It's very difficult to soundproof a wall. The best sound barrier is a high dense material, like concrete, or multiple layers of drywall. Fiberglass insulation wlll do very little to reduce sound transmission. If you have the typical wood stud construction, the sound will transmit directly through the wood. That is why they recommend staggering the studs, so that there is no continuous wood material through the wall from one side to the other. I think the best thing you can do is to stagger the studs and add a few addtional layers of drywall.
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