system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:ELI5:Why do ears hurt in a quiet room when headphones are turned up to full volume, but not at the same volume in a noisy environment? Is it not incurring the same damage?
gpt
There's a term in hearing science known as signal to noise ratio. It refers to how loud what you want to hear is in relation to background noise. The auditory processing center in the brain tries to distinguish the signal (e.g. what is coming from your headphones) from background noise. In a quiet room, the signal to noise ratio is high, so you don't need an excessive volume to distinguish from background noise. In this case, full volume is too much for the auditory system, which causes the pain. The ears are designed to hurt when sounds are damaging-inducing loud.

In a noisy environment, the signal to noise ratio is initially lower. You feel the need to increase the volume of your headphones to increase the ratio. The auditory processing system is working hard and distracted by competing signals, so your headphones don't seem as loud even though they are.

Having the headphones at the same volume would incur the same damage, regardless of environment.