Answer:
The reasonable value = 2.96 × 10^(-1) µW
Step-by-step explanation:
* Lets explain how to solve the problem
- A mobile base station in an urban environment has a power
measurement of 8 µW at 225 m
- The propagation follows an inverse cube power law
- We need to find the reasonable value to assume at a distance
678 m from the base station
∵ The propagation follows an inverse cube power law
- The power would have been decreased by a factor 1/n³
times the power as a distance increasing
∵ n = the ratio between the distances
∵ The distance are 675 m and 225
∴ n = 675/225 = 3
∴ 1/n³ = 1/3³ = 1/27
- The reasonable value is the product of the power measurement of
8 µW and 1/27
∴ The reasonable value = 8 × 1/27 = 8/27 µW = 0.296296
∴ The reasonable value = 2.96 × 10^(-1) µW
The reasonable value to assume the distance 675m from the BS is [tex]\mathbf{=2.963 \times 10^{-1} \ \mu W}[/tex]
The inverse of any given value refers to the reciprocal of the value.
Let consider that "a" is an inverse of "b"; this can be mathematically expressed as:
[tex]\mathbf{b = \dfrac{1}{a}}[/tex]
Now, from the given question;
The propagation follows an inverse cube power law such that:
[tex]\mathbf{P = \dfrac{1}{n^3}}[/tex]
where;
n = ratio between two distance
[tex]\mathbf{=\dfrac{675 \ m}{225 \ m}}[/tex]
= 3 m
∴
[tex]\mathbf{P = \dfrac{1}{3^3}}[/tex]
[tex]\mathbf{P = \dfrac{1}{27}}[/tex]
Finally, the reasonable value is the product of the power measurement at 8µW with the propagation;
[tex]\mathbf{= 8 \mu W \times \dfrac{1}{27}}[/tex]
[tex]\mathbf{= \dfrac{ 8 \mu W}{27}}[/tex]
[tex]\mathbf{=0.2963 \ \mu W}[/tex]
In scientific notation, it becomes:
[tex]\mathbf{=2.963 \times 10^{-1} \ \mu W}[/tex]
Learn more about inverse law here:
https://brainly.com/question/9953034
