Sound proofing and treating room acoustics are two separate issues. I commonly get asked about how to stop a drummer or band from annoying the neighbours and asked will acoustic foam reduce noise. The simple answer is, no. Some of this confusion is propagated by various retailers misleadingly selling acoustic foam for the purpose of reducing sound escaping from a room. Acoustic foam panels and bass traps are designed to reduce acoustic reflections (reverberation) within the room. For example, reducing the harsh sound of a drum kit or improving the accuracy of an audiophile listening room. That is, improving the listening experience. Acoustic panels will reduce the overall sound levels within the room, but will have a negligible effect on high volume noise escaping from the room.
Most commonly, neighbours are annoyed by low frequencies from an audio system or a band rehearsing. Low frequencies essentially travel through any coupled structure, that is, through walls. The low frequencies don’t need to be very loud to be annoying, and they can penetrate throughout the structure of neighbouring houses. The best way to stop low frequencies from escaping is to build a ‘decoupled structure’ within an existing room which is well constructed and sealed. The inner room can be an insulated stud wall structure sitting on rubber blocks, ideally on a concrete slab.