At high and medium frequencies, sound is like water. That means that a small gap can spoil the insulation. That's why recording studios are built as ‘boxes with

At high and medium frequencies, sound is like water. That means that a small gap can spoil the insulation. That's why recording studios are built as ‘boxes within boxes’. Low frequencies require mass-spring systems in which the walls are decoupled. Sound absorption panels don't do anything about insulation. They just condition the sound inside the room or make it less "echoy". DIY Sound isolation is very, very difficult. If you want to do it, call an acoustic company that knows what they are doing. Not a generic construction company.