A tuning fork and a sonometer wire were sounded together and produce $4$ beats per second. When the length of sonometer wire is $95 cm$ or $100 cm,$ the frequency of the tuning fork is ..... $Hz$
Medium
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(a) Probable frequencies of tuning fork be $n + 4$ or $n - 4$
Frequency of sonometer wire $n \propto \frac{1}{l}$.
$\therefore $ $\frac{{n + 4}}{{n - 4}} = \frac{{100}}{{95}}$ or $95\,(n + 4) = 100(n - 4)$
or $95n + 380 = 100n - 400$ or $5n = 780$ or $n = 156$
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