What should be the length of the dipole antenna for a carrier wave of frequency ` 3 xx 10^8` Hz?

Explanation

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

### Step 1: Understand the relationship between speed, frequency, and wavelength
The speed of electromagnetic waves (light) in a vacuum is given by the formula:
\[ C = f \times \lambda \]
where:
- \(C\) is the speed of light (\(3 \times 10^8\) m/s),
- \(f\) is the frequency (in Hz),
- \(\lambda\) is the wavelength (in meters).

### Step 2: Rearrange the formula to find the wavelength
We can rearrange the formula to solve for the wavelength \(\lambda\):
\[ \lambda = \frac{C}{f} \]

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

### Step 4: Calculate the wavelength
Perform the calculation:
\[ \lambda = 1 \text{ meter} \]

### Step 5: Determine the length of the dipole antenna
The length of a dipole antenna is typically half the wavelength:
\[ \text{Length of dipole antenna} = \frac{\lambda}{2} = \frac{1 \text{ meter}}{2} = 0.5 \text{ meters} \]

### Final Answer
The length of the dipole antenna should be \(0.5\) meters.

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