Sound proofing is achieved by blocking or detaching sound carrying materials. A “sound proof” frame wall can use the offset framing method.
Use a 2×6 top & bottom wall plate and then use 2×4 wall studs vertically, 16″ on-center or 16″ apart. They will not extend to the other edge or side of the wall plates. Then frame the other side with 2×4 wall studs, 16″ on-center and stagger the spacing so that no wall studs touch the others. It is like building two separate 2×4 walls on each edge of the 2×6 plate.Very little sound transmission occurs between these off-set wall studs.
Then fill the wall cavity with acoustical sound batt “insulation” which is a rock wool like insulation batt that is typically sold at drywall supply wholesalers. The off-set studs do no touch so the sound from one wall surface is not transmitted through the studs to the other drywall surface because they don’t touch.
Next I suggest using an acoustical suspended ceiling system and add the sound batt above the ceiling tiles to muffle or attenuate the noise. Any doors or windows tend to be the weakest link and allow sound transmission through these openings. The wall and ceiling is easier to control, doors and windows tend to behave as holes in the wall.