A room within a room (RWAR) is one method of isolating sound and preventing it from transmitting to the outside world where it may be undesirable.
Most sound transfer from a room to the outside occurs through mechanical means. The vibration passes directly through the brick, woodwork and other solid structural elements. When it meets with an element such as a wall, ceiling, floor or window, which acts as a sounding board, the vibration is amplified and heard in the second space. A mechanical transmission is much faster, more efficient and more readily amplified than an airborne transmission of the same initial strength.
The use of acoustic foam and other absorbent means is less effective against this transmitted vibration. The transmission can be stopped by breaking the connection between the room that contains the noise source and the outside world. This is called acoustic decoupling.