A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________ Hz

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Solution

Q.
A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________ Hz. [2024]

Ans.
(6)    $f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$

$f_{1} = \frac{1}{2} \sqrt{\frac{6}{μ}},$    $f_{2} = \frac{1}{2} \sqrt{\frac{54}{μ}}$

$\frac{f_{1}}{f_{2}} = \frac{1}{3},$ $f_{2} - f_{1} = 12$

   $f_{1} = 6$ $H z$

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