A405 hz tuning fork and a piano key are struck together, and no beats are heard. when a 402 hz tuning fork and the same piano key are struck, three beats are heard. what is the frequency of the piano key?

The difference between the frequencies of the piano key and the tuning fork gives the frequency of the beats.

When the tuning fork is 405 Hz, and no beats are heard, then the piano key is also 405 Hz.

When the piano key is 405 Hz and the tuning fork is 402 Hz, then 405 - 402 = 3 beats are heard.

The piano key is 405 Hz.

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