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
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
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Maximum line of sight range is achieved when both antenna heights are equal.
Updated On: Mar 18, 2026
- \(\frac{h}{2}\)
- \(\frac{h}{4}\)
- \(2h\)
- \(\frac{2h}{3}\)
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The Correct Option is A
Solution and Explanation
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.
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.
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