Your overall advice seems to be: define what I need and then calculate the performance of each elements in the system and make choices based on achieving the minimum performance required.
Exactly! It's the same as buying a car, cell phone, house, or anything else: first define what you want, then find the product that does that. However, just like with cars, houses, and cell phones, so to with studio isolation and acoustics: the product that does what you want normally costs more than you expected!
Could you offer some books or links related to this measurement?
I'd suggest two books: "Master Handbook of Acoustics" by F. Alton Everest (that's sort of the Bible for acoustics), and "Home Recording Studio: Build it Like the Pros", by Rod Gervais. The first one will give you the background in acoustics that you need to be able to design a studio, and the second one will give you the basics for actually designing it and building it.
even after a lot of research, this "MSM resonance" you refer to seems very mysterious.
The concept itself is simple: "MSM" stands for "Mass-Spring-Mass", and it's the principle in the world of physics that governs how a weight bounces up and down on a spring, or how a pendulum swings, or how your car shock-absorbers work. It's all about "resonant systems". Any time you have a mass that can bounce on a spring, you have a resonant system. It wants to resonate (vibrate) only at it's natural resonant frequency, and does NOT want to vibrate at other frequencies. Think of pushing a kid on a swing: there's a natural frequency that the kid will swing at, and no matter how hard you try, you cannot make the king-and-swing go faster or or slower for long. If you push harder, the
amplitude of the swinging increases, but the
frequency does not: the kid still moves at X cycles per minute. Which is why the pendulum was so popular in clocks: it's good at keeping time. If you grab the poor kid on the swing and force the swing to go slower by just walking it back and forth, the swing will only keep that speed for as long as you force it, but as soon as you let go, it goes back to swinging at it's natural rate. If you push the kid gently in sync with the natural rate, then the amplitude increases. If you push out of sync, then the amplitude decreases.
So to with your wall or window: it has one "leaf" of mass, then a space that is filled with air, then another leaf of mass: It's a resonant system, and it wants to resonate only at it's natural frequency. And at that frequency, it does not isolate at all: It is resonating, so it will not only transmit that frequency to the other side, but also amplify it. So for example, if your wall is tuned to 49 Hz, and you play a G1 on your 6 string bass guitar using the 3rd fret on the E string, then the wall will resonate along with that note, pass it through to the other side, amplified, because a "G1" is 49 Hz. But if you play a C2 using the 3rd fret on the A string, that's 65.4 Hz, so the wall won't resonate with that, won't pass it through, and won't amplify it. The key, then, is to tune your wall so that it's natural resonant frequency is lower than the lowest note you want to isolate! It seems obvious after reading that explanation, but not so obvious before! There's a lot about acoustics that isn't obvious at first glance.
In fact, it turns out that you need to get the resonant frequency of your wall at least one octave below the lowest note you need to isolate.
Do you have any resources you can offer for how to calculate the dB reduction of a wall, door or window sufficiently enough to compare their performance and decide what will be required to achieve consistent performance?
To tune your wall you need to adjust the mass on each side, and the air gap between them. The more mass you put on each leaf, the lower the resonant frequency. The larger the air gap is, the lower the resonant frequency. The equation for calculating it is not that complicated:
f0 = C [ (m1 + m2) / (m1 x m2 x d)]^0.5
... but that only tells you what the resonant frequency is: It doesn't tell you what the isolation is. To get that, you need more equations. But in order to understand the other equations, you'll first need a little more background. So I'll repeat part of a post that I did for another forum member a while back, that gives you the necessary details...
As I mentioned above, isolation is "all or nothing". That also means that if you don't isolate ALL sides of the room (including ceiling and floor), then you won't have any isolation at all! Think of this: Imagine there's a guy who wants to have an aquarium in his living room, because he likes to look at fish, so he goes to the store and buys a metal frame to make his aquarium. But then he thinks: "I only need to see them from the front, so I'll just buy one sheet of glass to put on that side, and leave the rest open". How well do you think that aquarium will hold water?
Obviously, it won't hold water at all! But that is what you would be doing if you only isolate your ceiling...
In other words, if you do need to isolate your room from anything, then you need to isolate it form
everything. You cannot isolate a room in only one direction, just like you cannot build an aquarium with glass on only one side. As soon as you put water in it, the water will simply gush out and splash all over, in ALL directions, even the direction where the glass is, since the water will go over, under, and around that glass. If you only isolate one side of your studio, then when you pour sound into it, the sound will gush out and splash all over, in all directions, including the direction where that one isolation wall was, because the sound will go under, over, and around that wall, as if it wasn't even there.
So, therefore, if you do need isolation, then you need the build the same amount of isolation in all directions around your room, and in all aspects: every wall, ceiling, floor, door, window, electrical conduit, HVAC duct, and everything else, must all be isolated to the same level. Acoustic isolation is onl as good as the weakest point, so if you isolate your studio fantastically all around except for the window, then you might as well not isolate anything, because sound will take the "easy" path out through that window...
It is "all or nothing". Many first time studio builders have a hard time understanding this concept, and think they can get away with only isolating some parts of their room, but that simply does not work. The laws of physics apply to everyone the same, even those people who don't understand them, or don't want to accept them!
There's basically only two methods for isolating a typical home studio. You can try to do it with "Mass Law", which is the principle of physics that governs a single-leaf wall built from heavy, dense materials, or you can try to do it as a proper "room-in-a-room", which is more correctly called a "fully decoupled two-leaf MSM isolation system".
If you decide to go with a single leaf wall (door, window, ceiling, etc.), then it is governed by Mass Law. That's a simple equation that tells you how much isolation you will get, based only on the surface density of the wall: how much does each square meter of your wall ( / door / window / ceiling) weigh, in kg/m2? Here's the Mass Law equation:
TL(dB)= 20log(W) + 20log(f) -47.2
M is the surface density of the wall (mass per unit area (kg/m²) ),
F is the center frequency of the third-octave measurement band that you are interested in.
If you use that, then you can predict the isolation for ever single frequency on the musical spectrum, and you can draw a graph that shows exactly what your isolation will be. You can then compare that graph against the spectrum of each instrument that you will be playing in your room, to see if your proposed wall is going to stop the amount of sound that you need it to stop. If not, then you can increase the mass of your proposed wall, more and more, until eventually you get to the right mass that provides the right isolation for YOUR situation.
The problem with Mass Law is that it is not your friend! If you take a close look at that equation, you'll see that it implies that each time you DOUBLE the mass of the wall, you will get an increase of 6 dB in isolation. That's in theory, which assumes your mass is perfect: in practice, with real-world materials, you can expect an increase of maybe 4 or 5 dB each time you double the mass. So let's say you do that math, and figure out that your hypothetical 2 inch thick sheetrock wall will provide about 40 dB of isolation, but you actually need 55 db of isolation (purely hypothetical: I don't know how much you actually need!). Using Mass Law, you would simply double the thickness of your wall from 2 inches to 4 inches (to get twice the mass), and that would increase the isolation from 40 dB to 45 dB. Then you would double the thickness again, from 4 inches to 8 inches, and that would get you 50 dB of isolation. Then you would double the thickness (and mass) one more time, from 8 inches to to 16 inches cm, to get you to 55 dB of isolation. Simple!
Except that I'm pretty sure you do not want walls that are built up from 16 inches thickness of sheetrock !
Clearly, Mass Law is not very friendly, if you need decent isolation. Which is why studios are never built like that! You cannot get decent isolation with a single-leaf wall, because Mass Law prevents it.
So you need the other system: fully-decoupled two-leaf MSM isolation, more commonly called "room-in-a-room". Basically, that just adds a second set of walls, floor, ceiling, doors, windows, built inside the shell that you already have from Mass Law. The two walls together are NOT subject to Mass Law: they are subject to an entirely different set of equations, because they create a resonant system. And with this system, you get an increase of 18 dB each time you double the mass, which is a much happier proposition! However, there's a drawback: it is a resonant system, so it is no longer just one equation that describes ow the wall isolates. There are several equations, and each one applies to just a part of the spectrum. For the part of the spectrum below the resonant frequency of the wall, Mass Law still applies. For the part of the spectrum around the resonant frequency of the wall and up to about 1.4 times the resonant frequency), resonance applies, and the wall isolates LESS than Mass Law. In fact, the wall can actually
amplify sounds at that frequency, instead of attenuating them, so obviously it is important to tune the wall such that resonant frequency is way below the audible spectrum. Above that, you get your 18 dB per octave increase in isolation, which is great.... until you get to the frequency where the wavelengths of the sound waves are smaller than the distance between the two leaves of the wall, when internal resonance once again robs you of isolation, and you only get an increase of around 12 dB per octave. Then there's also the point where sound waves hitting the wall at certain angles happen to coincide with certain conditions related to the building materials that you used to make the wall, and you get another drop in isolation: this is called the "coincidence dip". And above that, you get an increase of around 12 dB per octave again.
So a 2-leaf MSM wall needs to be designed such that all of this dips and curves and lines and regions match what you need, for your studio. But overall, it will be MUCH cheaper and MUCH more effective to build a wall this way, than to build a single-leaf wall, which is controlled by Mass Law.
And now that the explanation is out of the way, here's the full set of equations that you need:
The equations for calculating total isolation of a two-leaf wall are simple:
First, for a single-leaf barrier you need the empirical Mass Law equation (similar to the one above, but not frequency specific):
TL = 14.5 log (M * 0.205) + 23 dB
Where: M = Surface density in kg/m2
For a 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)
m2 mass of second leaf (kg/m^2)
d=depth of cavity (m)
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 x d) - 29 ...[for the region where f0 < f < f1]
R = R1 + R2 + 6 ...[for the region where f > f1]
Where:
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
And that's it! Nothing complex. Any high school student can do that. It's just simple addition, subtraction, multiplication, division, square roots, and logarithms.
- Stuart -