Question

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

Answer 1

Length of the steel rod, l = 100 cm = 1 m
Fundamental frequency of vibration, $\nu =2.53kHz=2.53\times {10}^{3}Hz$
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 nodes is $\frac{\lambda }{2}$
$\therefore l=\frac{\lambda }{2}$
$\therefore l=\frac{\lambda }{2}\lambda =2l=2\times 1=2m$
The speed of sound in steel is given by the relation:
$v=v\lambda =2.53\times {10}^3\times 2=5.06\times {10}^{3}m/s=5.06km/s$