A low-cost and easy to manufacture static structure and method for soundproofing walls, floors, and/or ceilings of rooms in new and/or existing construction utilizes an asphalt based flexible membrane as one or more sound absorbing layers which may be applied to an existing wall panel or first applied to one or more unmounted wall panels to form a laminated structure which is then affixed to the walls, floor or ceiling to be soundproofed. The wall panel is preferably gypsum wallboard. Each sound absorbing layer, in addition to soundproofing, may also serve to prevent or at least reduce air or water infiltration to and from the room.