I've been researching the same thing for my shop. Some things I've learned are that you need good insulation and a dense barrier like drywall, especially drywall mounted on resillant channels. Another post recently suggested backerboard like that used under tile flooring.
I hear that the most effective barrier has the highest density. Lead is used in sound studios. For residential and light commercial I believe 2 or even 3 layers of 5/8 drywall over a framed wall would be a fairly cost effective solution. A poured masonry wall or solid grouted block wall would probably work also. There is a vinyl sheeting barrier with an STC (sound transmission coefficient) of 26 and a thickness of .10". Lead has an STC of 21. It's almost $7.00/sq. ft!
I'm soundproofing my two-car garage workshop right now. There are three things you need to do to make a room soundproof. First make the room air tight. That will stop sound leaks. Second, put mass on the walls. I'm putting two layers of sheetrock up. Third, break the path of sound transmission (vibration). I'm lining the stud faces with Armaflex. Armaflex is a pipe insulation with sound deadening properties. It's a rubbery substance. You can spend a lot of money trying to soundproof a room. There are many methods. All of the best methods require you build a room within a room.
We built 3/4 plywood walls around both our DC units and stapled used 5/8" thick foam carpet pad to the inside. If you have to use new pad, it is not expensive. You have to allow the units to exhaust the incoming air and the box should allow easy access to change bags.
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