Question

A steel rod of 100 cm is clamped at its middle. The fundamental frequency of longitudinal vibration of the rod is $2.53kHz$. The speed of sound in the rod is ____ $m{s}^{-1}$

• A. $5.06\times {10}^{3}m{s}^{-1}$
• B. 240
• C. 480
• D. 1200

Answer 1

The correct option is A $5.06\times {10}^{3}m{s}^{-1}$

Given, L$=100cm=1m$

$v=2.53kHz=2.53\times {10}^3$

As the given rod is clamped at middle hence there will be a nod at middle

Hence,

$\begin{array}{c}Length,L=\frac{\lambda }{4}+\frac{\lambda }{4}=\frac{\lambda }{2}\\ \lambda =2L=2m\\ Speed,v=V\lambda =2.53\times {10}^3\times 2\\ =5.06\times {10}^{3}m{s}^{-1}\end{array}$

Hence,

the speed of sound in the rod is $5.06\times {10}^{3}m{s}^{-1}$

So, option $A$ is correct answer.