A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

Question

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in water drum to half of its length. The fundamental frequency of the air column is now equal to:

Answer 1

Test each option against the data. After filing, the beat frequency is 2, so the new frequency of A must be \(340 \pm 2 = 338\) or \(342\) Hz, and it must be higher than the original.
(1) 335 Hz: initial beats \(= 5\); after filing to 338 Hz beats \(= 2\). Consistent.
(2) 345 Hz: initial beats 5, but filing increases the frequency, so it cannot fall to 342 Hz or 338 Hz. Not consistent.
(3) 338 Hz: initial beats \(= 2\), not 5. (4) 342 Hz: initial beats \(= 2\), not 5.
Only 335 Hz works.
Answer: (1) 335 Hz

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

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The Correct Option is A

Solution and Explanation

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