A steel rod 100 cm long is clamped at its midpoint. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 KHz. What is the speed of sound in steel.

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A steel rod 100 cm long is clamped at its midpoint. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 KHz. What is the speed of sound in steel.

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10.12 km/s

5.06 km/s

2.53 km/s

20.24 km/s

answer is B.

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Detailed Solution

For a rod vibrating longitudinally fundamental frequency
$f = \frac{υ}{2 L}$
$\begin{aligned} \Rightarrow v = f (2 L) = (2.53 \times 10^{3}) (2) (1) \\ v = 5.06 \times 10^{3} m / s = 5.06 km / s \end{aligned}$