The last I looked into it (years ago), sound dampening material was PRICEY. A contractor suggested insulation in the stud bays and two layers of drywall on each side.

Image: Akoustos AB Whereas a traditional drywall screw holds a panel of drywall snug against the wooden studs that make up the structure of a room, the Sound Screw features a flexible spring just ...

Use rugs to absorb sound waves and reduce bass travel through walls and floors. Place a subwoofer on a sound-isolating pad, raise it above the floor, and install bass traps to minimize noise.