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MHT CET 2025 (21 Apr, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2025 (21 Apr, Shift 1)

Q33MHT CET 2025 · 21 APR · SHIFT 1Medium

Stationary Waves & Vibrating Strings

Two uniform wires of same material are vibrating under the same tension. If the 11st overtone of 11st wire is equal to the 22nd overtone of 22nd wire and radius of 11st wire is twice the radius of 22nd wire, the ratio of length of 11st wire to that 22nd wire is

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Answer: (a)

  1. n∝1Lrn \propto \dfrac{1}{Lr}; first overtone =2n1= 2n_1, second overtone =3n2= 3n_2.
  2. 2L1r1=3L2r2⇒L1L2=2r23r1=26\dfrac{2}{L_1 r_1} = \dfrac{3}{L_2 r_2} \Rightarrow \dfrac{L_1}{L_2} = \dfrac{2r_2}{3r_1} = \dfrac{2}{6}
  3. So the answer is (a) 1:31:3.
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