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Is the frequency of a vibrating string equal to the frequency of the sound it creates? For example, if a string is vibrating at 440Hz, would the sound it creates be 440Hz as well?

Furthermore, would a string with a fundamental frequency of 440Hz make a sound of 440Hz when vibrating?

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    $\begingroup$ YES to both questions. $\endgroup$
    – Gert
    Commented Nov 2, 2021 at 1:37

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if a string is vibrating at 440Hz, would the sound it creates be 440Hz as well?

Yes. You can imagine that each particle on the string is oscillating at 440 Hz. As each particle oscillates, it drags neighboring air particles along with its motion, so each air particle around the string will also vibrate at 440 Hz. Since the sound created comes from the air particles' oscillations, you would hear a 440 Hz pitch sound.

Furthermore, would a string with a fundamental frequency of 440Hz make a sound of 440Hz when vibrating?

You would indeed hear a 440 Hz sound that correponds to the string's fundamental frequency. However, take note that you will likely hear higher frequencies of sounds corresponding to the higher harmonics - unless the string is oscillating perfectly at its fundamental mode with no higher harmonics.

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