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MHT CET 2023 (10 May, Shift 2) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2023 (10 May, Shift 2)

Q67MHT CET 2023 · 10 MAY · SHIFT 2Medium

Stationary Waves & Vibrating Strings

Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the $2$ nd overtone of $2$ nd wire and radius of the first wire is twice the radius of the $2$ nd wire then the ratio of length of first wire to $2$ nd wire is

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Answer: (a)

$n \propto \dfrac{1}{Lr}$ ; first overtone $= 2n_1$ , second overtone $= 3n_2$ .
$\dfrac{2}{L_1 r_1} = \dfrac{3}{L_2 r_2} \Rightarrow \dfrac{L_1}{L_2} = \dfrac{2r_2}{3r_1} = \dfrac{1}{3}$
So the answer is (a) $1:3$ .

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