In the space wave propagation of radio waves if the height of both the antennas is h and the radius of the earth is R, then the maximum line of sight distance is equal to the:

  1. 2Rh
  2. \(\sqrt{2Rh}\)
  3. \(2\sqrt{2Rh}\)
  4. None of these

Answer (Detailed Solution Below)

Option 3 : \(2\sqrt{2Rh}\)
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Detailed Solution

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CONCEPT:

Space wave communication:

  • A space wave travels in a straight line from the transmitting antenna to the receiving antenna.
  • Space waves are used for line-of-sight (LOS) communication as well as satellite communication.
  • At frequencies above 40 MHz, communication is essentially limited to line-of-sight paths.
  • At these frequencies, the antennas are relatively smaller and can be placed at heights of many wavelengths above the ground.
  • Because of the line-of-sight nature of propagation, direct waves get blocked at some point by the curvature of the earth as illustrated in the figure.
  • If the signal is to be received beyond the horizon then the receiving antenna must be high enough to intercept the line-of-sight waves.

F1 Prabhu.Y 27-08-21 Savita D3

  • The maximum line-of-sight distance dM between the two antennas having heights hT and hR above the earth is given by,

\(\Rightarrow d_M=\sqrt{2Rh_T}+\sqrt{2Rh_R}\)

Where R = radius of the earth

EXPLANATION:

Given hT = hR = h

  • The maximum line-of-sight distance dM between the two antennas having heights hT and hR above the earth is given by,

\(\Rightarrow d_M=\sqrt{2Rh_T}+\sqrt{2Rh_R}\)

\(\Rightarrow d_M=\sqrt{2Rh}+\sqrt{2Rh}\)

\(\Rightarrow d_M=2\sqrt{2Rh}\)

  • Hence, option 3 is correct.
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