Had an old room at the building where I had my Screen Printing company. It was soundproofed by the folks that had the building before me. They operated a radio station there and that is where they did advertisements and stuff.
What they did was they had put up studs on the walls, filled the gaps between the studs with "egg carrier" foam. The foam can be bought from Dollar General and it is called a "Bed Mattress Top". Then there was 1/2 inch plywood walls connected to the studs. The walls had carpet tacked to the plywood.
We had a hell of a time tearing that stuff out.. is why I know what they did to it... But, you couldn't hear ANYTHING outside of that room.. not even the circular saws that were going to gut the room.