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

A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . In which direction does the wave travel?

Options

  1. ANegative x -direction
  2. BPositive x -direction
  3. CPositive y -direction
  4. DNegative y -direction

Correct answer

A. Negative x -direction

Step-by-step solution

The given equation of the wave is y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . Comparing this with the standard wave equation y = A (kx + t) , we observe that the argument of the sine function has a positive sign between the spatial and temporal terms. For a point of constant phase, kx + t = constant . Differentiating with respect to time t , we get k dx dt + = 0 , which gives the wave velocity v = dx dt = - k . Since the velocity is negative, the wave travels in the negative x -direction.

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