A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be

Let n be frequency of tuning fork.
Let \(\mathrm{n}_1, \mathrm{n}_2\) be frequency of wire at tension \(\mathrm{T}_1, \mathrm{~T}_2\) respectively.
\(\begin{aligned}
\mathrm{n} & \propto \sqrt{\mathrm{~T}}...(i) \\
\mathrm{n}_1 & =\mathrm{n}-6 ...(ii)\\
\mathrm{n}_2 & =\mathrm{n}+6...(iii)
\end{aligned}\)
\(\begin{array}{ll}
\therefore & \frac{\mathrm{n}_1}{\mathrm{n}_2}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{225}{256}}=\frac{15}{16} \\
\therefore & \frac{\mathrm{n}-6}{\mathrm{n}+6}=\frac{15}{16}...from(i), (ii),(iii) \\
\therefore & 16 \mathrm{n}-96=15 \mathrm{n}+90 \\
\therefore \quad & \mathrm{n}=186 \mathrm{~Hz}
\end{array}\)