Question

A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode? (Radius of earth = 6400 km)

Answer 1

The maximum line-of-sight distance dMdM between two antennas having heights hThT and hRhR above the earth is given by dM=2RhT−−−−−√+2RhR−−−−−√dM=2RhT+2RhR where hThT and hRhR are the heights of the transmitting and receiving antennae.
Substituing, we get: dM=2×64×105×32−−−−−−−−−−−−−−√+2 times64×105×50−−−−−−−−−−−−−−−−−√mdM=2×64×105×32+2 times64×105×50m
dM=64×10210−−√+8×103×10−−√mdM=64×10210+8×103×10m
=144×102×10−−√m=45.5km

Answer 2

Answer:

The maximum distance between the two antennas for satisfactory communication in the LOS mode is approximately 10256.68 meters (or 10.26 km).

Explanation:

To calculate the maximum distance between the two antennas for Line-of-Sight (LOS) communication, we can use the formula:

$d = \sqrt{2Rh}$

where d is the maximum distance between the two antennas, R is the radius of the earth, and h is the sum of the heights of the two antennas.

Here, R = 6400 km, h = 36 m + 49 m = 85 m.

Substituting these values in the formula, we get:

$d = \sqrt{2 \times 6400 \times 85} \approx 10256.68\text{ m}$

Therefore, the maximum distance between the two antennas for satisfactory communication in the LOS mode is approximately 10256.68 meters (or 10.26 km).

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