A ground receiver station is receiving a signal at 500 MHz transmitted from a ground transmitter at a height of 300 m located at a distance of 500 km. It is coming via

Options

A. Ground wave
B. Space wave
C. Sky wave
D. Satellite communication

Answer

To solve the problem of determining the type of communication used for a signal transmitted from a ground transmitter, we will analyze the given parameters step by step.

### Step 1: Identify the Given Information
- Frequency of the signal: \( f = 500 \, \text{MHz} \)
- Height of the transmitter: \( h = 300 \, \text{m} \)
- Distance from the transmitter to the receiver: \( d = 500 \, \text{km} \)

### Step 2: Determine the Frequency Range for Each Communication Type
1. **Ground Wave:** Used for frequencies less than \( 2 \, \text{MHz} \).
2. **Space Wave:** Used for frequencies greater than \( 30 \, \text{MHz} \).
3. **Sky Wave:** Used for frequencies between \( 2 \, \text{MHz} \) and \( 20 \, \text{MHz} \).
4. **Satellite Communication:** Also used for frequencies greater than \( 30 \, \text{MHz} \).

### Step 3: Analyze the Frequency of the Signal
Since the frequency of the signal is \( 500 \, \text{MHz} \), we can eliminate the ground wave and sky wave options because they do not cover this frequency range. This leaves us with:
- Space Wave
- Satellite Communication

### Step 4: Calculate the Range for Space Wave Communication
The range \( R \) for space wave communication can be calculated using the formula:
\[ R = \sqrt{2 \cdot h \cdot R_e} \]
where \( R_e \) is the radius of the Earth, approximately \( 6.4 \times 10^6 \, \text{m} \).

Substituting the values:
\[ R = \sqrt{2 \cdot 300 \, \text{m} \cdot 6.4 \times 10^6 \, \text{m}} \]
Calculating this step-by-step:
1. Calculate \( 2 \cdot 300 = 600 \).
2. Calculate \( 600 \cdot 6.4 \times 10^6 = 3.84 \times 10^9 \).
3. Now take the square root:
\[ R = \sqrt{3.84 \times 10^9} \approx 62000 \, \text{m} = 62 \, \text{km} \]

### Step 5: Compare the Calculated Range with the Distance
The calculated range for space wave communication is \( 62 \, \text{km} \), while the distance to the receiver is \( 500 \, \text{km} \). Since \( 62 \, \text{km} < 500 \, \text{km} \), space wave communication is not suitable.

### Step 6: Conclusion
Since the only remaining option is satellite communication, we conclude that the signal is coming via **satellite communication**.

### Final Answer
The signal is coming via **satellite communication**.

---