Question

The height of a transmitting antenna is 320 m and the height of a receiving antenna is 20 m. The maximum distance between them for satisfactory communication in LOS mode is:

• A. 16 km
• B. 64 km
• C. 80 km
• D. 45.5 km

Hint:

In LOS communication, the distance depends on the heights of both antennas and the radius of the earth. Higher antenna heights increase the maximum communication distance.

Answer 1

The Correct Option is C

The maximum distance between two antennas for Line of Sight (LOS) communication is given by: \[ d = \sqrt{2 R h_1} + \sqrt{2 R h_2} \] Where: - \( d \) is the maximum distance
- \( R \) is the radius of the earth (6400 km)
- \( h_1 \) is the height of the transmitting antenna (320 m = 0.32 km)
- \( h_2 \) is the height of the receiving antenna (20 m = 0.02 km)
Substitute the given values into the formula: \[ d = \sqrt{2 \times 6400 \times 0.32} + \sqrt{2 \times 6400 \times 0.02} \] \[ d = \sqrt{4096} + \sqrt{256} \] \[ d = 64 + 16 = 80 \, \text{km} \] Thus, the maximum distance between the two antennas for satisfactory communication is 80 km.