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Why does the two ray model predict a fourth power law at long range?

  • A.The atmosphere absorbs the signal more strongly at long distances
  • B.The reflected ray is attenuated twice by the ground surface
  • C.The antennas' effective apertures shrink as the range increases
  • D.The direct and reflected rays nearly cancel, leaving a small difference

Answer: D

At grazing incidence the reflection coefficient approaches minus one, so the two rays almost cancel and what survives is proportional to the small path difference, which itself falls with range, giving an inverse fourth power law rather than an inverse square. That is why coverage falls off so sharply beyond a certain distance. Absorption, double attenuation and aperture are not the mechanism. A near cancellation leaving a small residue is a common source of unexpectedly steep power laws.

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