Question

The equation y=a sin(wt-kx) represents a plane wave travelling in a medium along the x-direction, y being the displacement at the point x at time t. Given that x is in meter and t in second, state the units of k and w. What physical quantity does w/k represent? Justify your answer. State whether the wave is travelling in the negative or positive x-direction

Answer 1

The unit of k is

$$m^{-1}$$

The unit of w is

$$s^{-1}$$

w/k represents phase velocity of the wave.

$$\dim \frac{w}{k}=\frac{s^{-1}}{m^{-1}}=\frac{m}{s}=\dim v$$

The wave is travelling in the positive x-direction.