this post was submitted on 04 Jun 2024
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So, just to ignore your budget, I have the Sony XM4 headphones (over ear), and... they are okay. In the heat, they get very sweaty, and there are annoying sounds you can't turn off (on/off beep, and a voice which tells you when it has connected). The noise cancellation is good for constant noises but not sudden ones. Overall, I wouldn't recommend/buy them again, as they are just fine.
I have tried some in ear ones from Xiaomi (not sure which exactly) which I bought for my partner, and they are, in my limited experience, just fine too, especially for the price (<$50). I don't know about any long-term idiosyncrasies though, so take that with a pinch of salt. These ones look a bit better: Redmi Buds 5 Pro. https://www.amazon.co.uk/Xiaomi-Redmi-Buds-Black-BHR7660GL/dp/B0CQKHK626/
This is kinda the nature of active noise cancellation, unfortunately. Blocking out sudden noise is just technically very challenging. Works great for airplane noise, not so much for crying babies.
Sony's XM line is in my opinion just about the best ANC headphones money can buy, in terms of noise cancelling and sound quality combo. I can understand your point about them getting sweaty. Part one of blocking noise is good sound insulation, which tends to hold in heat as well. I live in a colder climate so that works out well for me. You could get in-ear ones, although obviously they don't block out noise as well.
What do you mean that blocking sudden noise in technically very challenging? I might be wrong, but from what I have gathered is that ANC is based on playing a "negative" of a pressure wave picked by the microphones in phase with the original wave. Thus it has to react to all sounds in the time that the pressure wave travels from the microphone to the ear, so it shouldn't matter whether the noise is constant (airplane) or sudden (gunshot).
Of course if the headphones have some kind of pass-through active, then it might take a while until software decides to activate ANC, but that is not a limitation of ANC itself
That's the theory, but it's almost impossible to do in practice. Your microphone and speaker are imperfect at capturing and reproducing sounds. The phase timing is incredibly sensitive. You only have milliseconds to do the processing and generation.
That's why practical noise cancelling relies on feedback loops. A second microphone inside captures the result of the cancellation, and based on that adjustments can be made to the negative signal. This allows you to correct for lots of sources of error and achieve quite a good result. Of course, for a sudden noise like a gunshot, by the time the feedback loop can really kick in, the noise is already over.