You could use spray foam and trim it so it is flush.
I would also look at putting something between the studs and drywall to prevent sound from being from the Sheetrock to the studs and resonate on the other side of the wall. A bead of silicone caulk or rubber elastomer.
Samanthas-Dad t1_j9dqhpz wrote
Reply to Insulation alternatives? (For soundproofing purposes) by infinitycurvature
You could use spray foam and trim it so it is flush.
I would also look at putting something between the studs and drywall to prevent sound from being from the Sheetrock to the studs and resonate on the other side of the wall. A bead of silicone caulk or rubber elastomer.