Question

In communication with the help of antenna, the range covered (for the line of sight propagation) is initially \(d\). If the height of antenna is doubled, the range covered would become

• A. \(3d\)
• B. \(\sqrt{2}\,d\)
• C. \(4d\)
• D. \(2d\)

Hint:

In line-of-sight communication, range varies as the square root of antenna height.

Answer 1

The Correct Option is B

Step 1: Relation between range and height of antenna.
For line of sight communication, the range is given by:
\[ d = \sqrt{2Rh} \] where \(R\) is the radius of the earth and \(h\) is the height of antenna.

Step 2: Initial range.
\[ d_1 = \sqrt{2Rh} \]
Step 3: New height of antenna.
When height is doubled:
\[ h' = 2h \]
Step 4: New range.
\[ d_2 = \sqrt{2R(2h)} = \sqrt{2}\sqrt{2Rh} \]
Step 5: Express in terms of original range.
\[ d_2 = \sqrt{2}\,d \]
Step 6: Conclusion.
The new range becomes \(\sqrt{2}\,d\).