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

Two waves propagating in the same direction through the same region possess equal frequencies, wavelengths, and amplitudes. If each wave has an amplitude of 4 mm and the phase difference between the waves is 90^ , what is the resultant amplitude?

Options

  1. A4 mm
  2. B4 2 mm
  3. C8 mm
  4. D2 2 mm

Correct answer

B. 4 2 mm

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 = A₂ = 4 mm and = 90^ . Substituting the values: A_R = 4^2 + 4^2 + 2(4)(4) 90^ Since 90^ = 0 : A_R = 16 + 16 + 0 = 32 = 4 2 mm

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