I learned that with fourier expansions any function can be approximated by an infinite sum of sine and cosine waves. Is it possible to use this fact to create an arbitrary distribution of sound and silence in a given room. Using a simple example, is it possible to make it so there is noise in one half of a room and silence in the other by placing speakers in the right location playing the right frequencies as prescribed by the correct fourier expansion. I am not only interested in whether this is theoretically possible but also whether this would be possible practically, or maybe the sound diffuses too much for this to work well. Thanks!