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  4. 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?

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Q. 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?

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Solution:

In fundamental mode,
$l=2\left(\frac{\lambda}{4}\right)=\frac{\lambda}{2}$
image
$\Rightarrow \lambda=2 l$
Given $l=100\, cm ,\, v=2.53\, kHz$
Using $v=v \lambda$
$\Rightarrow v=2.53 \times 10^{3} \times 2 \times 100 \times 10^{-2}$
$=5.06 \times 10^{3} m / s$
$=5.06\, km / s$