Question

The displacement of a progressive wave is represented by $y=A\,sin\left(\omega t-kx\right) $ where $x$ is distance and $t$ is time. The dimensions of $\frac{\omega}{k}$ are same as those of

• A. velocity
• B. wave number
• C. wavelength
• D. frequency

Answer 1

Answer: (A)

$y=A\,sin\,\left(\omega t-kx\right)$
As $\left(\omega t-kx\right)$ represents an angle which is dimensionless, therefore
$\left[\omega\right]=\frac{1}{\left[t\right]}=\left[T^{-1}\right]$ and $\left[k\right]=\frac{1}{\left[x\right]}=\left[L^{-1}\right]$
$\left[\frac{\omega}{k}\right]=\frac{\left[T^{-1}\right]}{\left[L^{-1}\right]}=\left[LT^{-1}\right]=$ velocity