What should be the length of dipole antenna for a carrier wave having frequency `3xx10^(8)` Hz?

Options

A. 5m
B. 0.5m
C. 1.5m
D. 1m

Answer

To find the length of a dipole antenna for a carrier wave with a frequency of \(3 \times 10^8\) Hz, we can follow these steps:

### Step 1: Identify the given frequency
The frequency of the carrier wave is given as:
\[ f_c = 3 \times 10^8 \text{ Hz} \]

### Step 2: Use the speed of light to find the wavelength
The speed of light \(c\) is approximately \(3 \times 10^8\) m/s. The relationship between speed, frequency, and wavelength is given by the formula:
\[ c = f_c \cdot \lambda \]
Where:
- \(c\) is the speed of light,
- \(f_c\) is the frequency,
- \(\lambda\) is the wavelength.

Rearranging the formula to find the wavelength:
\[ \lambda = \frac{c}{f_c} \]

### Step 3: Substitute the values
Substituting the known values into the equation:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{3 \times 10^8 \text{ Hz}} = 1 \text{ meter} \]

### Step 4: Calculate the length of the dipole antenna
The length of a dipole antenna \(L\) is given by the formula:
\[ L = \frac{\lambda}{2} \]
Substituting the value of \(\lambda\):
\[ L = \frac{1 \text{ meter}}{2} = 0.5 \text{ meters} \]

### Step 5: Conclusion
Thus, the length of the dipole antenna for the given frequency is:
\[ L = 0.5 \text{ meters} \]

### Final Answer:
The length of the dipole antenna should be **0.5 meters**.

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