Tuning fork A has frequency 512 Hz. Tuning fork B produces 9 beats per second with A. Fork B is filed so that its frequency increases by exactly 12 Hz, and the new beat frequency is 3 beats per second. If the original frequency of fork B is N Hz, find N.
Physics · Wave Motion · beat and properties of sound
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Question

Tuning fork A has frequency 512 Hz. Tuning fork B produces 9 beats per second with A. Fork B is filed so that its frequency increases by exactly 12 Hz, and the new beat frequency is 3 beats per second. If the original frequency of fork B is N Hz, find N.

Physics · Wave Motion · beat and properties of sound

G1 Physics · Accepted Answer

Initially, |f₂−512| = 9. Therefore, f₂ = 503 Hz or 521 Hz. After filing, f₂(new) = f₂+12. If f₂ = 503 Hz, then f₂(new) = 515 Hz, giving |515−512| = 3 Hz. If f₂ = 521 Hz, then the new frequency is 533 Hz and the beat frequency would be 21 Hz. Hence, N = 503.