Free-Space Path Loss Equation - finding the constant for d in km and f in MHz?

HzIn summary, the conversation discusses transforming equation 1 into equation 2 to show their equivalence. The homework equations for this problem are also mentioned, with a note about adding subscripts for units. The person attempting the solution has a highlighted constant that should be 32.45, according to their notes and Wikipedia. The conversation also touches on the properties of logarithms and a potential error in the conversion of units in equation 2.
  • #1
Phazall
2
0
1. Problem Statement
Transform equation 1 into equation 2 to show they're equivalent.


Homework Equations


relevent equations.png

*Please note that I added a subscript to each variable indicating the units.

The Attempt at a Solution


the attempt at the solution.png



The highlighted constant shown in my attempt at the solution is supposed to be 32.45 according to both my notes and wikipedia http://en.wikipedia.org/wiki/Free-space_path_loss.

Thank you very much!
 
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  • #2
log(ab) = log a + log b
log(abc) = log a + log b + log c
log(a/b) = log a - log b.
Etc.
OK I see you already know that.

I can't make out your writing but in your eq. 2, λm should = cm/fHz. Maybe that's where your problem lies.

I would have started by converting the original argument of the log function into the units
they want you to wind up with, but your way works too,
 
Last edited:

1. How is the Free-Space Path Loss Equation used in scientific research?

The Free-Space Path Loss Equation is used to calculate the signal loss that occurs when a signal travels through free space, without any obstacles or interference. This is important in scientific research as it helps to determine the strength and quality of a signal at a given distance and frequency.

2. What is the constant in the Free-Space Path Loss Equation and why is it important?

The constant in the Free-Space Path Loss Equation is known as the path loss exponent, denoted as "n". This constant takes into account the environmental factors and characteristics of the signal, such as frequency and distance. It is important because it allows for accurate calculations of signal strength and loss over varying distances and frequencies.

3. How do you find the constant for distance (d) in kilometers and frequency (f) in megahertz in the Free-Space Path Loss Equation?

The constant can be found by using a formula that takes into account the distance (d) in kilometers and frequency (f) in megahertz. This formula is n = 20log(d) + 20log(f) - 27.55. By plugging in the appropriate values for d and f, the constant can be calculated.

4. Can the Free-Space Path Loss Equation be applied to all types of signals and frequencies?

While the Free-Space Path Loss Equation is commonly used for radio frequency signals, it can also be applied to other types of signals such as light and sound waves. However, the equation may need to be modified in order to account for differences in the characteristics of these signals.

5. How does the distance and frequency affect the path loss in the Free-Space Path Loss Equation?

The distance and frequency both have a significant impact on the path loss in the Free-Space Path Loss Equation. As distance increases, the path loss also increases, meaning that the signal strength decreases. Similarly, as frequency increases, the path loss also increases, resulting in a weaker signal at a given distance.

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