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Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats and frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease by 3 Hz. If the frequency of A is 425 Hz, the original frequency of B is -

1. 430 Hz
2. 428 Hz
3. 422 Hz
4. 420 Hz

Correct answer: 420 Hz

Solution

Beat = |fA - fB| = 5, so fB = 420 or 430 Hz. Increasing B's tension raises fB; the beat frequency decreased to 2 Hz, meaning fB moved closer to 425 Hz. That only happens if fB started below A, so the original frequency of B is 420 Hz.

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