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This is much more expensive, but significantly lowers the number of steps needed to sound-proof a room. You install like normal, and it is specially made to absorb sounds and frequencies. Dry blown insulation requires that you attach a netting to the exposed wall, which catches the cellulose and holds it on the wall. It takes a bit more time, but it is doable by yourself without expensive equipment. All you need is a standard hopper. . Purchase it in bulk, then cut it to fit each panel of the wall. Slide it in place and attach to the back of the wall according to the manufacturing instructions. This is much harder to work with, and get right, but it can be cheaper and makes much less of a mess. To use it:  Wear a respirator at all times. Seal any electrical boxes with soundproof caulk.  Cut your insulation (R-11 fiberglass works well) with a utility knife. Screw backing boards, like 1/2 plywood, to the edges of the wall to provide a base for drywall nails. Attach the resilient channels, long metal bars, horizontally across the wall. Instead of installing the first sheet like normal then proofing and installing the second, simply apply the glue straight to the first sheet. Work in a zig-zag pattern, covering the whole sheet and then install it like normal. Afterward, continue on with the noise-proof caulking. Basically, sound is transmitted through vibrations, so touching walls will vibrate each other more than walls that don't touch. Decoupling is when you separate the walls to prevent sound transmission. Keep in mind that resilient channels are prone to failure, and is not specified by the Steel Stud Manufacturers Association, so be careful. You could also:  Float the walls or floor Isolating studs with joist gasket tape. STC is used to tell you how good a material is at soundproofing. A higher STC means it will do much better at soundproofing. Aim for materials with an STC between 30-40.
Consider buying "quiet rock" instead of normal drywall. Try installing the simpler, easier "dry blown" cellulose. Fill the cavity between the studs with a fiberglass or mineral wool insulation instead of damp blown cellulose Apply a single layer of drywall with soundproofing compound. Isolate or float your drywall off of the studs by using resilient channel or sound isolation clips. Understand Sound Transmission Class (STC) ratings when choosing construction materials.