Physics

The equation of a wave is given by $$y=a sin\omega \left (\dfrac {x}{v}-k\right )$$, where $$\omega$$ is angular velocity and $$v$$ is linear velocity. The dimensions of $$K$$ will be


ANSWER

$$[T]$$


SOLUTION
The quantity $$\left (\dfrac {\omega x}{v}-\omega k\right )$$ inside the sine function has dimension of angle and hence $$\omega k$$ is dimensionless being angle.
But $$[\omega ]$$ $$=[T^{-1}] $$, therefore $$[k]=[T]$$
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