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

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Question

(B) When a rod of length $L$ is clamped at its middle,the fundamental mode of longitudinal vibration has a node at the center and antinodes at the end

Vedclass · Accepted Answer

$5.06$

Vedclass · Answer

(B) When a rod of length $L$ is clamped at its middle,the fundamental mode of longitudinal vibration has a node at the center and antinodes at the ends.This corresponds to a standing wave where the length of the rod $L$ is equal to half the wavelength,i.e.,$L = \lambda / 2$.Given $L = 100 \, cm = 1 \, m$,we have $\lambda / 2 = 1 \, m$,which implies $\lambda = 2 \, m$.The fundamental frequency is given as $f = 2.53 \, kHz = 2.53 	imes 10^3 \, Hz$.The speed of sound $v$ is given by the relation $v = f \lambda$.Substituting the values,$v = (2.53 	imes 10^3 \, Hz) 	imes (2 \, m) = 5.06 	imes 10^3 \, m/s$.Since $10^3 \, m = 1 \, km$,the speed is $5.06 \, km/s$.

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

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