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It’s been a while since I took acoustics, but the rule of thumb is something like every time you double mass, you reduce sound transmission by half. Cheapest way to do that is to double up the drywall on one half of the wall. Doubling on both sides sees diminishing returns, and isn’t worth it.
Craftsmanship is important, cracks bleed sound. This comes into play at drywall joints and on the baseboard and at the ceiling. You can buy expandable foam at Home Depot to fill these joints.
Filling the wall with pink insulation helps, too, if you’re building it from scratch. Air is the best insulator (assuming it is contained), that’s what the foam is doing (air bubbles contained in the goo).
PS – In theory, Jim, the other Jim is correct. That’s how to think about it. Throwing random foam up on the walls is pointless. It needs to be thought of as sealing every surface thoroughly.
Bass (long wave sound) is the hardest to isolate (Kevin V’s point), at that point your talking about building an acoustically isolated floor to keep it out of the structure…