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

A sine wave propagates through a medium. What is the minimum distance between two particles that always possess the same speed?

Options

  1. A/2
  2. B/3
  3. C/4

Correct answer

B. /3

Step-by-step solution

Let the equation of the propagating sine wave be y = A ( t - kx) . The velocity of a particle at position x and time t is given by: v = y t = A ( t - kx) The speed of the particle is the magnitude of its velocity: |v| = A | ( t - kx)| For two particles at positions x₁ and x₂ to always possess the same speed, their speeds must be equal for all values of time t : | ( t - kx₁)| = | ( t - kx₂)| This condition implies: t - kx₁ = ( t - kx₂) + n Since this must hold true for all time t , the coefficient of t on both sides

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