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In an experiment with sonometer a tuning fork of frequency $256 \mathrm{~Hz}$ resonates with a length of $25 \mathrm{~cm}$ and another tuning fork resonates with a length of $16 \mathrm{~cm}$. Tension of the string remaining constant the frequency of the second tuning fork is
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The correct answer is:
$400 \mathrm{~Hz}$
The wavelength of the sound is proportional to the length of wire. Also, the velocity of sound is same in both cases, so
$\begin{aligned}
& \Rightarrow & v_{1} &=v_{2} \\
\Rightarrow & & f_{1} \lambda_{1} &=f_{2} \lambda_{2} \\
\Rightarrow & 256 \times 25 &=f_{2} \times 16 \\
\Rightarrow & & f_{2}=\frac{256 \times 25}{16}=400 \mathrm{~Hz}
\end{aligned}$
$\begin{aligned}
& \Rightarrow & v_{1} &=v_{2} \\
\Rightarrow & & f_{1} \lambda_{1} &=f_{2} \lambda_{2} \\
\Rightarrow & 256 \times 25 &=f_{2} \times 16 \\
\Rightarrow & & f_{2}=\frac{256 \times 25}{16}=400 \mathrm{~Hz}
\end{aligned}$
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