Question

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, assuming a distance of 0.9 km from the base station, what would be a reasonable power value, in µW?

Give your answer in scientific notation to 2 decimal places

Answer 1

The answer is below

Step-by-step explanation:

The inverse fourth power law states that the intensity varies inversely to the fourth power of the distance from the source. That is as the distance increases, the intensity decreases.

Let I represent the intensity and let d represent the distance from the source, hence:

I ∝ 1 / d⁴

I = k / d⁴

Where k is the constant of proportionality.

Given that at a power of 25W = 25*10⁻⁶ W, the distance (d) = 225 m. We can find the value of k.

25*10⁻⁶ = k / 225⁴

k = 225⁴ * 25*10⁻⁶ = 64072.27

Hence:

I = 64072.27 / d⁴

At a distance (d) = 0.9km = 900 m, we can find the corresponding power:

I = 64072.27 / 900⁴

I = 9.77 * 10⁻⁸ W