An aluminium rod having a length 100 ,cm is c | vedclass

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(B) The speed of longitudinal waves in a rod is given by $v = \sqrt{\frac{Y}{\rho}}$,where $Y$ is Young's modulus and $\rho$ is density.Substituting t

Vedclass · Accepted Answer

$2740$

Vedclass · Answer

(B) The speed of longitudinal waves in a rod is given by $v = \sqrt{\frac{Y}{ho}}$,where $Y$ is Young's modulus and $ho$ is density.Substituting the values: $v = \sqrt{\frac{7.8 	imes 10^{10}}{2600}} = \sqrt{3 	imes 10^7} = \sqrt{30 	imes 10^6} \approx 5477.2 \,m/s \approx 5480 \,m/s$.Since the rod is clamped at the middle,the middle point acts as a node (displacement node) and the free ends act as antinodes.For the fundamental mode of vibration of a rod clamped at the center,the length of the rod $L$ is equal to half the wavelength $\lambda/2$ (as the distance between two consecutive antinodes is $\lambda/2$).Thus,$L = \frac{\lambda}{2} \implies \lambda = 2L = 2 	imes 1.0 \,m = 2.0 \,m$.The frequency $f$ is given by $f = \frac{v}{\lambda} = \frac{5480}{2} = 2740 \,Hz$.

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