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The way that sound waves are detected in your ear or in a microphone are fundamentally the same. Your ear and a microphone both have a lightweight membrane that is sensitive to sudden changes in pressure. In the ear this is called an Ear Drum.

By sensitive, I mean that high pressure pushes it and low pressure pulls it. It physically moves like the skin of a drum.

This movement can be detected, in a microphone it is detected by attaching a magnet to the vibrating membrane, and having a loop of wire near the magnet, but not attached to it. When the magnet moves relative to the wire a voltage is induced in the wire. This is called Faraday's Law. In your ear the process of measuring is more complicated but is essentially based on measuring the vibrations of the eardrum.

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