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
- Af(x, t) = A ( t T + x vT )
- Bf(x, t) = A ( t T + x v )
- Cf(x, t) = A ( t T - x v )
- 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 )