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

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Question

In a guitar, two strings A and B made of the 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

Correct Answer: A — 524 HzStep-by-step Solution:Beat frequency = |fA − fB| = 6 Hz and fA = 530 Hz.So fB = 530 + 6 = 536 Hz   or   fB = 530 − 6 = 524 Hz.When tension in B is decreased, frequency of B decreases (since f ∝ √T).If fB = 536 Hz (higher than A): decreasing tension reduces fB toward 530 Hz, bringing it closer to fA, so beat frequency would decrease. This contradicts the observation.If fB = 524 Hz (lower than A): decreasing tension further reduces fB (e.g., to 523 Hz), moving it further from fA = 530 Hz. Beat frequency increases to 7 Hz. This is consistent.Therefore, the original frequency of B = 524 Hz.Why Other Options Are Incorrect:Option B (536 Hz): Decreasing tension would bring fB closer to fA, reducing beat frequency to less than 6 Hz, not increasing it.Options C and D: Neither 537 nor 523 Hz gives a beat frequency of exactly 6 Hz with fA = 530 Hz.Key Concept:Beat frequency = |f1 − f2|. Frequency of a string ∝ √(Tension). Decreasing tension decreases frequency. To determine which of the two possible frequencies is correct, observe how beat frequency changes when a parameter is altered.

In a guitar, two strings A and B made of the 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:

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In a guitar, two strings A and B made of the 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:

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