roots, and logarithms.
- Stuart -
***FOOTNOTE: This is the CORRECT version of the equation! gearjunk1e picked up on an error in an earlier version of this article, where there was an error in the second line. It used to read: "R = (R1 + R2)/2 + 20log(f * d) - 29...". but that is not correct. The "/2" factor should not be there. The correct version is as show above: R = (R1 + R2) + 20log(f * d) - 29..." Thanks, Andrew! (Now I'm trying to figure out where that wrong version came from! Who added the extra factor, and why? Hmmm......)
