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MHT CET 2026 (20 May, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2026 (20 May, Shift 1)

Q17MHT CET 2026 · 20 MAY · SHIFT 1Medium

Stationary Waves & Vibrating Strings

Two vibrating metal wires of the same material of length 'L' and '3L' and have radii '2r' and 'r' respectively. They are stretched under same tension. Both the wires vibrate in their fundamental modes. The ratio n1n2\frac{n_1}{n_2} is [n1n_1 and n2n_2 are the frequencies of first and second wire respectively]

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Answer: (b)

  1. n=12LTπr2ρ⇒n∝1Lrn = \dfrac{1}{2L}\sqrt{\dfrac{T}{\pi r^2\rho}} \Rightarrow n \propto \dfrac{1}{Lr} for same TT and material.
  2. n1n2=L2r2L1r1=3L⋅rL⋅2r=32\dfrac{n_1}{n_2} = \dfrac{L_2 r_2}{L_1 r_1} = \dfrac{3L \cdot r}{L \cdot 2r} = \dfrac{3}{2}
  3. So the answer is (b) 1.5:11.5:1.
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