Question

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 ?

Answer 1

Length of the steel rod, $l=100cm=1m$
Fundamental frequency of vibration, $f=2.53kHz=2.53\times {10}^{3}Hz$
When the rod is plucked at its middle, an antinode (A) is formed at its centre, and nodes (N) are formed at its two ends, as shown in the given figure.

The distance between two successive node is $\lambda /2$

$\therefore l=\lambda /2$

$\lambda =2l=2\times l=2m$

The speed of sound in steel is given by the relation:

$v=f\lambda$

$=2.53\times {10}^3\times 2$

$=5.06\times {10}^{3}m/s$

$=5.06km/s$