Sound proofing usually refers to what you do to a room to keep the sound inside the room. If you don’t want to hear what is going on inside the room in the rest of the house, that would be sound proofing. Carpet will help a little bit with that but to do it the right way you need to build a sturdier wall. Thick, massive walls are best for sound proofing.

If you are trying to eliminate echos inside the studio, that is different than sound proofing. Acoustic foam on the wall is designed for that purpose but it does little to prevent sound from going through the walls. Carpet on the walls will help with echos somewhat. Anything to cut down on hard surfaces inside the studio will help.

There is some good stuff on studio acoustics here:

http://www.acoustics101.com/basics.asp
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