To transmit a signal of 3 KHz frequency, the minimum length of antenna is ______ km

Options

A. 20
B. 25
C. 50
D. 75

Explanation

To find the minimum length of an antenna required to transmit a signal of 3 kHz frequency, we can follow these steps:

### Step 1: Convert Frequency to Hertz
The given frequency is 3 kHz. We convert this to hertz:
\[ \text{Frequency} (f) = 3 \text{ kHz} = 3 \times 10^3 \text{ Hz} \]

### Step 2: Use the Wavelength Formula
The wavelength (\(\lambda\)) can be calculated using the formula:
\[ \lambda = \frac{C}{f} \]
where:
- \(C\) is the speed of light, approximately \(3 \times 10^8 \text{ m/s}\)
- \(f\) is the frequency in hertz.

Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{3 \times 10^3 \text{ Hz}} = 10^5 \text{ m} \]

### Step 3: Calculate Minimum Length of Antenna
The minimum length of the antenna (\(L\)) is given by:
\[ L = \frac{\lambda}{4} \]
Substituting the value of \(\lambda\):
\[ L = \frac{10^5 \text{ m}}{4} = 2.5 \times 10^4 \text{ m} \]

### Step 4: Convert Length to Kilometers
To convert meters to kilometers, we divide by 1000:
\[ L = \frac{2.5 \times 10^4 \text{ m}}{1000} = 25 \text{ km} \]

### Final Answer
The minimum length of the antenna required to transmit a signal of 3 kHz frequency is:
\[ \text{Minimum length of antenna} = 25 \text{ km} \]

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