Question

In communication system, the range for line of sight propagation in case of earth is \( d \), for the height of antenna \( h \). If \( h \) is doubled then the new range is

• A. \( \frac{d}{\sqrt{2}} \)
• B. \( \frac{\sqrt{2}}{d} \)
• C. \( \frac{d}{2} \)
• D. \( \sqrt{2} \, d \)

Hint:

Doubling the height of the antenna increases the range by a factor of \( \sqrt{2} \).

Answer 1

The Correct Option is D

Step 1: Understanding the relation between range and height.
The range \( d \) for line of sight propagation depends on the height \( h \) of the antenna, and it is given by \( d = \sqrt{2Rh} \), where \( R \) is the radius of the Earth. If the height of the antenna is doubled, the new range becomes \( d_{\text{new}} = \sqrt{2R \cdot 2h} = \sqrt{2} \cdot \sqrt{2Rh} = \sqrt{2} \cdot d \).
Step 2: Conclusion.
Thus, the new range is \( \sqrt{2} \, d \), which corresponds to option (D).