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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 . Determine the dimensions of A , a , and T .

Options

  1. AL , L⁻¹ , T⁻¹
  2. BL⁻¹ , L , T
  3. CL , T , L
  4. DL , L , T

Correct answer

D. L , L , T

Step-by-step solution

The argument of the exponential function must be dimensionless. Therefore, the terms x a and t T are dimensionless. Since x represents position, its dimension is L . For x a to be dimensionless, the dimension of a must be L . Since t represents time, its dimension is T . For t T to be dimensionless, the dimension of T must be T . The exponential term e^ - ( x a + t T )^2 is a dimensionless quantity. Therefore, the dimension of A must be the same as the dimension of y . Since y represents the displacement of the wav

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