The fundamental frequency of a sonometer wire | vedclass

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(C) The fundamental frequency of a sonometer wire is given by $n = \frac{1}{2l} \sqrt{\frac{T}{m}}$.Case $1$: Tension is increased by $44\%$. The new

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$5$

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(C) The fundamental frequency of a sonometer wire is given by $n = \frac{1}{2l} \sqrt{\frac{T}{m}}$.Case $1$: Tension is increased by $44\%$. The new tension $T' = T + 0.44T = 1.44T$.The new frequency $n' = n + 6$.$n + 6 = \frac{1}{2l} \sqrt{\frac{1.44T}{m}} = 1.2 \left( \frac{1}{2l} \sqrt{\frac{T}{m}} \right) = 1.2n$.$0.2n = 6 \Rightarrow n = 30 \ Hz$.Case $2$: Length is increased by $20\%$. The new length $l' = l + 0.2l = 1.2l$.The new frequency $n'' = \frac{1}{2l'} \sqrt{\frac{T}{m}} = \frac{1}{2(1.2l)} \sqrt{\frac{T}{m}} = \frac{n}{1.2} = \frac{30}{1.2} = 25 \ Hz$.The change in frequency is $|n - n''| = |30 - 25| = 5 \ Hz$.

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