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There is a common understanding that active-noise-cancelling headphones protect your hearing because they reduce outside noise and allow you to listen on the headphones at a lower level but they do not directly address the question of hearing loss.

For example in the article How noise-cancelling headphones help to protect your ears published on the "Western Hearing Service" website. They talk about the ability to listen at lower volume but no direct studies on hearing over time. E.g.

A study published in the Ear and Hearing journal found that listening to music with headphones at 70 per cent volume for just an hour can bring you to the threshold of your safe listening limit. By using noise-cancelling headphones that enable you to enjoy your favourite music at a lower volume, you are able to listen safely (60 per cent volume or lower) for longer without the risk of hearing damage.

Although there is a common understanding that they do protect hearing through lowering the level of noise required to hear what you want to listen do, have they been directly evaluated for their ability to protect hearing.

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    The question "Could [this] damage your hearing in some way?" is impossible to answer; there is always the possibility of some damage that we haven't understood or anticipated. Try rephrasing to ask for evidence about the claim you quote. – Paul Johnson Aug 22 '18 at 7:23
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    There is no difference between silence due to lack of any sound wave and silence due to two soundwaves cancelling each other. So the answer is no, except that noise cancellation will not be perfect. The only way in which the noice cancellation could cause damage is if the headphones produce sounds outside human's hearing range that might cause the damage. – Giacomo Alzetta Aug 22 '18 at 7:42
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    @PaulJohnson I'm not sure what you mean by asking for evidence because the expectations is that all answers come with evidence. As for impossibility to answer is it you don't know how a test could be constructed to answer the question or do I need to be more specific / technical about what hearing loss means – user1605665 Aug 22 '18 at 9:00
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    @user1605665 so you have no notable claim, making this question explicitly off topic. – jwenting Aug 22 '18 at 9:11
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    I think that the citation you provide is detracting from the question, because it seems like a notable claim but isn't the claim you are questioning. Rephrasing the question to focus on a clearer claim like "does active noise cancellation protect your hearing from loud noises as well as passive earplugs?", and reducing the space dedicated to "Here's an example of something I'm not asking about" might result in a more answerable question. – Kamil Drakari Aug 22 '18 at 17:38

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