If you can, stagger the studs in the wall so a stud is only connected to one panel of sheet rock. Then fill the wall with fiberglass insulation, snaking the insulation between the adjoining studs. That keeps the wall from becoming a drum, and damps out higher frequencies. We did this when building the house and it's amazing how well it works. Of course, your room will be two inches smaller :-)
What's the best way to soundproof a room on budget
I'm starting to research ways to reduce sound transmission through a wall since I'll be moving in a few months and my new living space will share one wall with another family. What I am thinking is nailing cork board onto the wall and then covering the cork board with inexpensive foam pyramids. I think I could do thewholewall (8-9 feet high? 14 feet wide) for around $500-$600 dollars going this route. Any suggestions for whats worked for you?