Part of the difficulty in damping sound is that it moves in two ways. Both high- and low-pitched noises can be airborne, like a child’s incessant piano practice that comes through a wall. Low-pitched noise, like the grating sound of a chair scraping the floor above, tends to move as vibration through a structure’s framing. Sometimes it’s a combination of the two, like from a TV mounted on a common wall.
A compounding issue is that it takes only a very small gap to let in a lot of sound.
“If you have a weakness in a wall that is only 1 percent of the total area, the sound transmitted through could double,”
Soundproofing 101 provides some good basic explanations of the issues involved in soundproofing solutions.
Casual noise can be reduced to a very tolerable level by simply “beefing up” existing walls, floors and ceilings. However, if you want to achieve significant soundproofing, then a dedicated construction plan is in order. The room within a room is the most sound isolated system you can build.
It does sound extreme but I have considered this for a bedroom. Or even scaling it down into a enclosed sleep chamber, just to let me have a quite space to sleep.