I would like to soundproof the wall between a master bathroom and hallway bathroom. Basically my bathroom and my kids bathroom. The existing 2x4 wall is not insulated. Do you think if I filled in the cavities of the wall with blown in insulation this would help? My thought was to access the top of the wall plate from the attic and cut a 2" diameter hole in the top plate of each cavity and stuff loose insulation into each cavity. I'm just afraid when all is said and done it won't work..