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.
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The trick is in that the circuit doesn’t need to act before sound moves 1cm. The circuit can be late and in fact it always is . Ever noticed that ANC only changes a low huming sounds rather than the crispy high sounds? Also Ever noticed that it never completely gets rid of them but only makes them quieter? The first part is because ANC is slow and it can only work with slow changes and low frequency sound is a slow change. The second part is that even with the slow changes ANC is always a little behind so it never is totally inversing the phase, it’s off by a few degrees.
Full cancellation happens at 180 degree phase shift which corresponds to half a wavelength delay. ANC needs to be between 0 and quarter wavelength late for ANC to work properly if it’s more than that, ANC will add to noise rather than attenuating it. There’s a lot of wiggle room. At low frequencies it’s closer to 0 because these waves are so long and change pressure slowly, that proportionally the little delay is smaller ( phase is simply a portion of a wave). Towards the higher pitched sounds, the frequency is so high that ANC can’t keep up – a tiny delay causes big change in phase. Eventually at some point ANC is too late and it starts adding noise rather than reducing it. Usually around 3kHz with the good headsets today.
The low sounds that ANC cancels are around 100Hz. We’re talking about waves 1/100th of a second. Half a wave of this is 1/200th of a second. During this time the sound travels 1.7m. Now since at this point we’re already 180* out of phase, ANC doesn’t need to inverse the signal, just mix it with itself but delayed. It won’t work perfectly but it hints at something.
I know this isn’t very ELI5 but the takeaway from this is that ANC doesn’t need to be perfect to work. The second, more confusing part is that in anything that repeats (which is waves) delay and inversion are almost the same thing. By inverting the wave you make an up, where there was down and down, where there was up. If the wave is repeating on and on and on, you can just copy it and delay this copy until it aligns just like the inverted version. You can draw a wave on two strips of paper and slide the paper to see how waves go into alignment and out of it as you “delay” one strip.
An person who designs an ANC decides for what frequencies the circuit inverses the signal (where the delay is negligible compared to the wave period) and when to nuance it so that even though it’s late, it still has at least some effect. This is hard to imagine without drawings but you can do some phase exercises on paper, where you draw a phase shift on checkered paper and count the difference on each spot and plot the resultant waveform. You’ll see that even though the waves not always cancel completely, they still attenuate and that’s exactly what ANC headphones do – they don’t need to be perfectly on time, just enough to do at least a little part of their job.
People don’t know this but sound cancellation happens in your ear and headphones even without ANC, except the canceled sound is not necessarily noise but music. Because phase shift can happen through delay, you can bounce a wave two times so that it aligns with itself out of phase. This causes many headphones to have strong dips in their response – the driver produces sound at this frequency but then the wave destroys itself. We call that destructive interference. You can see them on [a popular headset here](https://www.rtings.com/images/graphs/headphones/hyperx/cloud-ii/frequency-response-graph.png). The deep notch at 4kHz and the smaller notches above 10k are caused by phase cancellation just like it happens in ANC but purely acoustically and without any electronics. In the first dip it’s quite clear that the wave is almost perfectly out of phase with itself and the notch ends up really deep. in the smaller notches on the right, the cancellation wasn’t nearly as strong most likely because the phase wasn’t perfectly aligned. There may be other factors at play but I just wanted to get this point across.
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