Hey Skye, congratulations on that "baby in your life "!!!! Yup, they certainly do seem to have an effect on your plans... not to mention your sleeping schedule...
Anyway I had a meeting with a draftsman recently who gave me a rough estimate more than my original budget, but less than your spend, and definitely doable.
Excellent! A realistic budget is a key part of building a studio. and the general rule here is to take your original budget, add yesterday's date, multiply by a random number between 2 and 50, divide by a small fraction, then add a zero on the end, just in case. That normally gets you close....
More seriously, I'm sure your draftsman has a better grasp of costs than most people, but if he hasn't done a studio before then he's probably still underestimating a bit. There are "things" and "techniques" in studio design that aren't done the same way as for a typical house, office, shop or school. So I would add about 10% to 20% on top of what he suggested, and you'll probably be in the ball park. Not trying to scare you! Just being realistic.
I am a little concerned about freezing to death - as my fellow Central Highlander will attest, it's been a frosty winter in these parts, and the idea of sitting on a refrigerated block for 12 hrs a day is less than appealing. My budget definitely won't stretch to in-floor heating, the family home gets preference over that!
Then I would suggest a suitable laminate wood flooring on top of the concrete, fairly thick, with a good thermal underlay, also fairly thick. The underlay will probably be something like 5mm, and the laminate flooring about 10 mm or so. That doesn't sound like much, but unless you live at the south pole, it should be more than enough. The HVAC system will take care of keeping the room air at the right temperature and humidity, so the room will feel just fine and comfortable.
Just how many layers would you have to glue to get something that won't rattle and ping like a drum?
Math time! The density of concrete is about 2200 kg/m3, so a 15 cm (6") slab will weigh about 330 kg/m2 (68 PSF). The density of marine grade plywood is about 500 kg/m3, so in order to get the same surface mass as for a concrete slab (330 kg/m2), you would need to make it about 66 cm (26") thick, which works out to about 34 layers of 19mm (3/4") plywood....
The numbers don't lie....
It's not about "rattling and pinging", but rather about the resonance of a lightweight floor suspended over a cavity. ALL materials have a natural resonant frequency, which depends on several things but is mostly related to the mass (surface density, linear density, etc.). If you hang a mass on a spring, then you create a second resonant system the resonates at a frequency defined almost entirely by the mass and the "resilience" of the spring. A floor suspended over a cavity is exactly that: The floor itself is the mass, and the air in the cavity is the "spring" (we don't usually think about air as being "springy" from our point of view as humans, but for sound waves it sure is!). So you have two resonances going on there: that of the floor material itself, and the much greater resonance of the tuned "mass-spring" system. The "tuning" is set by two things only: the surface density of the floor (kg/m2) and the depth of the air cavity. Increase either of those, and the resonant frequency goes down. Resonant theory says that in order for that to not be a problem in your studio, you need to get the resonant frequency down below 1.414 times the lowest frequency of interest. In reality, that's not good enough, and you have to get it down to no more than half the lowest frequency. So if you want to isolate the entire audible spectrum (20 Hz to 20 kHz), then you need to get a resonant frequency of under 10 Hz. That's pretty hard to do, unless you use very massive materials, or very large air gaps. If you are interested, the equation for calculating the fundamental resonant frequency of a panel by itself is:
Fr = 0.45 * vL * b[(1/l)^2 + (1/h)^2]
where b is the panel thickness (meters), l and h it's length and height (meters) and vL is the longitudinal velocity of sound in the partition (m/s) given by vL = [E / (p * (1 - s^2))]^1/2 [where E is Young's modulus of elasticity, s is it's Poisson ratio and p it's density].
(It gets a bit complex...)
Fortunately, the equation for calculating the fundamental resonant frequency of such a floor is very simple: F = 60 / SQRT (M * D) Where M is the surface density (kg/m2) of the floor materials, and D is the depth of the air cavity in meters. (The number 62 is a constant that encompasses things like air density, air temperature, the speed of sound in air, those other weird terms above, and a few other things that don't change much.) So for a single sheet of 19mm plywood over a 10 cm cavity (depth of a 2x4), the frequency would be about 67 Hz. Add another layer and it goes down to about 46 Hz. Add two more layers (total 4 layers) and it goes down to 32 (can you say "bass guitar"). Add ANOTHER 4 layers (total of 8!) and it is down to 21 Hz. Add another 8 layers, (total 16!!!), and you get down to 15 Hz. Finally double that lot (32 layers now....) and you get down to 10 Hz. Bingo! But watch that step at a the edge, as you walk out the door!
OK, so you could use a deeper cavity and less mass, but it's still not much fun: for a 20cm cavity (2x8 joists) you could get by with just 19 layers of plywood on your floor, and for 30 cm depth (2x12 joists), you'd need a paltry 13 layers. Bigger joists? Sure. Let's try massive 20" joists (50 cm). Much better! You only need 8 layers now!!!
That's why I just have to giggle a bit when I see those knuckleheads over on YouTube frantically "floating" their floors on 2x4 studs with a couple of layers of thin plywood on top, and swearing that they are doing Something Incredibly Useful for their room.... If only they would do the math.... sigh!
On the other hand, a concrete "slab on grade" (poured directly on top of Mother Earth, with a waterproof membrane, of course, and probably sand/gravel too) is the best darned floor you can get for a studio. Best in terms of isolation, and also for actual room acoustics. You have the mass of the concrete, no air gap at all, and the entire planet acting as damping! It's hard to improve on that!!!!
- Stuart -