Insulation in the cavity does several things at once.
- It damps resonance of the cavity itself, specifically standing waves. Standing waves can rob you of a considerable amount of isolation.
- It damps the resonance of the MSM system itself: Without that damping, you lose considerable isolation.
(Simple demonstration of the effect of damping on resonance: find a nice floor tom, and hit it hard with a heavy drumstick. Now fill the interior with pillows / blankets / parkas / etc. Hit it just as hard with the same stick. Notice the difference! First hit = "BOOOOOOOooooommm": Second hit= "thuk").
- It lowers the frequency at which resonance occurs. This is probably the largest and most advantageous effect. The higher the resonant frequency is, the worse the isolation is. You can see this effect in your own calculations, where you show F0=155 Hz for the wall without insulation, and 111Hz for the wall with insulation. There's something wrong with your math, though, as those frequencies are way too high or solid brick walls. About ten times too high.
- It reduces the level of sound passing through the wall directly.
- It changes the properties of the air in the cavity, from adiabatic to isothermal. This refers to the way heat is dissipated by the contents of the cavity. Isothermal is a much more efficient mechanism for heat transfer.
- As a result of this change to isothermal, the apparent "stiffness" of the cavity changes. The cavity appears to be about 0.7 times less stiff, with insulation. In other words, the "spring" in the MSM equation appears to be "softer" or "springier" if you prefer, with insulation than it is with just air.
- It lowers the speed of sound inside the cavity, which in itself has several beneficial effects, but mostly increased apparent depth. An easy way of thinking of this is that the cavity "appears" deeper to the sound waves passing through it: they take longer than they would have to cross the gap (because they are going slower than they would through empty air), thus the gap appears larger from their point of view.
Overall, without insulation you could be losing as much as 20 dB of isolation, and at least 6 dB. (Some studies show a max loss of 16 dB, others suggest higher. 20 dB is a reasonable estimate).
Here's a graph that shows the difference in isolation for a wall similar to what you are proposing, with and without cavity insulation:
The curve marked "E" is for the wall with an empty cavity, as you are proposing. Rating is STC44. The curve marked "D" is for the same wall where the cavity is completely filled with fiberglass insulation. Rating is STC52. That's an 8 point improvement in isolation, and that's using the STC rating system, which doesn't even consider low frequencies, and isn't a useful indicator of studio isolation anyway, but even so shows a large improvement.
Here's another graph for a different type of wall, showing various degrees of cavity fill and the isolation the achieve, all other factors being equal.
In this case, Rw isolation increases from 45 dB with no insulation in the cavity, to 62 dB with the cavity filled with fiberglass insulation. That's a difference of 17 dB, with the only change to the wall being filled with insulation, or being empty.
the m1 & m2, mass of each leaf indicates kg/m^2. Isn't it a density unit instead of mass?
Surface density, yes. That's correct. Surface density is what you need for calculating the resonant frequency. Surface density is the amount of mass in one square unit of your wall. In other words, it takes into account the thickness of your specific wall, not just the cubic density of the material. So if you were to take an angle grinder and cut out a section of your wall measuring 1m by 1m, "surface density" is how much that section would weigh. Sometimes also called "surface mass".
Density for brick is around 2100 kg/m2 (rule of thumb: different bricks could be a bit higher or lower. Clay brick is probably a bit lower, maybe 1800 or so, but I don't have the exact figure on hand). Thus, your surface density (assuming your bricks are laid running-bond, one layer thick), where you said your two types of bricks are 0.146 and 0.220 m thick, would be 2100 x 0.146 = 307 kg/m2, and 2100 * 0.22 = 462 kg/m2, respectively, for normal brick. Or assuming a figure of 1850 for your clay bricks: 1850 x 0.146 = 270 kg/m2, and 1850 * 0.22 = 407 kg/m2,
Not sure why you are using 94.5 in your calculations. I don't see where that came from.
I didn't go through all your math, but something seems to be off somewhere. According to my MSM calculator, the resonant frequency without insulation would be around 11 Hz, and with insulation it would be around 8 Hz. Total isolation (with insulation) should be about 62 dB. (theoretically)
- Stuart -
Translate This Page
(And cool in summer).