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5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95 \mathrm{~m}$ or $1 \mathrm{~m}$. The frequency of the fork will be:
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Verified Answer
The correct answer is:
$195 \mathrm{~Hz}$
$195 \mathrm{~Hz}$
Probable frequencies of tuning fork be $n \pm$ 5
Frequency of sonometer wire, $n \propto \frac{1}{l}$
$$
\begin{aligned}
&\therefore \frac{n+5}{n-5}=\frac{100}{95} \Rightarrow 95(n+5)=100(n-5) \\
&\text { or, } 95 n+475=100 n-500 \\
&\text { or, } 5 n=975 \\
&\text { or, } n=\frac{975}{5}=195 \mathrm{~Hz}
\end{aligned}
$$
Frequency of sonometer wire, $n \propto \frac{1}{l}$
$$
\begin{aligned}
&\therefore \frac{n+5}{n-5}=\frac{100}{95} \Rightarrow 95(n+5)=100(n-5) \\
&\text { or, } 95 n+475=100 n-500 \\
&\text { or, } 5 n=975 \\
&\text { or, } n=\frac{975}{5}=195 \mathrm{~Hz}
\end{aligned}
$$
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