The electric field component of an electromagnetic wave in vacuum is $\vec E= 3 \cos(1.8y +5.4 × 10^8t)\hat i\, N/C$, where y is in meter and t is in seconds. The frequency of the wave is (approximately)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 86 MHz
The electric field of an EM wave is given as:
$\vec{E} = 3 \cos (1.8 y + 5.4 \times 10^8 t) \hat{i}\ \text{N/C}$
General form: $\vec{E} = E_0 \cos (k y - \omega t)$
Here, $\omega = 5.4 \times 10^8\ \text{rad/s}$
Frequency: $f = \frac{\omega}{2 \pi} = \frac{5.4 \times 10^8}{2 \pi} \approx 8.59 \times 10^7\ \text{Hz}$
Final Answer: $f \approx 8.6 \times 10^7\ \text{Hz}$