An open organ pipe vibrating in its fundamental mode produces 8 beats per second with a 512 Hz tuning fork. The length of the pipe is then decreased slightly, and the beat frequency becomes 2 beats per second. What was the original fundamental frequency of the pipe?
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Question

An open organ pipe vibrating in its fundamental mode produces 8 beats per second with a 512 Hz tuning fork. The length of the pipe is then decreased slightly, and the beat frequency becomes 2 beats per second. What was the original fundamental frequency of the pipe?

Options

G1 Physics · Accepted Answer

Initially, |fₚ−512| = 8. Therefore, fₚ = 504 Hz or fₚ = 520 Hz. For an open organ pipe, f ∝ 1/L. Shortening the pipe increases its frequency. Since shortening causes the beat frequency to decrease from 8 Hz to 2 Hz, the pipe frequency must initially lie below 512 Hz. Therefore, fₚ = 504 Hz. Correct option: A.