OpenStax College Physics for AP® Courses, Chapter 17, Problem 10 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. A studio wants to demonstrate destructive interference using two sound sources and this is the principal that noise-canceling headphones are based on; they have microphones in them that measure the sound that's coming from the exterior and then it produces a sound of the exact same type but in opposite phase such that it cancels the external sound. So if you have one sound source producing a sound with an antinode crest here— a positive antinode in other words— and then yet the other sound source is producing a sound with the trough antinode or the negative antinode at the same position then these two will add together to make zero and this will be perfect destructive interference. So what these lines are representing is maybe the pressure amplitude of the sound and so the pressure amplitude is greatest at this position midway between the two sources and whereas from the other source, the pressure amplitude is at its minimum midway between the two sources and when this is true, they will have destructive interference. So the sources have to be producing sound that has the same frequency such that this, you know, the length of each wave has to be same—same wavelength or the same frequency— and the volume should be the same so these are the two restrictions on the source— same frequency and same volume— and if the volume were different then one source would be winning in this competition like if this was, you know, that high and then the result would be something like this, it would still be some pressure here because not all of its being subtracted away by this blue line. Okay! And also you need to have enough distance between these two sound sources such that you can have at least a half wavelength in order for it, you know, to position a positive antinode at the same location as a negative antinode. It would be a bit challenging to have a perfect setup just like this because these sound sources are exactly out of phase so it would be difficult to connect them to some device that would produce such perfectly timed sounds but if you had much more distance between them then surely there will be someplace where a crest will overlap with a trough and there would be destructive interference somewhere.