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.

 

[PJC01]

I can say that yes, it is theoretically possible to use Fourier expansions to create customized noise patterns in a room. This is because sound waves can be broken down into their component frequencies, and by manipulating the amplitudes and phases of these frequencies, we can create different patterns of sound and silence.

In your example, it is possible to create a distribution of noise and silence in a room by strategically placing speakers and playing the appropriate frequencies based on the Fourier expansion. However, in practice, there may be some limitations to achieving this perfectly. Factors such as the room's size, shape, and materials can affect how sound waves travel and interact, potentially causing diffusions that could disrupt the desired noise pattern.

Additionally, the human ear is not equally sensitive to all frequencies, so achieving a perfectly balanced distribution of sound and silence may be challenging. However, with advanced technology and careful calibration, it is possible to create a close approximation of the desired noise pattern in a room.

Overall, while it is theoretically possible to use sound waves and Fourier expansions to create customized noise patterns in a room, achieving it in practice may require careful consideration and fine-tuning. Further research and experimentation in this area could lead to advancements in sound engineering and acoustic design.