ELI5: Your brain is used to hearing yourself speak, and when we have headphones in our speech seems softer and dominated by the music, so we instinctively speak louder to give our brains a relatively consistent feedback.
I’ll also add that speech recognition software is more accurate when people are speaking louder than normal to compensate for a relative decrease in one’s ability to hear himself speaking, meaning that this talking louder actually does improve our communicative ability.
If you’re interested, there is the related, and intuitively understandable phenomenon known as Lombard Speech. This is the effect one experiences when in a loud environment, and you speak louder to compensate. The [Lombard effect](https://en.wikipedia.org/wiki/Lombard_effect)is the basis for common modern audiology/hearing tests.
[Here is a link to the original paper](http://paul.sobriquet.net/wp-content/uploads/2007/02/lombard-1911-p-h-mason-2006.pdf).
This same phenomenon has been shown in many animals such as bats and fish. Perhaps more easily explained is the case in birds in loud, urban areas and cities, who will actually sing louder because of the noise.
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