A steel rod 100, cm long is damped at into middle. fundamental frequency of longitudinal vibrations

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14.Waves and Sound

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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 $km/s$)

A

$6.2$

B

$5.06$

C

$7.23$

D

$7.45$

(AIIMS-2018)

Solution

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 $(i)]$

$=2.53 \times 10^{3} \times 2 \times 100 \times 10^{-2}$

$=5.06 \times 10^{3} m / s$

$=5.06 km / s$

Standard 11

Physics

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