signal strength of wireless transmission ~ 1/ r^3

[Osawa_Odessa]

I wonder if the statement is true.
The signal strength of wireless transmission attenuates very rapidly - at a rate of 1/r^3 where r is the distance)
I think it should be 1/r^2 because both electric and magnetic field are directly proportional to 1/r.
Can you give your opinion?

 

[albbg]

The electromagnetic fields behaves in a complete different way depending on how you are observing it close to the antenna. Roughly you can divide the space into two regions: "near-field" and "far-field".

In the near-field zone, the form of magnetic (H) and electric (E) fields is very complex and is not easy at all to determine how they behaves and also calculate the Poynting vector (it should also be function of time). However, for a an Herzian dipole, H should decay as 1/r^2 while E at a rate of 1/r^3.
In far field, instead, both will decay as 1/r, then as you said, the power will follows 1/r^2.

 

[nschutten]

In addition to the above: in the far field, signal strength is indeed proportional to 1/r^2, but note that this is under open space conditions. In e.g. indoor environments, signal strength may drop off at a higher order (e.g. 1/r^2.5 or 1/r^3).