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class code: SPS22 teacher: Mr. Elert
classroom: A314 office: A214
test day: Friday phone: (718) 724–8500 ext. 2141
email: elert@midwoodscience.org

Physics A: Problem Set 13: Doppler Effect

recommended reading

Barron's Let's Review: 11.11 Doppler Effect
physics.info: Doppler Effect (Sound), Doppler Effect (Light)
Wikipedia: Doppler effect
HyperPhysics: Doppler Effect
Khan Academy: Introduction to the doppler effect
YouTube: The Doppler Effect

classwork

  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.)

    1. The wind at Dodge City is blowing from the east to the west.
    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. The wind in the blue region is blowing from the southeast to the northwest.
      2. The wind in the red region is blowing from the northwest to the southeast.
      3. The air in the two color region is circulating counterclockwise.
      4. There is a tornado at the center of this region.

homework

  1. Bats use echolocation to visualize their world. They send out ultrasonic squeaks from their little bat mouths and then listen for the echos with their giant bat ears. The characteristics of the echo will vary depending on the characteristics of the object reflecting the squeak.
    1. How will the echo from a large object (like a tree trunk) compare to a small one (like a tasty insect)?
    2. How will the echo from an object moving away from the bat (like an escaping insect) compare to one from an object moving toward the bat (like an insect about to become lunch)?
    1. An echo from a large object will have a greater amplitude or intensity than an echo from a small object. Intensity and amplitude are measureable quanitites with physical meaning, which makes that last sentence a good answer to this question. In human terms, an echo from a large object would be louder than an echo from a small object, but loudness is a perceptual term that might not make sense to a bat. Bats don't use echolocation like we use hearing. For them, it is probably more like sight is to us. A bat might say something like a tree "sounds bigger" than an insect like we sould say a tree "looks bigger" than an insect. Likewise, a bat would probably not say a tree "sounds louder" anymore than we would say a tree "looks brighter". When bats acquire speech, someone needs to ask them about this.
    2. The echo from an object moving away from the bat would have a lower frequency than an object moving toward the bat. Humans call the frequency of a sound its pitch. Whether bats have a concept of pitch or not is open to discussion. (Discuss it on your own time.)
  2. 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?
    The left side of the sun (the side with the higher frequency light) is moving toward the earth. The right side (the side with the lower frequency) is moving away from the earth. The sun is moving, but it isn't going anywhere — not going anywhere relative to the earth, that is. It's not getting closer or farther. It's not moving north, south, east, or west. These directions don't even have meaning in space. The sun is rotating.