In a plane electromagnetic wave the electric field osciliates sinusoidally with frequency `3X10^(5)` Hz. Then wavelenght of the wave in vaccuum is

Options

A. `10^(2)m`
B. `10m`
C. `10^(4)m`
D. `10^(3)m`

Answer

To find the wavelength of the electromagnetic wave in vacuum given the frequency, we can use the formula that relates the speed of light (C), wavelength (λ), and frequency (f):

\[ C = \lambda \cdot f \]

Where:
- \( C \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \) meters per second.
- \( \lambda \) is the wavelength in meters.
- \( f \) is the frequency in hertz.

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency \( f = 3 \times 10^5 \) Hz
- Speed of light \( C = 3 \times 10^8 \) m/s

2. **Rearrange the formula to solve for wavelength (λ):**
\[ \lambda = \frac{C}{f} \]

3. **Substitute the known values into the formula:**
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{3 \times 10^5 \text{ Hz}} \]

4. **Perform the division:**
- First, simplify the numbers:
\[ \lambda = \frac{3}{3} \times \frac{10^8}{10^5} \]
- This simplifies to:
\[ \lambda = 1 \times 10^{8-5} = 1 \times 10^3 \text{ m} \]

5. **Final result:**
\[ \lambda = 10^3 \text{ m} \]
Therefore, the wavelength of the wave in vacuum is \( 1000 \) meters.