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Put your hand on a speaker for an example of solid-matter sound transfer. Lift it off to create dead air space, and you lose that transfer. Put a piece of fiberglass insulation on the speaker and lightly touch it. Little to no sound. Then squish it down. It will transfer vibration when squished, but not when fluffed.
In common carpentry practice, a "sound wall" that ideally insulates neighboring rooms from each other's sound has TWO seperate stud runs, seperated by an inch of dead air so that there are no solid-matter connections between the two rooms. The studs on one wall can shake from the bass in that room while leaving the studs of the neighboring room undisturbed.
Foam and fiberglass have the best sound insulation properties because they have greater surface area to catch frequencies on the surface, an irregular structure inside so as to catch sound waves inside their structure that get through the initial surface, and lots of dead air space inside them to minimize solid-matter transfer of sound. The solid portions are also flimsy enough to absorb the vibration, not transfer it through the substance.
The next thing to consider is installing a substance with a different density than the other materials in the wall so as to achieve a qualitative decease in sound insulation, not just a quantitative decrease. (If wood traps the frequencies in range "Y" but allows range "X" frequencies to penetrate, then you want a material that catches the "X" frequencies.) Fiberglass or other common insulation serves that purpose: additional wood or drywall will not.
Homosote (a lightweight, wooden pressboard) also serves that purpose well. You install it underneath the drywall in panels so as to double the thickness of your walls, but triple (or more) the sound insulation. It catches different frequencies and more sound waves than drywall due to the irregular and lighter inner structure.
[This message has been edited by Lawrence (edited April 12, 2003).]