The electric field E associated with an electromagnetic wave is given by \( E = E_0\sin(kx - \omega t) \). The speed of the wave is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{\omega}{k} \)
A wave travels with the speed at which a point of constant phase moves.
\( \displaystyle kx - \omega t = \text{constant} \)
Differentiating with respect to time,
\( \displaystyle k\,\frac{dx}{dt} - \omega = 0 \;\Rightarrow\; v = \frac{dx}{dt} = \frac{\omega}{k} \)
This is the wave speed \( v = \omega/k \), equal to \( c \) for an electromagnetic wave in vacuum.
Shortcut: Check the dimensions: \( k \) is in \( \mathrm{m^{-1}} \) and \( \omega \) in \( \mathrm{s^{-1}} \). Only \( \omega/k \) has the unit \( \mathrm{m\,s^{-1}} \) of a speed.
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Nature of Electromagnetic Waves – “… k is the magnitude of the wave vector (or propagation vector) k and its direction describes the direction of propagation of the wave. The speed of propagation of the wave is (ω/k).”