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

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(C) Length of the steel rod,$l = 100 \; cm = 1 \; m$.Fundamental frequency of vibration,$
u = 2.53 \; kHz = 2.53 	imes 10^3 \; Hz$.When the rod is c

Vedclass · Accepted Answer

$5.06$

Vedclass · Answer

(C) Length of the steel rod,$l = 100 \; cm = 1 \; m$.Fundamental frequency of vibration,$
u = 2.53 \; kHz = 2.53 	imes 10^3 \; Hz$.When the rod is clamped at its middle,a node $(N)$ is formed at the centre,and antinodes $(A)$ are formed at its two free ends. The length of the rod corresponds to the distance between two antinodes,which is $\lambda/2$.Thus,$l = \lambda/2$,which implies $\lambda = 2l = 2 	imes 1 = 2 \; m$.The speed of sound in steel is given by the relation $v = 
u \lambda$.$v = 2.53 	imes 10^3 \; Hz 	imes 2 \; m = 5.06 	imes 10^3 \; m/s$.$v = 5.06 \; km/s$.

$A$ 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 (in $km/s$) of sound in steel?

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