In general you want to block air exchange. Air caries sound very well.
(Try opening your car's window as a train is going by.)
Next you want weight. Heavy things (drywall lead sheets etc.) block
You also want to prevent any direct solid connections. Stagger wall
studs or use special isolation devices to keep the sound from traveling
through the wall (remember the two cans on a string (well wire actuarially
worked) you want to break the wire).
Filling in wall cavities with sound absorbing materials (accustical
fiberglass bats) will do a little.
Point source control (special absorption material) at the source of the
sound will also help.
Foam transmits certain lower frequency sounds very well, actually
accentuating them. I put 2" foam sheet on my exterior, now I can hear
the neighbors kids running upstairs ,[ at first I thought it was an
animal in the house] houses are separated by 8 ft.
It depends on what frequency you are trying to stop, lower
frequencies need more mass as sound waves get longer the lower sound
goes. That is why you hear the bass, long waves need mass to be
absorbed. It realy depends on the sound-source to be blocked
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