Question

The electric field part of an electromagnetic wave in vacuum is

$E=3.1\cos [\left(1.8\frac{rad}{m}\right)y+(5.4\times {10}^8\frac{rad}{s})t]\hat{i}$.The frequency corresponding to the given part of the electromagnetic wave is?

• A. $5.4{10}^{8}Hz$
• B. $8.6{10}^{7}Hz$
• C. $3.2{10}^{8}Hz$
• D. $4.8{10}^{7}Hz$

Answer 1

The correct option is B $8.6{10}^{7}Hz$

Given equation

$E=3.1\cos [\left(1.8\frac{rad}{m}\right)y+(5.4\times {10}^8\frac{rad}{s})t]\hat{i}$...........(i)

Standard equation at electromagnetic wave in terms of electric field,

$E=E_0\cos (ky+wt)$.........(ii)

If the wave is moving in $-y$ direction

Wave length, $\lambda =\frac{2\pi }{Coefficientofy}$

$=\frac{2\pi }{1.8}=\frac{2\times 22/7}{1.8}$

$\lambda =\frac{44}{1.8\times 7}=3.49=3.5m$

velocity of wave, $v=\frac{\text{coefficient of l}}{\text{coefficient of y}}$

$v=\frac{5.4\times {10}^8}{1.8}=3\times {10}^8$

frequency, $f=\frac{v}{\lambda }=\frac{3\times {10}^8}{3.5}=8.6\times {10}^7$ Hz
Hence, the correct option is $\left(B\right)$