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MHT CET 2026 (14 May, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2026 (14 May, Shift 1)

Q18MHT CET 2026 · 14 MAY · SHIFT 1Medium

Stationary Waves & Vibrating Strings

Two uniform strings A and B made of steel are vibrating under the same tension. If the 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 lengths of the strings is

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Answer: (d)

First overtone $= 2n$ , second overtone $= 3n$ , and $n \propto \dfrac{1}{Lr}$ (same $T$ , same material).
$\dfrac{2}{L_A r_A} = \dfrac{3}{L_B r_B}$
$\dfrac{L_A}{L_B} = \dfrac{2 r_B}{3 r_A} = \dfrac{2}{3\times2} = \dfrac{1}{3}$
So the answer is (d) $1:3$ .

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