Question

If the height of the tower used for LOS communication is increased by 21%, the percentage change in range is?

• A. 5%
• B. 10%
• C. 15%
• D. 12%

Answer 1

The Correct Option is B

To determine the percentage change in range when the height of a tower used for LOS (Line of Sight) communication is increased, we need to use the formula for the range of LOS communication:

\(d = \sqrt{2Rh}\)

where:

• \(d\) is the distance or range of communication.
• \(R\) is the radius of the Earth (approximately 6400 km).
• \(h\) is the height of the tower.

When the height \(h\) is increased by 21%, the new height \(h'\) will be:

\(h' = 1.21h\)

The initial range \(d_1\) is given by:

\(d_1 = \sqrt{2Rh}\)

The new range \(d_2\) with the increased height will be:

\(d_2 = \sqrt{2R \cdot 1.21h} = \sqrt{1.21} \cdot \sqrt{2Rh}\)

Therefore, the new range \(d_2\) is:

\(d_2 = \sqrt{1.21} \cdot d_1\)

Since \(\sqrt{1.21} \approx 1.1\), this means the range also increases by approximately 10%.

Therefore, the percentage change in range is 10%. This matches the correct option.