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

Two periodic waves with amplitudes A₁ and A₂ travel through a region. Given that A₁ > A₂ , what is the difference between the maximum and minimum possible resultant amplitudes?

Options

  1. A2 A₁
  2. BA₁ + A₂
  3. C2 A₂
  4. DA₁ - A₂

Correct answer

C. 2 A₂

Step-by-step solution

The resultant amplitude A of two waves with amplitudes A₁ and A₂ having a phase difference is given by A = A₁^2 + A₂^2 + 2A₁A₂ . The maximum resultant amplitude occurs when = 1 , which gives A_ max = A₁ + A₂ . The minimum resultant amplitude occurs when = -1 , which gives A_ min = |A₁ - A₂| . Since A₁ > A₂ , A_ min = A₁ - A₂ . The difference between the maximum and minimum resultant amplitudes is A_ max - A_ min = (A₁ + A₂) - (A₁ - A₂) = 2A₂ .

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