Panels for use in building construction (partitions, walls, ceilings, floors or doors) which exhibit improved acoustical sound proofing in multiple specific frequency ranges comprise laminated structures having as an integral part thereof one or more layers of viscoelastic material of varied shear moduli which also function as a glue and energy dissipating layer; and, in some embodiments, one or more constraining layers, such as gypsum, cement, metal, cellulose, wood, or petroleum-based products such as plastic, vinyl, plastic or rubber. In one embodiment, standard wallboard, typically gypsum, comprises the external surfaces of the laminated structure.