Step 2Soundproofing theory
One way to understand soundproofing is to differentiate between two types of sound: impact and airborne. To cut the transmission of airborne sound you need mass. To reduce impact sound (as in footsteps, hammering, etc) you need air, i.e. isolation. So the ideal solution is a room within a room: floating floors, walls and ceilings decoupled from the building's structure and from each other. You want small 1/4 inch gaps everywhere so sound vibrations cannot transmit from walls, to floor, to ceiling below, then you need to fill those gaps with something which will seal them completely and stay elastic, such as acoustic caulk. You want your walls, floors and ceiling to be heavy. You can either use multiple layers of sheetrock or even MDF and slather a damping glue between them such as Greenglue or buy ready-made solutions such as Quietrock.
Of course, this being sound, it gets more complicated than that. Other factors need to be considered, the most counter intuitive one being the notion of the triple leaf effect. This article explains it beautifully, but it boils down to a simple fact: a wall with two (or more) cavities will perform a lot worse than a wall with one. Most walls in apartments or homes have one cavity, so if you attach a resilient channel to an existing wall and add a layer of sheetrock you might actually be LOWERING your STC rating (of course this is simplifying things again: you might be blocking more high frequencies but the low frequencies, the ones you really want to stop, will go through more easily). Either you need to tear down one side of the wall to attach your resilient channel to the studs, or you must add layers to the existing wall without leaving any air space in between. Also, don't forget your floor and ceiling: these should be treated like walls, both for sound proofing and sound treatment. You can't just soundproof one part of your room: because of sound conduction, building a single, beautiful soundproof wall just won't work.
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