A standard tuning fork has frequency 400 Hz. An unknown fork produces 7 beats per second with it. The unknown fork is filed in such a way that its frequency increases by exactly 10 Hz, after which the two forks produce 3 beats per second. What was the original frequency of the unknown fork?
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Question

A standard tuning fork has frequency 400 Hz. An unknown fork produces 7 beats per second with it. The unknown fork is filed in such a way that its frequency increases by exactly 10 Hz, after which the two forks produce 3 beats per second. What was the original frequency of the unknown fork?

Options

G1 Physics · Accepted Answer

Initially, |f−400| = 7, so f = 393 Hz or f = 407 Hz. After filing, the frequency becomes f+10. If f = 393 Hz, then f+10 = 403 Hz, and the new beat frequency is |403−400| = 3 Hz. If f = 407 Hz, then the new frequency is 417 Hz and the beat frequency would be 17 Hz. Therefore, f = 393 Hz. Correct option: A.