The best sound insulation I have come across so far is the “Rockwool Acoustic insulation”.
Click on the image to be taken to ebay where it can be purchased.
Because of the relatively low cost I tend to install this type of insulation as standard between stud work throughout a property. Ill also always use it in between floor joists.
It really helps keep the noise level to a minimum. I have recently used it between a bedroom and bathroom stud wall, it was in an old 1890’s house and although plaster lathe walls the noise was really noticeable as we where
taking all the old plaster back to the stud work I installed this everywhere for the customer and feedback has been amazing.
So definitely invest in this when you next have the plasterboard off a stud wall.
It has a thermal resistance of 0.034 w/mk and it is classed as a non-combustible material.