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

It is given in the question that:

Length of the steel rod, l = 100 cm = 1 m
Fundamental frequency of vibration, ν = 2.53 kHz = 2.53 × 103 Hz
When the rod is clamped at its middle, antinodes (A) are formed at its ends, a node (N) is formed in the middle.

The distance between two successive antinodes is λ2.
The speed of sound in steel is given by the relation:
v = νλ 
= 2.53×103 × 2 
= 5.06×103 m/s 
= 5.06 km/s