Noise-canceling headphones are an application of destructive interference. Each

Question

Noise-canceling headphones are an application of destructive interference. Each side of the headphones uses a microphone to pick up noise, delays it slightly, then rebroadcasts the noise next to your ear where it can interfere with the incoming sound wave of the noise. Suppose you are sitting 1.8 m from an annoying, 200 Hz buzzing sound.

What is the minimum headphone delay, in ms, that will cancel this noise? (The answer isn't T = 1/f ...there is something I'm missing here as the answer isn't 5ms)

Explanation / Answer

from the given data

wavelength of the sound, lamda = v/f

= 343/200

= 1.715 m

for distructive interfrence, path diffrnce = lamda/2

= 1.715/2

= 0.8575 m

so, delay time = 0.8575/343

= 0.0025 s

= 2.5 ms

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