The equation of wave is given by $y = A \sin \omega \left[ \frac{x}{v} - k \right]$, where $\omega$ is the…

The equation of wave is given by $y = A \sin \omega \left[ \frac{x}{v} - k \right]$, where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimensional formula of $\omega$ is
  1. (a) $[\text{LT}]$
  2. (b) $[\text{T}]$
  3. (c) $[\text{T}^{-1}]$
  4. (d) $[\text{T}^2]$

Solution

Here, $\omega \cdot \frac{x}{v} = \text{dimensionless}$ $\Rightarrow \omega \left[\frac{L}{LT^{-1}}\right] = [M^0 L^0 T^0] \Rightarrow [\omega T] = [M^0 L^0 T^0]$ or $[\omega] = \frac{[M^0 L^0 T^0]}{[T]} \Rightarrow [\omega] = [T^{-1}]$

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