Calculate the length of quarter wave antenna for transmission frequency of 20 MHz.

Explanation

To calculate the length of a quarter wave antenna for a transmission frequency of 20 MHz, follow these steps:

### Step 1: Convert the frequency to hertz
The frequency given is 20 MHz. We need to convert this to hertz.
\[ 20 \text{ MHz} = 20 \times 10^6 \text{ Hz} \]

### Step 2: Use the formula for wavelength
The speed of electromagnetic waves (light) in a vacuum is approximately \( C = 3 \times 10^8 \text{ m/s} \). The relationship between speed, frequency, and wavelength is given by:
\[ C = \text{frequency} \times \text{wavelength} \]
From this, we can derive the wavelength (\( \lambda \)):
\[ \lambda = \frac{C}{\text{frequency}} \]

### Step 3: Substitute the values into the wavelength formula
Substituting the values we have:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{20 \times 10^6 \text{ Hz}} \]

### Step 4: Calculate the wavelength
Now, performing the calculation:
\[ \lambda = \frac{3 \times 10^8}{20 \times 10^6} = \frac{3}{20} \times 10^2 = 0.15 \times 10^2 = 15 \text{ m} \]

### Step 5: Calculate the length of the quarter wave antenna
The length of a quarter wave antenna (\( L \)) is given by:
\[ L = \frac{\lambda}{4} \]
Substituting the value of \( \lambda \):
\[ L = \frac{15 \text{ m}}{4} = 3.75 \text{ m} \]

### Final Answer
The length of the quarter wave antenna for a transmission frequency of 20 MHz is **3.75 meters**.

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