One of the Business cars on a Frecciarossa train has a designated area in which no external sounds are permitted. That means mobile phones, talking, music, etc. It's typically called "Business Area Silenzio" in Italian, but might also be called a "Silence Area" or "Business Quiet."
Note that while the level of quiet might make for ideal sleeping conditions, that's not the primary intention of the Silenzio section - the seats don't recline any more than they do in the other Business sections of the train.