In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency

Question

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:

Accepted Answer

Difference of $f_A$ and $f_B$ is 6 Hz. If tension decreases, $f_B$ decreases to $f_B'$. New difference $|f_A - f_B'| = 7 	ext{ Hz}$. Since the beat frequency increased, $f_A > f_B$. Thus $f_A - f_B = 6 	ext{ Hz} \implies 530 - f_B = 6 \implies f_B = 524 	ext{ Hz}$.

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