shitty situation man...
the biggest mistake I have seen people make when treating spaces themselves is not having a good plan going into it. they end up spending a lot of money and never really addressing the real problems (i once saw a guy auralex the extruding edges of a soffit because he had read that corners are "really bad for sound"
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while there is some valuable information in the posts above, I don't believe that you "have" to do any one thing to acquire a desired result, and don't believe one should dive right into nesting rooms and tearing down existing structures right off the bat. chances are those materials, which cost money, are the same materials that you'll end up buying, costing money again. Also, these techniques will end up being very costly and not get to the heart of the problem.
so first things is first; identify your issues and what is causing them. For example, you wanna play loud guitar whenever you feel like it because its your damn house. Your neighbor is preventing this because he finds the sound levels in his house objectionable. Probably because he's a dick, but thats a problem I dont think we'll be able to solve.
so what is allowing the transmission from point A to point B?
ASS RIPPING GUITAR!!!! because its being fed through and amplifier so that it can be heard at a reasonable level by other musicians, who are also playing amplified music, in a room that can also be considered an amplifier which is on a loft over a garage which is ANOTHER amplifier. OH YEA and there's also a dude in that room hitting these weird round things that amplify the collision of his stick and a piece of stretched plastic, which is ALSO being amplified by that room, the garage beneath it, and ultimately in the combination of all of it, the entire structure of your house. which then oscillates the air around your house with enough energy to be intrusive to your neighbor.
as with a lot of problems, you need to look at it simultaneously from the inside/out and the outside/in, its the only way IMO to keep costs down.
so start at the top. are playing volumes louder than they need to be because no one can hear each other? in that case you're looking at it outside/in, how is what is happening outside effecting inside. you would solve this with acoustic control to provide more coherent solid reproduction, and/or using wedges for personal monitoring. or are you like me and love to open up your amps and have a drummer that plays like he means it, and that's just how loud it needs to be? then you're looking at it inside/out. more than likely its a combination of both, which is why you need to see both perspectives.
room acoustics are very simple compared to real vibration control implementation such as highway noise, industrial generators and power plants, so i'm sure as a community we can help you solve your problem.
i tend to refer to rooms as amplifiers, because most of what we hear is not the sound source, but their reflections around the room and back to your ear. there's a reason when you go to old train stations foot steps are so loud, its additional acoustic energy supporting the initial wave and in terms of contemporary rooms, the wave folding back on itself from each reflection. Depending on the dimensions, lower frequency longer wave length, rooms will support some wavelength in its reflections (modes) and defeat others (nodes). In a case such as yours where you have two out of three axial modes at the same wavelength, your box is going to resonate. this is why you see a lot of subwoofer boxes as cubes, all three axial modes support a single resonance, which keeps a simple low frequency driver "boomier" than it would be otherwise. notice, however that no cabinets made for a wider frequency range are EVER made as a cube, they sound awful, most of your sound is comb filtered and its terrible. Also why you never see a professional sound room as a square, much less a cube.
at 20x20 you're really heavily supporting around 28-30Hz, and all of its upward harmonics. that poses a huge problem both outside/in and inside/out.
since there's no way you're going to be to stop a 28 cycle resonance outright, you'll need to implement trapping. I suggest researching sympathetic traps and helmholtz resonators, don't buy into these foam "traps" they're not traps they are absorption and won't do anything for you on the large scale or under 200 cycles. sympathetic traps resonant at a designed frequency, which you then dampen, they give the low end a playground to escape to until it tires itself out, very effective. there are many different kinds so if you have any questions feel free to ask.
also check simple things like that windows seal well, that there is actually insulation in the ceiling and not just a vapor barrier, absorptive hatches can be made inexpensively to seal over windows and vents when you play, and you can reenforce doorways in the same manner.
two pieces of the same type of gypsum coupled directly to one another does hardly more than one by itself. the basic concept behind sound control is impeding the propagation of the wave. a structure, such as a sheet rocked wall, insulation or a person standing in the way, dampens the wave as it oscillates three dimensionally (at minimum), so that with each cycle of vibration the wave looses energy to vibrate the next particle, and so on. the simplest dampener is a mass on the end of a spring which is in a fluid (air is a fluid), the drag ("friction") from the mass requires more energy from the spring to restore its starting position, and with no external force being reapplied, the spring stops moving. the two coupled pieces of same density material offers the same dampening as one the thickness has little meaning, what needs to be achieved is CHANGES in density. This is one of the many reasons air space tends to help, but when you need a room to be really solid and you cant take up the kind of footprint staggered studs require, a great solution is a layer of 5/8" fire check, layer of green glue (they sell it in buckets now its way more affordable), and a layer of 5/8" water check. two different gypsum densities with green glue converting vibration to heat. solid. resilient channels are also nice because it turns your entire structure into an independent dampener. i have had success using them and other similar "iso-track" systems, but they can increase the cost of a project (but they can also decrease it if you know how to do it).
if you were to build any additional walls you would need to dampen (insulate) the reflective side of the existing wall and you would then want to use double rock or iso-track, you COULD do both, but its overkill and ive never tried to hang anything heavier than homosote, quietrock or single 3/4" gypsum on the tracks. any volume of air needs to be treated the same way as any room or cabinet, modes and node will exist in each and every volume. this actually brings me back to another good point someone made about decoupling (floating) the floors. especially since you are on an elevated floor, i would highly suggest looking into this, even if its something as simple as neoprene, something to keep the waves oscillating the air instead of putting their energy into the framing of your house. when you do this, you'll notice that all your stuff doesn't sound as "full", but its just relative to how boomy it was before, and when interior acoustics are applied you wont wanna hear your rig directly on the floor ever again. there's a lot of squabble about floated floors, its mostly arguing semantics. TECHNICALLY a floor can only be floated concrete to concrete with a very elaborate series of decoupling springs in between, this is technically true because only then is your room REALLY decoupled. In my opinion, every little bit counts, and experience has shown startling improvement to some structures, enough to where i always do it. Oh yea, and if you build second walls, put them on the decoupled floor, this also gives you the opportunity to change your axial mode dimensions.
so after all that rambling I hope there's at least a few new things to think about, and I do hope that you send over more information about your space, maybe some pictures, spl measurements, proximity to neighbors, ceiling height, existing construction materials et al, so we can help you through this.
okay i think im done talking for now...
-Jesse Baccus, theaudioengine
