An electromagnetic wave is passing through a small volume of space. The energy in the volume oscillates with
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → double the frequency of the wave
The energy density of the wave depends on the square of the field. With \( E = E_0\sin\omega t \) at the given point,
\( \displaystyle u = \varepsilon_0 E^{2} = \varepsilon_0 E_0^{2}\sin^{2}\omega t \)
\( \displaystyle u = \frac{\varepsilon_0 E_0^{2}}{2}\left(1 - \cos 2\omega t\right) \)
The energy term varies as \( \cos 2\omega t \), so it oscillates with angular frequency \( 2\omega \), that is, with double the frequency of the wave. (It never becomes negative: it goes from zero to its maximum twice in each cycle of the field.)
Why the other options are incorrect
Option (1) zero frequency — Incorrect. The energy is not constant; it rises and falls as the field does.
Option (2) half the frequency of the wave — Incorrect. Squaring a sinusoid doubles its frequency; it does not halve it.
Option (3) the frequency of the wave — Incorrect. The fields oscillate at the wave frequency, but the energy, being proportional to \( E^{2} \), repeats every half cycle.
Note: This question is from beyond the NCERT textbook and it appears to be out of the CUET 2026 Physics syllabus.