Ncert Exercises & Solutions

15.18 Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Frequency of string A, ν_{A} = 324 Hz

Frequency of string B = ν_{B}

Beat ’ s frequency, n = 6 Hz

Initial beat' s frequency :

n_{1} = |ν_{A} \pm ν_{B}|

6 = 324 \pm ν_{B}

ν_{B} = 330 Hz or 318 Hz

The frequency is directly proportional to the square root of tension .

So the frequency decreases with a decrease in the tension in a string .

Hence, the frequency of B cannot be 330 Hz .

∴ ν_{B} = 318 Hz

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