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

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Solution

Q.
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 [2020]

1 523 Hz

2 524 Hz

3 536 Hz

4 537 Hz

Ans.
(2)

Frequency of string A, $υ_{A} = 530$ $Hz$ and beat frequency $Δ υ_{1} = 6$ $Hz.$

Since, $υ_{B} = υ_{A} \pm Δ υ_{1},$ we have $υ_{B} = 536$ $Hz$ or $524$ $Hz$

Now, when tension on the string is reduced, its frequency reduces.

Now, the beat frequency, $Δ u_{2} = 7$ $Hz$

$∴$ The original frequency of B, $υ_{B} = 524$ $Hz$

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