The magnetic field in a plane electromagnetic wave is given by \( B = 3 \times 10^{-7}\sin(1.5x + 5 \times 10^{8}t)\,\mathrm{T} \), where \( x \) is in meter and \( t \) is in second. The wavelength of the wave is: (Take: \( \pi = 3 \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 m
Comparing with the standard form of a wave, \( B = B_0\sin(kx + \omega t) \), the coefficient of \( x \) is the propagation constant (wave number) \( k \), and the wavelength is \( \lambda = 2\pi/k \).
\( k = 1.5\,\mathrm{rad\,m^{-1}} \)
\( \displaystyle \lambda = \frac{2\pi}{k} = \frac{2 \times 3}{1.5} = 4\,\mathrm{m} \)