A steel rod $100\, cm$ long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\, kHz$. What is the speed of sound in sound is steel ? (in $km/s$)
AIIMS 2018, Medium
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In fundamental mode, $l=2\left(\frac{\lambda}{4}\right)=\frac{\lambda}{2}$
$\Rightarrow \lambda=2 l \ldots(i)$
Given, $l=100 cm , v=2.53 kHz =2.53 \times 10^{3} Hz$
We know that,
$v=v \lambda$
$=v \times 2 l$ [from equation $(i)]$
$=2.53 \times 10^{3} \times 2 \times 100 \times 10^{-2}$
$=5.06 \times 10^{3} m / s$
$=5.06 km / s$
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