Staggered/double studs plus 2 layers of super-dense drywall (Firewall) both sides as well as fibreglas internal insulation will give the best sound-insulation for the adjoining room. This sound-insulation is called STC (Sound transmission Class) Rating. Compared to a normal drywall with say 37 STC rating, the described wall can double the sound-proofing capabilities up to 60 STC.
STC Ratings
Study Diagrams
STC Ratings
Study Diagrams