With traditional noise cancellation, the noise you are cancelling has to come from one direction while your "quiet zone" is in a the opposite direction. It is all about racing electrons against air particles. The type of cancellation that you want to do could only be possible to the extent that the noise consists of tones which last long enough for your waveform to be generated and sent back (music, for instance). Even then, the cancellation would only happen in a limited space where your waveform is out of phase with the incoming waveform. In other areas, your waveform may even increase the volume. Try wiring one speaker on a stereo with reverse polarity and see how much that reduces the volume in the room. That's the level of noise cancellation that you are talking about.