The Physics
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Opus in profectus

Doppler Effect (Light)

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Problems

practice

  1. There are hundreds if not thousands of television stations across North America that claim to use "doppler radar" when reporting weather related news. In keeping with the general level of hype that is Twenty-first Century TV weather, most if not all of these stations never show actual doppler radar images in their broadcasts. Instead, what they show are reflectivity images. A radar pulse is sent out, the strength of the echo is measured, and the results are displayed as a certain color that indicates the intensity of precipitation. A typical color code would be green for light rain, yellow for moderate, red for intense, and so on.

    A real doppler radar image like the one below shows something different. In this mode, a radar pulse is sent out, the frequency of the echo is measured, and the results are displayed as a certain color that indicates the velocity of the precipitation. The colors are often assigned in a manner that imitates the color shifts seen when the doppler effect is applied to visible light — red, orange, and yellow for raindrops blowing away from the radar antenna and green, blue, and violet for raindrops blowing toward the radar antenna. (Color assignments vary from one radar system to another, however, so these are not absolute rules.)

    Color doppler radar image

    The image above was taken from the NOAA National Weather Service radar station in Dodge City, Kansas on 7 May 2007 that was operating in doppler mode.

    1. What was the direction of the wind at the radar site in Dodge City (located near the upper left hand corner of the image)?
    2. There is an unusual two-color region located in the center of this image just to the southwest of a small town called Greensburg.
      1. What is the wind direction in the blue region?
      2. What is the wind direction in the red region?
      3. What is the overall airflow pattern in this unusual two-color region?
      4. What is probably going on here?

    (Note: Wind direction indicates where the wind is coming from, not where the wind is going to.)

  2. Use this variation of the doppler effect equation…
     
    Δλ  ≈ ±  v  = ±  speed of source relative to observer
    λ c speed of sound

    to answer this set of related questions…

    1. How fast and in what direction would a car have to move to make a yellow traffic light (580 nm) appear green (530 nm)?
    2. How fast and in what direction would a car have to move to make a red traffic light (680 nm) appear green (530 nm)?
    3. "I swear I saw a green light. The doppler efffect must have made it look green. You shouldn't give me a ticket for running a red light. It's not my fault. You should give a ticket to Christian Doppler." Would this reasoning get you out of a traffic ticket?
  3. Write something different.
  4. Write something completely different.

conceptual

  1. When viewed from the northern hemisphere of the Earth, light coming from the left side of the sun is seen to have a slightly shorter wavelength than the light from the right side. (The situation is reversed when the sun is viewed from the southern hemisphere.) What do these observations tell you about the sun?