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MHT CET 2026 (11 Apr, Shift 2) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2026 (11 Apr, Shift 2)

Q21MHT CET 2026 · 11 APR · SHIFT 2Medium

Stationary Waves & Vibrating Strings

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

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Answer: (b)

  1. n∝1Lrn \propto \dfrac{1}{Lr} (same TT, same material); first overtone =2n1= 2n_1, second overtone =3n2= 3n_2.
  2. 2L1r1=3L2r2\dfrac{2}{L_1 r_1} = \dfrac{3}{L_2 r_2}
  3. L1L2=2r23r1=23×2=13\dfrac{L_1}{L_2} = \dfrac{2 r_2}{3 r_1} = \dfrac{2}{3\times2} = \dfrac{1}{3}
  4. So the answer is (b) 13\dfrac{1}{3}.
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