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

Explanation

Here, `l=100cm =1m, v=2.53k Hz=2.53xx10^(3)Hz`
When the rod is cleampled at the middle, then in the fundamental mode of vibration of the rod, a node is formed at the middle and anitnode is formed at each end.
Therefore, as is clear from figure.
`L=(lambda)/(4)+(lambda)/(4)=(lambda)/(2)`
`lambda=2L=2m`
As, `upsilon=vlambda`
`:. upsilon=2.53xx10^(3)xx2=5.06xx10^(3)ms^(-1)`