Verified answer

Acoustic foam will help reduce the higher frequency sound like voices but it won't do much of anything for the lower stuff. Lower frequency sound can only be stopped by adding something heavy to the wall or framing the wall specifically to break the continuous path of drywall-stud-dryall.

walls specifically made for sound insulation have two sets of studs, one that hangs one side of the drywall and one that hangs the other. Dense fiberglass bat insulation can be added between the studs for higher frequency noise reduction. The sole and top plates are typically 2x6 lumber and then 2x4 studs are framed in a zigzag footprint so the first stud is on one side, the next is on the other and so on.

You can renovate a wall to the same effect. Just pull the drywall off one side, then add a 2x2 to the bottom and top. Frame in new studs on that side of the wall in between the studs that are already there and add insulation. If you don't want to open up the wall then your best bet is to add 1x2 strips to the outside of the drywall between the current studs and then install a new layer of drywall onto those strips. Use strong anchors to attach the strips. The butterfly type that pushes through a small hole in the drywall then opens up would be best.

if you'd like to reduce sound without adding drywall, consider hanging panels wrapped in fabric. One of the most popular products for blocking sound in apartments is called Homasote. It's a lightweight composite product made of recycled newspapers and cellulose fibers. By wrapping Homasote panels in a nice fabric, you can reduce the noise coming through your walls by about 20 percent, while adding to your home's décor

I have seen garages with egg cartons glued to the walls!