After experimenting with varying the distance between a router and a computer, the signal strength formed a graph similar to the one below:


My theory as to why it decreases is that, as Wifi is being transmited from a point, it spreads out and the signal density (right term?) decreases.

However, I'm not sure, so:

  1. Why does signal strength decrease with distance?
  2. Why does it form a negative logarithmic graph?
  • $\begingroup$ Are you aware that your loss scale is already in dB, which is not linear to the inpit signal? Also, you might have a look at this post physics.stackexchange.com/questions/19642/… $\endgroup$ – user_na Aug 6 '17 at 9:01
  • $\begingroup$ The output on my computer was in dBm, but, as you pointed out, that is also logarithmic. Thank you :) @user_na $\endgroup$ – George Tian Aug 6 '17 at 9:03

Electromagnetic waves' intensities fall as $1/r^2$ assuming nothing gets in the way, but the geometry of the place you did this experiment will give a more complicated dependence that's unlikely to be a function of $r$ alone. If an exponential decay occurred, it would look linear when you plot decibels against distance, because the decibel scale is logarithmic. Your data show the decline in decibels slowing, i.e. the decay isn't quite exponential. I recommend plotting decibels against log-distance (or $e$^decibels against distance, but that would lead to too many orders of magnitude on the axes), which on an inverse-square model should become a straight line of gradient $-2$ assuming you take logarithms "the same way" for distance as for decibels. By this I mean multiplication by 10 should add 10 points, so the base of the logarithm would be $10^{0.1}$. Working instead with base-$e$ ("natural") logarithms, we expect a straight line of gradient $-\frac{20}{\ln 10}$ since multiplication by 10 would only add $\ln 10$ points.

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