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

\(d=\sqrt{2Rh}, d\propto \sqrt{h}\)
\(d'\propto \sqrt{1.21h} = 1.1h\)
Percentage change in d = 10% 

So, the correct option is (B): 10%

Answer 2

For Line-of-Sight (LOS) communication, the range of communication is given by:
\(R = \sqrt{(2 \times h \times d)}\)
where h is the height of the tower and d is the distance to the horizon.
Let's assume that the original height of the tower is h and the original range of communication is R. If the height of the tower is increased by 21%, the new height of the tower is 1.21h. The new range of communication is:
\(R' = \sqrt{(2 \times 1.21h \times d)} = \sqrt{(1.21)} \times \sqrt{(2 \times h \times d)} = 1.1 \times R\)
So the percentage change in range is:
\(\frac{(1.1R - R)}{R}\times100% = 0.1R / R * 100% = 10%\)
Therefore, the percentage change in range when the height of the tower is increased by 21% is 10%.
Hence, the correct option is (B): 10%.