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

A stretched string carries a wave in the positive x -direction with a wave speed of v . The displacement of the particle at x = 0 is described by f(t) = A (t/T) . Determine the wave equation.

Options

  1. Af(x, t) = A ( t T + x vT )
  2. Bf(x, t) = A ( t T + x v )
  3. Cf(x, t) = A ( t T - x v )
  4. Df(x, t) = A ( t T - x vT )

Correct answer

D. f(x, t) = A ( t T - x vT )

Step-by-step solution

For a wave traveling in the positive x -direction with speed v , the displacement f(x, t) at any position x and time t is given by the displacement at x = 0 at an earlier time t - x v . Given the displacement at x = 0 is f(t) = A ( t T ) . Substituting t with t - x v gives the wave equation: f(x, t) = A ( t - x v T ) f(x, t) = A ( t T - x vT )

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