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Two strings A and B of lengths, L_A=80 ~cm and L_B=x ~cm respectively are used separately in a sonometer. The ratio of their densities (d_A / d_B ) is 0.81 . The diameter of B is one-half that of A . If the strings have the same tension and fundamental frequency the value of x is :

Options

  1. A33
  2. B102
  3. C144
  4. D130

Correct answer

C. 144

Step-by-step solution

Given, T_A T_B =1, L_A L_B = 80 x D_A D_B = 2 1 , d_A d_B = 0.81 1 Let ₁ and ₂ be the linear densities. _A _B = ( D_A D_B )^2 d_A d_B = ( 2 1 )^2 0.81=4 0.81=3.24 f₁ f₂ = L_B L_A T_A T_B _B _ A 1= x 80 1 1 3.24 x=80 3.24 or x=144

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