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(C) The frequency of a sonometer wire is given by $n_w = \frac{1}{2L} \sqrt{\frac{T}{m}}$,which implies $n_w \propto \frac{1}{L}$.Let $n$ be the frequ

Vedclass · Accepted Answer

$205$

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(C) The frequency of a sonometer wire is given by $n_w = \frac{1}{2L} \sqrt{\frac{T}{m}}$,which implies $n_w \propto \frac{1}{L}$.Let $n$ be the frequency of the tuning fork.Since the beat frequency is $5 \, Hz$ in both cases,the wire frequency must be $n+5$ and $n-5$ respectively.For $L_1 = 20 \, cm$,$n_1 = n+5 = \frac{k}{20}$.For $L_2 = 21 \, cm$,$n_2 = n-5 = \frac{k}{21}$.Dividing the two equations: $\frac{n+5}{n-5} = \frac{21}{20}$.$20(n+5) = 21(n-5)$.$20n + 100 = 21n - 105$.$n = 205 \, Hz$.

$A$ tuning fork vibrating with a sonometer having $20 \, cm$ wire produces $5$ beats per sec. The beat frequency does not change if the length of the wire is changed to $21 \, cm$. The frequency of the tuning fork must be ..... $Hz$.

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