Radio Receiver problem (Path length difference)

In summary, a satellite signal has a wavelength that is twice as long at 6 degrees above the horizon as it is at 3 degrees.
  • #1
lemonlimesoap
4
0

Homework Statement



A radio receiver is set up on a mast in the middle of a calm lake to track the radio signal from a satellite orbiting the Earth. As the satellite rises above the horizon, the intensity of the signal varies periodically. The intensity is at a maximum when the satellite is 1 = 3° above the horizon and then again at 2 = 6° above the horizon. What is the wavelength of the satellite signal? The receiver is h = 4.0 m above the lake surface.

Homework Equations



r=dsin(theta)
(theta)m = m*(lambda/d)
y=L*tan(theta)

ym = (m*lambda*L)/d

The Attempt at a Solution


i know that the radio signal acts like light as it is reflected off the lake and the signal path length difference of the signal directly and the signal off the lake will give me the path length difference but the lambda solution i got was off according to my teacher.
 
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  • #2
Interesting problem. I had no idea how to approach it until you mentioned the reflected waves constructively interfering with the direct waves. So, no diffraction involved, just a matter of finding the hypotenuse of a triangle. Did you get about 75 m for the wavelength? I don't follow your equations, don't know what n, L, theta, ym and d are.
 
  • #3
Show your work, please, with a drawing attached.

ehild
 
  • #4
Delphi51 said:
Did you get about 75 m for the wavelength? I don't follow your equations, don't know what n, L, theta, ym and d are.
There are enough data given. The two angles belong to consecutive maxima. The incoming light beam can be considered parallel as the satellite is very far away. The path difference between the directly incident ray and the reflected ray has to be calculated at the given angles, see picture.

ehild
 

Attachments

  • mast.JPG
    mast.JPG
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  • #5
Thanks again, ehild. I had the diagram but forgot to subtract AB from AC.
The path difference works out to a wavelength of about 40 cm at 3 degrees and exactly twice as much at 6 degrees.
 
  • #6
"The intensity is at a maximum when the satellite is 1 = 3° above the horizon and then again at 2 = 6° above the horizon"

The path difference is equal to m*lambda for the first angle and (m+1)*lambda for the next one. :)

ehild
 

1. What is a radio receiver problem and how does it occur?

A radio receiver problem is a phenomenon that occurs when there is a difference in the length of the path that a radio signal takes to reach the receiver. This can happen due to various factors such as atmospheric conditions, obstructions in the signal path, or errors in the receiver's location. It results in a time difference between the arrival of the direct and reflected signals, causing distortion or interference in the received signal.

2. How does the path length difference affect the quality of the received signal?

The path length difference can cause multipath interference, where the direct and reflected signals arrive at the receiver at slightly different times. This results in overlapping signals, causing distortion, and reducing the signal strength. As a result, the quality of the received signal may decrease, leading to poor reception or complete loss of signal.

3. What are the common solutions to mitigate the radio receiver problem?

One solution is to improve the positioning of the receiver to minimize the path length difference. This can be achieved by using a higher antenna or placing the receiver in an open area with minimal obstructions. Another solution is to use directional antennas that focus on receiving signals from a specific direction, reducing the impact of multipath interference.

4. Can the radio receiver problem be completely eliminated?

No, it cannot be completely eliminated as it is a natural phenomenon caused by various factors. However, it can be minimized by using advanced technologies such as signal processing techniques, adaptive antennas, and error correction algorithms.

5. How does the radio receiver problem affect different types of radio signals?

The impact of the radio receiver problem varies depending on the type of radio signal. For example, analog signals may experience distortion, while digital signals may have errors in the received data. Additionally, high-frequency signals are more prone to path length difference due to their shorter wavelengths, while lower-frequency signals may be less affected.

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