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In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be

1. 524 Hz
2. 536 Hz
3. 537 Hz
4. 523 Hz

Correct answer: 536 Hz

Solution

The beat frequency is the absolute difference between the frequencies of the two strings. Initially, the beat frequency is 6 Hz, so the frequency of B could be either 530 + 6 = 536 Hz or 530 - 6 = 524 Hz. When the tension in B is decreased, its frequency decreases, and the beat frequency increases to 7 Hz. This implies that the original frequency of B must have been 536 Hz, as decreasing it would increase the beat frequency with A.

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