Question

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

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

Answer 1

The correct option is A velocity

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