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

A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Locate the maximum of the pulse at t = T and at t = 2T respectively.

Options

  1. Ax = -a and x = -2a
  2. Bx = a and x = 2a
  3. Cx = -a and x = a
  4. Dx = 2a and x = a

Correct answer

A. x = -a and x = -2a

Step-by-step solution

The given equation of the wave is y = A e^ - ( x a + t T )^2 . The maximum value of the pulse occurs when the exponent is zero, since the function e^ -z^2 is maximum at z = 0 . x a + t T = 0 x = - a T t At t = T , the position of the maximum is: x = - a T (T) = -a At t = 2T , the position of the maximum is: x = - a T (2T) = -2a

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