how do noise cancelling headphones work so fast

Question

So I understand the basic principles behind noise cancellation. You essentially use a microphone to record incoming sound waves and create an inverse wave that destructively interferes with the initial wave, thus, cancelling it out. But I don’t understand, practically, how this is done.

Let’s assume the sound wave makes contact with the microphone in the AirPod, which analyses the wave and shoots out an inverse wave, but by that point – the initial sound wave would surely have already reached my ears. The AirPod basically needs to cancel the sound wave before it moves roughly a centimetre or it’s too late.

The speed of sound (in a standard environment like air) is 343 meters per second or 34,300 centimetres per second; this means the AirPod has 1/34,300 seconds or ~0.03 miliseconds to do these operations to cancel the wave. That just seems absurd to me for such a tiny chip in the bloody AirPod.

Someone fix my confusion please.

In: 678

Answer 1

The other answers do a great job of describing how fast computers are, but in reality, they don’t need to be to solve this specific problem. (Although it certainly helps.)

The purpose of noise cancelling is to lessen the impact of sound that humans can and usually do hear. This constrains the bounds of frequency and amplitude that need to be negated, simplifying the problem.

Since every sound is a wave that goes on for some amount of time, the counter wave can actually start “late” and still be effective. Sure, it may lag in time, or maybe even slightly out of phase, but it will still mitigate some of the sound.

Fast computers mean that this can be done faster than you can perceive. However, instead of noise cancelling, imagine harmonizing instead. A singer doesn’t need to start singing in harmony on the very first soundwave to harmonize. Sure, it may take a noticeable amount of time to hear the harmony but the vast amount of the time the singer will sound in harmony, even as underlying sounds change.

Anyway, fast computers make this an easy problem. But they are not strictly necessary.