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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

Two wires possessing different densities but the same area of cross section are joined together at one end and stretched to a tension T . The velocity of a transverse wave in the first wire is twice that in the second wire. Determine the ratio of the density of the first wire to the density of the second wire.

Options

  1. A2
  2. B4
  3. C0.5
  4. D0.25

Correct answer

D. 0.25

Step-by-step solution

The velocity of a transverse wave in a stretched wire is given by v = T , where is the linear mass density. Since = A , where is the density and A is the cross-sectional area, the velocity can be written as v = T A . For the two wires, the tension T and area A are the same. Thus, v 1 . Given that v₁ = 2v₂ , we have: T ₁ A = 2 T ₂ A Squaring both sides: T ₁ A = 4 T ₂ A 1 ₁ = 4 ₂ ₁ ₂ = 1 4 = 0.25

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