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Q.15.16  A steel rod 100\: cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of  the rod are given to be 2.53\: kHz. What is the speed of sound in steel?

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When the rod is clamped at the middle at is vibrating in the fundamental mode, a node is formed at the middle of the rod and antinodes at the end. i.e.

\\\frac{L}{2}=\frac{\lambda }{4}\\ \lambda =2L\\ \lambda =0.2m

where L is the length of the rod.

Speed of sound in steel is

\\v=\nu \lambda \\ v=2.53\times 10^{3}\times 0.2\\ v=5060ms^{-1}

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