Insulation is not that good at stopping sound. You would be better off putting two layers of drywall on (plus the insulation). Double drywall on both sides is even better. We can make it even quieter but that would involve a more complex approach.
I actually have results of a very detailed study on what is best to help control sound. The study used scientific measurements and ratings for different materials used alone and in combination with different techniques.
Let me know, here, on in link in my sig, if you want the full blown conclusions.