How does soundproofing work in a studio?

Studio foam and fiberglass panels are meant to minimize the reflected sound in the room to improve the quality of the mix or performance. It is not designed to soundproof the room. The only way to truly soundproof a room is by using special building materials during construction, such as acoustic sheetrock, and isolating the vibration of the walls from external contact. Usually this involves creating a room within the room with an air barrier and isolating joist supports.