Question

The electric 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 $(v)$ of electromagnetic wave are}

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

Hint:

Always compare given equation with $E=E_0\sin(\omega t - kx)$ to extract $\omega$ and $k$.

Answer 1

The Correct Option is C

Concept:
Standard wave equation: \[ E = E_0 \sin(\omega t - kx) \] \[ f = \frac{\omega}{2\pi}, \quad v = \frac{\omega}{k} \]

Step 1: Identify parameters.
\[ \omega = 6 \times 10^5,\quad k = 0.01 \]

Step 2: Frequency calculation.
\[ f = \frac{6 \times 10^5}{2\pi} = \frac{3 \times 10^5}{\pi} = \frac{300}{\pi} \text{ kHz} \]

Step 3: Wave speed.
\[ v = \frac{\omega}{k} = \frac{6 \times 10^5}{0.01} = 6 \times 10^7 \text{ m/s} \]