A plane electromagnetic wave travels in vacuum along z-direction. If the frequency of the wave is 40 MHz then its wavelength is

Options

A. 5 m
B. 7.5 m
C. 8.5 m
D. 10 m

Explanation

To find the wavelength of a plane electromagnetic wave traveling in a vacuum, we can use the relationship between the speed of light, frequency, and wavelength. The formula is given by:

\[ \lambda = \frac{c}{f} \]

Where:
- \(\lambda\) is the wavelength,
- \(c\) is the speed of light in vacuum (approximately \(3 \times 10^8\) m/s),
- \(f\) is the frequency of the wave.

### Step-by-Step Solution:

1. **Identify the given values**:
- Frequency (\(f\)) = 40 MHz = \(40 \times 10^6\) Hz.
- Speed of light (\(c\)) = \(3 \times 10^8\) m/s.

2. **Use the wavelength formula**:
Substitute the values into the wavelength formula:
\[ \lambda = \frac{c}{f} = \frac{3 \times 10^8 \text{ m/s}}{40 \times 10^6 \text{ Hz}} \]

3. **Calculate the wavelength**:
- First, simplify the fraction:
\[ \lambda = \frac{3 \times 10^8}{40 \times 10^6} = \frac{3}{40} \times \frac{10^8}{10^6} = \frac{3}{40} \times 10^2 \]
- Now calculate \(\frac{3}{40}\):
\[ \frac{3}{40} = 0.075 \]
- Therefore:
\[ \lambda = 0.075 \times 100 = 7.5 \text{ meters} \]

4. **Conclusion**:
The wavelength of the electromagnetic wave is \(7.5\) meters.

### Final Answer:
The wavelength is \(7.5\) meters.

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