Inverse Power Law: Solve for Power at 400m

[mrdman]

Homework Statement

If the power at 100m is 5W, using inverse 2.5 power law, find the power at 400m.

Relevant Equations

1 / d ^ x

Hi everyone! Awesome forum!
I'm doubting myself on a problem about inverse square law.
I'll change the actual values from my homework problem as I want to check that I have the right idea rather than the specific numeric answer.

If I am using an inverse 2.5 power law and know the power at 100m is 5W.. If I want to find out the power at 400m, is the following correct...?

100m: 5W
200m: 5 * 1/2 ^ 2.5
300m: 5 * 1/3 ^ 2.5
400m: 5 * 1/4 ^ 2.5

So the answer will be: 5 * (0.25)^2.5
Which is 5 * 0.03125 = 0.15625W

I've had three attempts so far and keep getting varying answers each time!

 

[mjc123]

Looks right to me.

 

[mrdman]

Awesome! Many thanks.

 

[berkeman]

Homework Statement: If the power at 100m is 5W, using inverse 2.5 power law, find the power at 400m.
Homework Equations: 1 / d ^ x

If I am using an inverse 2.5 power law

Sorry for my dumb question, but this seems a bit confusing to me. There are two kinds of "power" that seem to be getting mixed in this question.

There is the decrease in radiant power from a source, which varies as the inverse of the distance squared (not to the power 2.5).

And there is the "power law" which refers to when a quantity varies with a constant exponent relationship:

https://en.wikipedia.org/wiki/Power_law

The constant exponent does not have to be "2" in general, and varies depending on the phenomena being described by the equation.

To me, it is very confusing to mix both concepts together in this question. It implies that somehow radiant power can drop off by the exponent 2.5 instead of 2. In the far field at least, I don't think that can happen. Can it?

 

[mrdman]

Hi.. I'm not 100% sure but it may help if I explained the context in which I am doing this calculation.
It is regarding power loss from a cell tower in a city environment. In this environment inverse square law doesn't work out in practice (city obstacles etc) so we were told to use 3.5 power law (I may be getting my terms mixed up. Is it called 3.5 power law?) Above in my example I changed it to 2.5 and changed all the values so I didn't get help with the specific answer, but rather the concept of how to solve it.

Hope that helps and I've not mixed up terms too much.