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MHT CET 2024 (16 May, Shift 2) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2024 (16 May, Shift 2)

Q50MHT CET 2024 · 16 MAY · SHIFT 2Medium

Stationary Waves & Vibrating Strings

Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$ , the ratio of the length of string $B$ to that of $A$ is

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Answer: (d)

$n \propto \dfrac{1}{Lr}$ ; first overtone of A $= 2n_A$ , second overtone of B $= 3n_B$ .
$\dfrac{2}{L_A r_A} = \dfrac{3}{L_B r_B} \Rightarrow \dfrac{L_B}{L_A} = \dfrac{3 r_A}{2 r_B} = \dfrac{3\times2}{2} = 3$
So the answer is (d) $3:1$ .

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