so let's say you had sheet of drywall then a stud wall then an air gap of 3-4" then another stud wall then drywall that would be a 2 leaf system?
If you change your "stud wall" to "stud frame" for clarity, then yes, that would be it! Like this: "
so let's say you had sheet of drywall on stud frame then an air gap of 3-4" then another stud frame with drywall, that would be a 2 leaf system?" Yup!
Would what I described be the best kind of isolation for a normal studio?
Yes, provided that you build it around all sides of the studio (4 sides plus ceiling), and seal it air-tight. A fully decoupled 2-leaf MSM system is, indeed, the best way of getting really good isolation at relatively low cost.
why does doubling the layer of drywall increase the noise reduction in the case I'm describing?
In a word: Mass. To stop sound, you need mass. Remember that I defined a "leaf" as being a "massive surface"? There's a reason for that, based on physics. In order to stop something that is moving, you have to put something in the way that is either rigid enough to stop it, or massive enough to stop it. The bigger the "thing" that you want to stop, the more mass you need. If you want to stop a bicycle, then a simple wooden wall will do, but if you want to stop a car then you are going to need a brick wall. But if you want to stop an 18-wheeler then you are going to need a massive concrete wall. The only thing that changes is how much mass you are putting in the way. If you had enough wood, you could stop the truck by using the same total mass of wood (even though it would take up much more space).
In other words, sound waves react to mass. When a sound wave hits a wall, it makes the wall vibrate in sympathy. If the wall is light weight, then it vibrates a lot: the sound gets transmitted through to the other side. If the wall is heavier (more massive) then the sound cannot make it vibrate so much, so less sound gets though. And if the wall is REALLY heavy, so that the sound cannot make it vibrate at all, then no sound gets through.
So mass is your friend. The more mass you put in a wall, the better it will isolate.
However, the laws of physics that deal with mass and vibration are not very helpful: "Mass Law" says that each time you double the entire mass of the wall, then your isolation goes up by 6 dB. That isn't very much. Let's say that you have a single-leaf drywall wall, and it is giving you 20 dB of isolation, but you need 44 dB of isolation. Mass law says that you double the mass for 6 dB increase, so you add another layer of drywall. There are now 2 layers, and you are getting 26 dB. So you double again: add another two layers (total of four) now you get 32 dB. Now you double again: four more layers (total of 8 ) and you get 38 dB: Now you double again (8 more layers, total of 16), and you get another 6 dB, for 44 dB total. That's one hell of a wall you have there now! You had to multiply the mass by sixteen to get an increase of just 24 dB! Clearly, this "mass law" thing is not as much a friend as you thought it was.
That's where the two-leaf wall comes in: It is not restricted to mass law. A 2-leaf wall is a tuned system, that works on a different principle of physics: that principle is called "Mass-Spring-Mass" or MSM. It means that you have one chunk of mass attached to a spring that is attached to another chunk of mass. This is a whole different ball game, that gets a bit more complicated to explain, but it beats simple mass law, hands down. However, it still needs mass in order to work! It just multiplies the effect of the mass...
1 more question. I assume you fill those 2 stud walls with some sort of rock wool or insulation?
Exactly. Insulation is part of the MSM system: it acts as a damper on the resonance, which is a good thing!
- Stuart -