Soundproofing the basement stairs soundproofing basement stairs.
Insulating floor joists in basement for sound.
Next you might want to consider using a soundproofing drywall such as quietrock for the ceiling.
Once the ceiling is buttoned up insulate the rim joist the floor framing around the perimeter of the house directly above the foundation wall.
Part of the problem with adding insulation for floor joists is securing such insulation between joists underneath the floor.
One thing a lot of people fail to do is to soundproof the basement stairs.
When the basement or crawl space has vents installed insulating joist bays.
Joist bays the open spaces between floor joists are prime hosts for insulation under specific circumstances.
Start by insulating the space between the basement ceiling joists with a sound dampening insulation like owens corning quietzone fiberglass insulation.
Hold the batts in place by stapling their paper faced vapor retarders to the lower edges of the joists.
The added layer of drywall plus the noise proofing sealant will improve the stc rating to between 41 and 45 depending on the flooring used on the above floor.
Make sure to use soundproof cocking to fill any holes or cracks.