A mobile base station in an urban environment has a power measurement of 25 µW at 225 m. If the propagation follows an inverse 4th-power law (Section 3.2.2), assuming a distance of 0.9 km from the base station, what would be a reasonable power value, in µW? Express your answer in scientific notation to 2 decimal place
I am curious why the propagation of EM (radio) waves from a mobile base station in an urban (or any) environment would follow an inverse 4th-power law, instead of the inverse square law that is typically associated with EM wave propagation.
Perhaps “Section 3.2.2” might give some context for its use in this case. Normally, the inverse 4th-power law is used as a baseline for EM waves reflected back to a radar transmitter, or as a baseline to correct errors in time-domain reflectometry measurements. There may be other uses; even so, this hypothetical question appears inconsistent with the physics equations relating energy densities over distance.
At this point, I assume the mathematician who created the text book question was unfamiliar with the correct application of the related physics equations, and chose an inconsistent scenario as an application for a hypothetical question using inverse 4th-power law.
If there is an alternative, I’d really like to know what it is.......
How many mathematicians does it take to change a light bulb? How many physicists? How many engineers?