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The principles for soundproofing ceilings and floors from below can also be applied to walls. For example, you can fit hat channels directly to the surface of an existing wall. If losing a little space in the room is not a problem, build a completely new, independent wall in front of the existing structure. This is most easily done with a metal stud wall as it is quick and creates little mess. Build it 1 inch away from the original wall. You can then insert acoustic bat between the stud uprights to create a soundproof layer.
Make sure that the open side of the ground-level channel is facing upward. In the others it should face downward.
Adding to the mass of a stud wall will help it to absorb sound. Adding blanket insulation will also improve its thermal insulation.
When creating a metal stud wall, make sure that the acoustic bat is rigid enough to remain vertical between the metal studs.
Excerpted from Do It Yourself Home Improvement
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