Loss of signal power in radio and wire transmission

[Jncik]

Homework Statement

For radio transmission in free space, signal power is reduced in proportion to the square
of the distance from the source, whereas in wire transmission, the attenuation is a fixed
number of dB per kilometer.

The Attempt at a Solution

this is not the whole problem

what i want to ask is when it says that the signal power is reduced in proportion to the square of the distance from the source does it mean that

if we have a distance of 1 and a signal loss of -6 db

then for distance 3 we will have a signal loss of -6*3^2 db?

and for wire it will be just -6*3?

 

[mark726]

I can confirm that the statement about signal power reduction in free space is accurate. This phenomenon is known as the inverse square law and it applies to all forms of electromagnetic radiation, including radio waves. The formula for this is P = P0/(4πr^2), where P is the signal power at a certain distance (r) from the source and P0 is the original power at the source. This means that as the distance increases, the signal power decreases exponentially.

To answer your question, yes, if the signal loss is -6 dB at a distance of 1, it would be -6*(3^2) = -54 dB at a distance of 3. This is because the signal power is decreasing by a factor of 9 (3^2) for every 1 unit increase in distance.

In contrast, for wire transmission, the attenuation is a fixed number of dB per kilometer. This means that for every kilometer the signal travels, it will decrease by a certain amount, regardless of the initial distance. So for a distance of 3 kilometers, the signal loss would simply be -6*3 = -18 dB.

It's important to keep in mind that these calculations are simplified and do not take into account other factors that can affect signal power, such as obstacles or interference. But in general, the inverse square law applies to free space transmission while a fixed attenuation applies to wire transmission. I hope this helps clarify the difference between the two types of transmission.