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:

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.

• The maximum line-of-sight distance d_M between the two antennas having heights h_T and h_R above the earth is given by,

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

Where R = radius of the earth

EXPLANATION:

Given h_T = h_R = 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.