Question

The electric field of an electromagnetic wave travelling through vacuum is given by the equation $E = E_0 \,sin\, (kx - \omega t)$. The quantity that is independent of wavelength is

• A. $k\omega$
• B. $ \frac{k}{\omega} $
• C. $k^2\omega$
• D. $\omega$
• E. $ {{k}^{2}}\omega $

Answer 1

Answer: (B)

Here, $k = \frac{2\pi}{\lambda}$,
$\omega = 2 \pi\upsilon$
$\therefore \quad \frac{k}{\omega} = \frac{2\pi/\lambda}{ 2 \pi \upsilon }$
$= \frac{1}{\upsilon\lambda} = \frac{1}{c}\quad\left(\because c = u\,\lambda\right)$
where $c$ is the speed of electromagnetic wave in vacuum. It is a constant whose value is $3 \times 10^{8}\, m\, s^{-1}$.