Question

The equation of a wave is given by
$y=A\sin \omega (\frac{x}{v}-a)$, where $\omega$ is the angular velocity and $v$ is the linear velocity of the wave. The dimensions of $a$ is

• A. $\left[M\right]$
• B. $\left[T\right]$
• C. $\left[L\right]$
• D. $\left[K\right]$

Answer 1

The correct option is B $\left[T\right]$

Given,
$y=A\sin \omega (\frac{x}{v}-a)$
We know that physical quantities having the same dimensions are added or subtracted.
Therefore, the dimensions of $a$ should be the same as the dimensions of $\frac{x}{v}$.
$\Rightarrow \left[a\right]=\left[\frac{x}{v}\right]$
$\Rightarrow \left[a\right]=\left[\frac{L}{L{T}^{-1}}\right]=\left[T\right]$