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They don't, It is your ears that interpret them as sound, other vibrations are interpreted as light by your eyes and yet others go completely unnoticed by your body, while others can kill you.
But how do vibrations in the air cause sound in the 1st place?
The 'vibrations' are actually rapid changes in pressure. Stretch an elastic band between your fingers and then pluck it. You can hear it vibrate right? What it's doing on each vibration, as it moves back and fourth, is to alternatively push and then pull the air backwards and forwards. Sound is a fluctuating pressure wave that travels out from the source a bit like ripples on a pond. The ear drum vibrates in sympathy with the sound wave and the fluctuating pressure wave is transmitted into the inner ear where it's converted into an electrical signal before it's conveyed to the brain.
I think perhaps the most fascinating thing about our hearing is our ability to distinguish the instruments or individual voices when we listen to an orchestra or people talking. This is amazing because simultaneous sounds from separate sources add together to make a highly complicated mixture of sounds. Yet we can untangle this complicated waveform by separating the different frequencies within our inner ear. Our hearing does a form of frequency analysis or Fourier transform of the sounds we hear - just to get technical for a moment.