Frequency Of Oscillating Fields

NCERT Class 12, Chapter 8 (Electromagnetic Waves) describes a plane electromagnetic wave using E = E₀ sin(kx − ωt) and B = B₀ sin(kx − ωt) with the same angular frequency ω and wave number k. Because the two fields are generated by the same oscillating source and continually regenerate each other, they share an identical frequency and reach their maxima and zeros together, meaning they oscillate in phase. Physically this must be so: Faraday's and Ampere-Maxwell's laws couple the space and time derivatives of the two fields, and a solution with two different frequencies could not satisfy both equations simultaneously. The in-phase relationship also guarantees that the wave's energy density never becomes negative anywhere. The option claiming the magnetic field oscillates at twice the electric frequency has no physical basis and would violate the coupled Maxwell equations. Likewise, the option doubling the electric field frequency contradicts the shared angular frequency in the wave expressions. The suggestion that the fields oscillate at unrelated frequencies is impossible, since a single wave cannot carry two independent frequencies in its coupled fields. A consistency check using the identical ω in both field equations confirms equal frequency and in-phase behaviour, so that option is correct.