A steel rod 100, cm long is clamped at its mi | vedclass

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(B) When a rod is clamped at its middle,the ends act as antinodes $(A)$ and the clamped point acts as a node $(N)$.In the fundamental mode,the length

Vedclass · Accepted Answer

$5.06$

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(B) When a rod is clamped at its middle,the ends act as antinodes $(A)$ and the clamped point acts as a node $(N)$.In the fundamental mode,the length of the rod $l$ corresponds to two segments of $\frac{\lambda}{4}$ each,so $l = \frac{\lambda}{4} + \frac{\lambda}{4} = \frac{\lambda}{2}$.$\Rightarrow \lambda = 2l$.Given: $l = 100\, cm = 1\, m$,frequency $f = 2.53\, kHz = 2.53 	imes 10^3\, Hz$.The speed of sound $v$ is given by $v = f \lambda$.Substituting $\lambda = 2l$:$v = f 	imes 2l = 2.53 	imes 10^3 	imes 2 	imes 1 = 5.06 	imes 10^3\, m/s$.Converting to $km/s$:$v = 5.06\, km/s$.

$A$ steel rod $100\, cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53\, kHz$. What is the speed of sound in steel? (in $km/s$)

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