Mineral wools are used as a form of insulation in many homes. While some batting, such as fiberglass rolls, can offer minimal protection against fire, there are other materials that work better. Rock wools or slag wools, for example, provide both thermal and acoustical insulation, and can be installed in both walls and ceilings. They're naturally non-combustible and are necessary additions in many building codes.
Panels excel at providing both noise protection. Typically fire panels are made from dense cement fibers that resist both heat and moisture. The density also helps protect against sound, but other panels -- made of more porous materials -- are specifically designed to absorb and deaden sound. Fire panels are necessary components of walls beneath stoves and fireplaces, while the sound panels make good additions for study rooms and dens that you might want to keep especially quiet.
Because caulks are used to seal gaps and cracks, they'll help protect against noise pollution -- more than many people realize -- but they're not designed specifically for soundproofing. However, a variety of sealants known as fire caulks are designed for fire insulation. These caulks (often colored red to denote their use) are made for sealing chimneys, fireplaces and furnace components where heat may be an issue.
Cement and concrete floors offer excellent protection against fire. This is the primary reason mortar foundations are required below fireplaces and fireplace surrounds. However, concrete offers only minimal protection against noise. A floor layer such as cork can absorb noise and deaden sounds much more easily, and works well for indoor soundproofing projects.