# Noise cancelling speakers to cancel sound in the room [duplicate]

A thought of mine from class, where not everyone is the "silent kid" type. The teacher would very often need to shout to keep the class barely quiet enough for the students who actually are paying attention. This drives me insane, and I often wish there was a way I could silence the entire classroom.

My idea comes from a feature headphones have, noise cancelling. The way I understand it, a microphone takes in the ambient sound and creates a similar sound at a different phase such that the two sound waves cancel each other out inside the listener's ear. My question is: can I route that other wave back out through a speaker such that the entire class can't communicate the "usual" way? An old question suggests that such a device would break conservation of energy, but I could be understanding it incorrectly.

• Do you mean like using a single speaker in the classroom that cancels the noise of students talking but allows the teachers words to be heard? – JMac Jan 22 at 13:52
• Comment for any teachers out there: if you are often shouting then there's a good chance you are missing a better way to achieve your aims. I say this not out a wish to criticise but from a wish to encourage you to find out what those other ways are. – Andrew Steane Jan 22 at 14:25
• I think that answer that talks of conservation of energy is talking about electromagnetic waves. Sound wave energy ends up in molecular motion and heat anyway. – anna v Jan 22 at 14:41
• @JMac Doesn't matter if the teacher gets silenced as well, as the teacher can simply drown out the students when shouting at them fails. As for the setup, anything reasonable to have in a class works. – 404 Name Not Found Jan 22 at 15:18
• Well if having the teacher get control of this unruly class is out of the question just give the teacher a microphone and an amp. If that’s to loud for other classrooms connect the microphone to your noise canceling headset. – candied_orange Jan 22 at 21:07

Well, Active Noise Control has been around for quite some time and there's a lot of applications developed based on those principles.

Apparently you cannot effectively cancel out one source if the main source and the cancelling source do not coincide in space. This, of course, has practical limitations, but it also depends on the wavelengths of interest. When the wavelength is quite big, you can achieve destructive interference in larger areas. If the distance between the two sources happens to be well shorter than half a wavelength, then if you consider omnidirectional radiation, then they will always maintain their phase relationship, which means that you could effectively cancel the main source quite effectively. Of course, this has a limited frequency range and as already mentioned it depends on the wavelength and the distance between the two sources.

Now, considering the fact that you have in mind using only one speaker which will be very far from some of the sources means that the frequency range for which you could achieve attenuation would be quite small. In addition to that, this would produce an increase in pressure in other positions. This is what makes active noise control on three dimensional systems (such as rooms) quite impractical. If you could introduce loudspeakers in each desk, then you could possibly achieve attenuation on a quite large area for some low frequencies. This would end up being a quite complex system though.

In addition to that, you would have to consider the fact that lowering low-frequency noise could potentially increase speech intelligibility, increasing the annoyance of other people talking!

I strongly apologize for not providing in-text references. If you are interested in learning more about Active Noise Control you can start with the Active Control of Noise and Vibration books by Hansen and regarding annoyance from increased speech intelligibility, you can find more information in the Effects of Noise Reduction on Speech Intelligibility, Perceived Listening Effort, and Personal Preference in Hearing-Impaired Listeners article by Brons et al. and the Effects of Interior Aircraft Noise on Speech Intelligibility and Annoyoance paper by Pearsons and Bennett.

• Re, "you cannot effectively cancel out one source if the main source and the cancelling source do not coincide in space." I think maybe you misunderstood something that you read. A sound-cancelling system has a microphone and a speaker, and it sends a signal to the speaker that cancels out what the microphone is hearing. It is effective at suppressing noise coming from any direction or distance, but it only works if your ear is very close to the microphone. (e.g., if your ear and the microphone are both in the ear-cup of a set of headphones.) – Solomon Slow Jan 22 at 15:01
• Apparently you cannot effectively cancel out one source if the main source and the cancelling source do not coincide in space. What if I have several microphone-speaker pairs in the center of the room? – 404 Name Not Found Jan 22 at 15:32
• @SolomonSlow thanks for the comment. Yes, you would need (at least) one microphone to sense the source. What you mention here is one of the ways to make ANC possible. It comes out that you either decide to cancel the "noise" in one spot, or you could design the system in such a way that you could try and minimise the power output of the source. This would result in a different signal being sent out the cancelling speaker though. If you are trying to cancel at one spot then (in theory at least) it doesn't really matter where your speaker and source are as long as your ear is close to the mic. – ZaellixA Jan 22 at 16:11
• @404NameNotFound as I said in the other comment, you have to either decide the spots that you want to cancel the "noise" and set mics as close to them as possible or try to minimise the power output of the source. Since the source is distributed (many people in different locations), I believe this would end up being not feasible. You would have to deal with a lot of adaptive filters (which you have to use in ANC systems anyway) that would have to correct for all the paths in the system (all the sources to each location and all the cancelling sources to each location!) – ZaellixA Jan 22 at 16:14
• I see. Well it was worth a shot :) Thank you for the explanations. – 404 Name Not Found Jan 26 at 7:42