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A steel rod $100 \mathrm{~cm}$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 \mathrm{kHz}$. What is the speed of sound in steel?
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Verified Answer
When the rod is clamped at the middle, a node is forrmed at the middle and 2 antinodes are forrmed at the two ends.
Here, $L=100 \mathrm{~cm}=1 \mathrm{~m}, v=2.53 \mathrm{kHz}=2.53 \times 10^3 \mathrm{~Hz}$
$$
\begin{aligned}
&\therefore \quad L=\frac{\lambda}{4}+\frac{\lambda}{4}=\frac{\lambda}{2} \Rightarrow \lambda=2 L=2 \mathrm{~m} \\
&\mathrm{v}=\mathrm{v} \lambda=2.53 \times 10^3 \times 2=5.06 \times 10^3 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
Here, $L=100 \mathrm{~cm}=1 \mathrm{~m}, v=2.53 \mathrm{kHz}=2.53 \times 10^3 \mathrm{~Hz}$
$$
\begin{aligned}
&\therefore \quad L=\frac{\lambda}{4}+\frac{\lambda}{4}=\frac{\lambda}{2} \Rightarrow \lambda=2 L=2 \mathrm{~m} \\
&\mathrm{v}=\mathrm{v} \lambda=2.53 \times 10^3 \times 2=5.06 \times 10^3 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
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