The length of half wave dipole antenna at 50 MHz is

Options

A. 5 m
B. 4 m
C. 3 m
D. 2 m

Answer

To find the length of a half wave dipole antenna at a frequency of 50 MHz, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Frequency to Hertz**:
The given frequency is 50 MHz. We need to convert this to Hertz (Hz).
\[ 50 \text{ MHz} = 50 \times 10^6 \text{ Hz} \]

2. **Use the Speed of Light to Find Wavelength**:
The relationship between the speed of light (C), wavelength (λ), and frequency (f) is given by:
\[ C = \lambda \times f \]
Where:
- \( C \) is the speed of light, approximately \( 3 \times 10^8 \text{ m/s} \)
- \( f \) is the frequency in Hz
- \( \lambda \) is the wavelength in meters

Rearranging the formula to find wavelength:
\[ \lambda = \frac{C}{f} \]

3. **Substitute the Values**:
Now, substituting the values into the equation:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{50 \times 10^6 \text{ Hz}} \]

4. **Calculate the Wavelength**:
Performing the calculation:
\[ \lambda = \frac{3 \times 10^8}{50 \times 10^6} = \frac{3}{50} \times 10^{8-6} = \frac{3}{50} \times 10^2 = \frac{3 \times 100}{50} = 6 \text{ meters} \]

5. **Determine the Length of the Half Wave Dipole Antenna**:
The length of a half wave dipole antenna is given by:
\[ \text{Length} = \frac{\lambda}{2} \]
Substituting the value of wavelength:
\[ \text{Length} = \frac{6 \text{ meters}}{2} = 3 \text{ meters} \]

### Final Answer:
The length of the half wave dipole antenna at 50 MHz is **3 meters**.