The magnetic field in a plane electromagnetic wave is given $B_y = 2 × 10^{-7}\sin (0.5 × 10^3x + 1.57 × 10^{11}t) T$. The frequency of the wave is

25.0 GHz

The correct answer is Option (3) → 25.0 GHz

Magnetic field of a plane EM wave: $B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.57 \times 10^{11} t) \, \text{T}$

General form: $B_y = B_0 \sin(kx + \omega t)$

Here, $\omega = 1.57 \times 10^{11} \, \text{rad/s}$

Frequency: $f = \frac{\omega}{2\pi} = \frac{1.57 \times 10^{11}}{2 \pi} \approx 2.5 \times 10^{10} \, \text{Hz}$

Converting to GHz: $f = \frac{2.5 \times 10^{10}}{10^9} = 25 \, \text{GHz}$

Answer: $f \approx 25 \, \text{GHz}$