An information signal of 150 MHz to be sent across a distance of 40 km. Which mode of communication is suitable?

Options

A. Ground wave propagation
B. Space wave propagation
C. sky wave propagation
D. Satellite communication

Answer

To determine the suitable mode of communication for transmitting an information signal of 150 MHz across a distance of 40 km, we can follow these steps:

### Step 1: Identify the Frequency Range
The given frequency of the information signal is 150 MHz. We need to categorize this frequency into the appropriate mode of communication based on established frequency ranges.

### Step 2: Analyze the Modes of Communication
The modes of communication and their frequency ranges are as follows:
- **Ground Wave Propagation**: Frequencies less than 2 MHz.
- **Sky Wave Propagation**: Frequencies between 2 MHz and 30 MHz.
- **Space Wave Propagation**: Frequencies greater than 30 MHz.
- **Satellite Communication**: Frequencies above 30 MHz (can also transmit in GHz).

### Step 3: Determine Applicable Modes
Since 150 MHz is greater than 30 MHz, it falls under both **Space Wave Propagation** and **Satellite Communication**.

### Step 4: Evaluate the Distance
Next, we need to evaluate whether the distance of 40 km can be effectively covered by either of these modes.

### Step 5: Calculate the Maximum Range for Space Wave Propagation
For space wave propagation, the maximum range can be calculated using the formula:
\[ r = \sqrt{2h \cdot R_e} \]
Where:
- \( r \) = range (in meters)
- \( h \) = height of the antenna (in meters)
- \( R_e \) = radius of the Earth (approximately \( 6.4 \times 10^6 \) meters)

### Step 6: Set Up the Equation
We set \( r = 40 \, \text{km} = 40000 \, \text{m} \):
\[ 40000 = \sqrt{2h \cdot 6.4 \times 10^6} \]

### Step 7: Solve for Height \( h \)
Squaring both sides:
\[ 40000^2 = 2h \cdot 6.4 \times 10^6 \]
\[ 1600000000 = 12.8h \times 10^6 \]
\[ h = \frac{1600000000}{12.8 \times 10^6} \]
\[ h = 125 \, \text{m} \]

### Step 8: Conclusion
The calculated height of the antenna (125 m) is achievable, which means that space wave propagation is suitable for transmitting the signal over a distance of 40 km.

Thus, the suitable mode of communication is **Space Wave Propagation**.

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