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AP EAMCET2011PhysicsWaves and Sound

Two uniform stretched 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

Options

  1. A2 : 3
  2. B1 : 2
  3. C1 : 3
  4. D1 : 4

Correct answer

C. 1 : 3

Step-by-step solution

Given, 1st overtone of A=2 nd overtone of B aligned & 1 l₁ T r₁^2 d = 3 2 l₂ T r₂^2 d & r₂ r₁ = 3 2 ( l₁ l₂ ) aligned But r₁=2 r₂ aligned & r₂ 2 r₂ = 3 2 ( l₁ l₂ ) & or l₁ l₂ = 1 3 l₁: l₂=1: 3 & aligned

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