Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A wave pulse travels on a string towards the positive X -axis with a speed v . At t = 0 , the shape of the string is given by g(x) = A (x/a) , where A and a are constants. Write the equation of the wave for a general time t .
Options
- Af(x, t) = A ( x - vt a )
- Bf(x, t) = A ( x - at v )
- Cf(x, t) = A ( x + at v )
- Df(x, t) = A ( x + vt a )
Correct answer
A. f(x, t) = A ( x - vt a )
Step-by-step solution
For a wave traveling in the positive x -direction with speed v , the wave equation f(x, t) must be a function of (x - vt) . Given the shape of the wave at t = 0 is g(x) = A ( x a ) . Replacing x with (x - vt) in the expression for g(x) gives the equation of the wave at any general time t . Thus, f(x, t) = g(x - vt) = A ( x - vt a ) .