Can Sound Waves Create Customized Noise Patterns in a Room?

[edenstar]

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!

 

[CWatters]

It's possible to cancel out sound or noise in small areas (google noise cancelling headphones) but it's very hard to do the same over large areas. I suppose under certain controlled conditions it might be possible to track a persons movements around a room and make it appear less noisy where ever the person happens to be - so to him it might appear as if one half of the room is quieter than the other. But for anyone else in the room the so called quiet area might even sound louder.

 

[Andy Resnick]

<snip>, 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.<snip>

This type of problem is called an 'inverse problem': you have the far-field distribution and want to back-calculate the source properties. Short answer- within reason you can do this, but it may require a *large* number of independently controlled speakers. Inverse problems are usually ill-conditioned.

 

[phinds]

Keep in mind the conditions which you stated, including "an infinite sum of sine and cosine waves" (and by the way, cosine waves are not necessary ... sine waves will do it). Do you think with real equipment you can create an infinite number of waves?

The fact that you cannot is, for example, the reason why "square waves" are never actually square. You can make them better and better approximations the better your equipment is but there isn't any equipment good enough to make waves that are literally square with mathematically sharp transitions.