A tuning fork gives 3 beats with \(50 \mathrm{~cm}\) length of sonometer wire. If the length of the wire is shortened by \(1 \mathrm{~cm}\), the number of beats is still the same. The frequency of the fork is

The frequency of a vibrating wire \(\mathrm{f}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\)
\(
\therefore \quad \mathrm{f} \propto \frac{1}{l} \Rightarrow \mathrm{fl}=\text { constant }
\)

Let the frequency of the fork be \(f\) and the initial and final frequencies of the wire be \(f_1\) and \(f_2\).

The number of beats heard before decreasing the length is \(f-f_1=3\)

The number of beats after decreasing the length is \(\mathrm{f}_2-\mathrm{f}=3\)
\(
\begin{array}{ll}
\therefore & \mathrm{f}_1 l_1=\mathrm{f}_2 l_2 \\
\therefore & (\mathrm{f}-3) 50=(\mathrm{f}+3) 49 \\
& 50 \mathrm{f}-49 \mathrm{f}=147+150 \\
\therefore \quad & \mathrm{f}=297 \mathrm{~Hz}
\end{array}
\)