To soundproof a door make it structurally strong enough to block noise by replacing it with a solid core door or by adding mass loaded vinyl soundproof blankets and panels to the existing door.
Soundproofing door panels.
Then seal the gaps with a door gasket door sweep or spray foam to prevent air leaks.
Use these panels to block sound leaking through any rectangular or squared opening.
Owens corning paintable white fabric square 48 in.
Sound absorbing acoustic insulation wall panels 2 pack model 02513 view the owens corning sound absorbing acoustic panels.
A lightweight sturdy and convenient acoustical sound dampening panel loaded with high density insulation enhanced with either 1lb or 2lb density mass loaded vinyl to reduce sound transmission.
For doors solid core is best check out this sweeten post to learn more and acoustic seals can be applied to the threshold and around the perimeter of the door to fill the gaps.
Owens corning paintable white fabric rectangle 24 in.
Excellent for windows doors and openings.