As far as I know, that will do NOTHING for sound "proofing". Soundproofing is near impossible. Sound insolation is what you are looking for, and there is no "cheap" way about it. What you need is a mass-air-mass type stricuture, and air-tight seals. The main way is to build a room inside a room. What that stuff deals with is room acoustics which a totally different thing from insolation. It makes the room sound better, but that only absorbs mid/high frequencies, so the room will be dead boomy/bassy. To stop the boominess you will need to build a basstrap, which you will find if you do a quick search. My suggestion is, if all you want is insolation, don't get this stuff. Buy air-tight door seals, something like
these for the door(s), and check to see if that's enough. If not you could try buying/building a new heavier, solid, door(with MDF, or something similar), with seals. If that isn't enough then you are going to need to either build a room inside a room, or a second wall where the adjoining wall of the to rooms is, that doesn't touch the existing wall and is sealed with caulk(if the sound comes throught the walls), or making a double door, ie. building a walkway into one of the rooms about a metre and installing a seconds door, all sealed, if it's just coming through the door(s)
