The Physics
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Opus in profectus

# Doppler Effect (Light)

## Practice

### practice problem 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 21st 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.)

Magnify

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. The radar site that produced this image is located in Dodge City (the upper left corner). The radar image in this region is red on the west side side and blue on the east side.
1. What is the wind direction in the red region?
2. What is the wind direction in the blue region?
3. What is the overall airflow pattern in this region?
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 red region?
2. What is the wind direction in the blue 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.

#### solution

1. About the area around Dodge City where the radar site is located.

1. The wind is blowing away from Dodge City on the red side — from the east to the west.

2. The wind is blowing toward Dodge City on the blue side — from the east to the west.

3. The air around Dodge City is blowing in one direction — from the east to the west.

2. About the two-color region near Greensburg.

1. The wind in the red region is blowing away from Dodge City — from the northwest to the southeast.

2. The wind in the blue region is blowing toward Dodge City — from the southeast to the northwest.

3. The air in the two color region is circulating counterclockwise.

4. There is a tornado at the center of this region.

Magnify

### practice problem 2

Use this variation of the doppler effect equation…
 ∆λ ≈ ± ∆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?

#### solution

Don't break the law.

### practice problem 3

Write something different.