Question

If the magnitude of the electric field of an electromagnetic wave in a medium is given by E = 10⁷ sin(6 × 10⁸ t - 0.01x) N C^-1, then the frequency and speed of the electromagnetic wave respectively are: (In the equation x is in metre and t is in second)

• A. $\frac{6 \times 10^8}{\pi}$ Hz, 3 $\times$ 10$^7$ m s$^{-1}$
• B. $\frac{3 \times 10^5}{\pi}$ Hz, 6 $\times$ 10$^7$ m s$^{-1}$
• C. $\frac{6 \times 10^5}{\pi}$ Hz, 3 $\times$ 10$^7$ m s$^{-1}$
• D. $\frac{6 \times 10^8}{\pi}$ Hz, 6 $\times$ 10$^7$ m s$^{-1}$

Hint:

For an electromagnetic wave $E = E_0 \sin(\omega t - k x)$, frequency is $f = \frac{\omega}{2\pi}$ and speed is $v = \frac{\omega}{k}$. Compare with the standard form to extract $\omega$ and $k$.

Answer 1

The Correct Option is D

The electric field is given as $E = 10^7 \sin(6 \times 10^8 t - 0.01 x)$, which is in the form $E = E_0 \sin(\omega t - k x)$.
Angular frequency $\omega = 6 \times 10^8$ rad/s, wave number $k = 0.01$ m$^{-1}$.
Frequency $f = \frac{\omega}{2\pi} = \frac{6 \times 10^8}{2\pi} = \frac{6 \times 10^8}{\pi}$ Hz.
Speed of the wave $v = \frac{\omega}{k} = \frac{6 \times 10^8}{0.01} = 6 \times 10^{10} \times 10^{-2} = 6 \times 10^7$ m s$^{-1}$.