A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases in $E_{1} a n d E_{2}$ respectively. If the value of $\frac{E_{1}}{E_{2}}$ is x/100,The value of x is _______

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answer is 9.

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Detailed Solution

$E n e r g y i n 1 l o o p \int \frac{1}{2} d m {[A \sin (k x) ω]}^{2} = \frac{λ A^{2} ω^{2}}{8} (M / L) ∴ R a t i o = \frac{3}{5} \times \frac{3}{5} \times \frac{1}{4}$

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