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  • 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?

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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best_answer

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}

Posted by

Sayak

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