Question

The electron field portion of an electromagnetic wave is given by (all variables in SI units) $E = 10^{-4} \sin ( 6 \times 10^5 t - 0.01 x)$ . The frequency $(f)$ and the speed $(ν)$ of electromagnetic wave are

• A. $f = 30 / \pi \, kHz$ and $ν =1.5 \times 10^7m / s^{-1}$
• B. $f = 90 / \pi \, kHz$ and $ν =6.0 \times 10^7m / s^{-1}$
• C. $f = 300 / \pi \, kHz$ and $ν =6.0 \times 10^7m / s^{-1}$
• D. $f = 600 / \pi \, kHz$ and $ν =7.5 \times 10^7 m / s^{-1}$
• E. $f = 900 / \pi \, kHz$ and $ν =8.0 \times 10^7m / s^{-1}$

Answer 1

Answer: (C)

$ \omega=6 \times 10^{5} =2 \pi f $
$ f =\frac{6}{2 \pi} \times 10^{5}=\frac{3}{\pi} \times 10^{5} Hz$
$=\frac{300}{\pi} \times 10^{3} Hz$
$=\frac{300}{\pi} kHz$
Wave speed $= \frac{\omega}{k} $
$= \frac{6 \times 10^{5}}{0.01}=6 \times 10^{7} m / s$