Question

If the sum of heights of transmitting and receiving antennas in line of sight communication is \(h\), then the height of receiving antenna, to have the range maximum is

• A. \(\frac{h}{2}\)
• B. \(\frac{h}{4}\)
• C. \(2h\)
• D. \(\frac{2h}{3}\)

Hint:

Maximum line of sight range is achieved when both antenna heights are equal.

Answer 1

The Correct Option is A

Step 1: Understand line of sight communication
The range \(R\) depends on heights of transmitting \(h_t\) and receiving \(h_r\) antennas: \[ R \propto \sqrt{h_t} + \sqrt{h_r} \] Step 2: Given total height
\[ h = h_t + h_r \] Step 3: Maximize range
To maximize \(R\) under constraint \(h_t + h_r = h\), use calculus or AM-GM inequality, maximum when \[ h_t = h_r = \frac{h}{2} \] Step 4: Conclusion
Height of receiving antenna should be \(\frac{h}{2}\) for maximum range.