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 1: Understand the formula for wavelength
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{c}{f} \]
where:
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) meters per second),
- \( f \) is the frequency in hertz (Hz).

### Step 2: Convert frequency to hertz
Given that the frequency is 50 MHz, we need to convert this into hertz:
\[ 50 \text{ MHz} = 50 \times 10^6 \text{ Hz} \]

### Step 3: Calculate the wavelength
Now we can substitute the values into the wavelength formula:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{50 \times 10^6 \text{ Hz}} \]

### Step 4: Perform the calculation
Calculating this gives:
\[ \lambda = \frac{3 \times 10^8}{50 \times 10^6} = \frac{3}{50} \times 10^{8-6} = \frac{3}{50} \times 10^2 = \frac{3 \times 100}{50} = \frac{300}{50} = 6 \text{ meters} \]

### Step 5: Calculate 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 λ we found:
\[ \text{Length} = \frac{6 \text{ m}}{2} = 3 \text{ m} \]

### Conclusion
Thus, the length of the half-wave dipole antenna at 50 MHz is **3 meters**.