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

Two sine waves propagate in the same direction within a medium. Each wave possesses an amplitude of A , and the phase difference between them is 120^ . The resultant amplitude is

Options

  1. A2 , A
  2. B3 , A
  3. C2A
  4. DA

Correct answer

D. A

Step-by-step solution

The resultant amplitude A_R of two waves with amplitudes A₁ and A₂ and a phase difference is given by A_R = A₁^2 + A₂^2 + 2A₁A₂ Given A₁ = A , A₂ = A , and = 120^ . Substituting these values, we get A_R = A^2 + A^2 + 2(A)(A) 120^ Since 120^ = - 1 2 , A_R = 2A^2 + 2A^2 (- 1 2 ) A_R = 2A^2 - A^2 A_R = A^2 = A

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