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. Determine the dimensions of A and a .
Options
- AL , T
- BL , L
- CL⁻¹ , L
- DL , L⁻¹
Correct answer
B. L , L
Step-by-step solution
The displacement of the string g(x) has the dimension of length, so [g(x)] = [L] . From the given equation g(x) = A (x/a) , the amplitude A must have the same dimension as g(x) . Therefore, [A] = [L] . The argument of the trigonometric function must be dimensionless. Thus, [x/a] = [M^0 L^0 T^0] . Since x represents position, [x] = [L] . Therefore, [a] = [x] = [L] . The dimensions of A and a are L and L respectively.