Title: Doppler Effect
Grade Level: High School Physics
Utah State Core Standard & Indicators:
Standard V: Students will understand the properties and applications of waves.
Objective 1: Demonstrate an understanding of mechanical waves in terms of general wave properties.
Indicators:
e. Explain the observed change in frequency of a mechanical wave coming from a
moving object as it approaches and moves away (i.e., Dopller Effect).
Narrative and Rational:
For this lesson, my students will play with Doppler Balls to actually experience the Doppler
Effect. I will introduce the concept of pitch and compare it to wave frequency. After using a computer
applet to qualitatively explain and explore sound waves, I will touch on why sonic booms occur. This will
be a good introduction to relativity theory in about a month. They will start understanding that there is
a difference in what an observer experiences and what a source experiences as they practice being the
observer and source. We will also talk about other applications of the Doppler Effect that are used all
around them both in nature (bats) and by humans (radar guns).
Next, I will teach the mathematics of the Doppler Effect. This will let them perform the
mathematics of what a source or observer will encounter as a result of the Doppler Effect. Once again,
preparing them to understand red/blue shifts in light and relativistic concepts.
As I teach the mathematics, I will shift from sound to light waves and talk about when light
waves are Doppler Shifted. This will lead to an interesting bit on astronomy (red and blue shifted stars)
and how something that was discovered in 1842 can still find relevance today. This will, hopefully, teach
them to pay attention to the “old” physics and try to figure out new ways to use the knowledge they
have. This will also be an introduction to Standard V, Objective 2, Indicator d where I will touch on the
astronomical implications of red and blue shifts in more detail.
Enduring Understanding:
My students will be able to use and understand terms to describe wave motion. They will be
able to draw the sound waves for a bullet at Mach 0.7, Mach 1, and Mach > 1. They will be able to
explain why the sound waves are compressed in front of a moving sound source and stretched out
behind the moving sound source. They will be able to explain a sonic boom. My students will be able to
calculate the observed frequency given the source frequency and vice versa.
Essential Questions (Example Discussion Questions):
What are some examples of how the Doppler Shift it used by humans or in nature?
Given a particular wave pattern, is the source moving? How?
What is the direction and speed of the object given this set of sound waves?
How does a sonic boom occur?
Why do we sometimes hear a double sonic boom?
Can you see a sonic boom?
What does Mach 3 mean?
If the observer is in the direct path of the source, how will they experience the Doppler Effect?
How do sound waves react in solids? Liquids? Gases?
Skill Focus Objectives:
Observed frequency/wavelength can be affected by movement of the source/observer. This
phenomenon applies to any type of waves.
f’ = fo((𝑣 ± 𝑣 o)/(𝑣 ± 𝑣 s))
f’ – frequency shift
fo – actual frequency
vo – observer velocity
vs – sources veloctiy
Vocabulary Focus:
Doppler Shift: The apparent change in the wavelength/frequency of sound waves that is caused by the
movement of the sound source, observer or both.
Frequency: The number of times something happens in a given period of time.
Pitch: The perceived frequency of a sound.
Sonic Boom: A loud noise produced by a source moving faster than the speed of sound.
Wavelength: The distance between consecutive compressions of a wave.
Preparation/Materials:
Solder Doppler Ball circuits.
Set up the following on my computer:
Doppler Effect Applet: http://www.molebash.com/doppler/home.htm
Sonic Boom Demonstration: http://www.youtube.com/watch?v=-d9A2oq1N38&feature=related
Review Doppler Effect: http://www.watchknow.org/Video.aspx?VideoID=10295
In the laboratory room:
Clear an area so that there is plenty of room for Doppler Ball experimentation.
Engage/Launch (10 minutes):
As the students walk into the room, hand them an activated Doppler Ball and Doppler Effect Worksheet.
When they have finished the Doppler Ball section of the worksheet, they will be directed to the
computers in the classroom.
Explore (30 minutes):
At the computers, students will use the applet to qualitatively explore the Doppler Effect. When they
are done with the worksheet I will show the class the sonic boom demonstration.
Explain/Summarize (30 minutes):
We will spend some time processing the exploration. I will ask if there are any questions, observations
or comments to this point?
I will ask students for some examples of how the Doppler Shift is used: radar guns, measuring the speed
of fastballs, tennis serves, etc., bats, echocardiograms (structure of heart), measuring the velocity of
galaxies.
I will randomly call on students to come to the board and draw sound waves for different types of
situations: stationary source and observer, Vs < Vsound, Vs = Vsound, Vs > Vsound.
I will ask why sound waves are compressed in front of a moving sound source and stretched out behind
the source?
Next I will give them the equation for the Doppler Shift using both frequency and wavelength. We will
discuss what happens to the frequency and wavelength as objects are approaching each other and
receding from each other. Next I will work a couple examples on the board for them using the
equations.
Evaluate/Assessment (15 minutes):
Show the class the Doppler Effect review video.
Ask the students to record in their science notebooks how they think sound waves would be
affected by different mediums (solids, liquids and gases) and explain their reasoning.
Direct them to the last four pages of their worksheet for their homework.
Doppler Effect Worksheet
Doppler Ball Section:
Now play catch with the ball and answer the following questions:
1. What is the pitch of the siren when the doppler ball is not moving?
2. What does the pitch of the siren do when the ball is moving toward you?
3. What does the pitch of the siren do when the ball is moving away from you?
4. Leave the ball stationary. What does the pitch of the siren do when you run
toward and away from the ball?
5. Throw the ball directly over someone’s head (CAREFULLY). Describe the pitch of the
siren.
If we could see them, what do you expect sound waves to look like coming from an object that
isn't moving?
Would you expect the pitch of the sound coming from this object to be affected?
Now please disconnect the buzzer on your Doppler Ball, return it to your instructor, and go to the
computers:
Go to the following website: http://www.molebash.com/doppler/home.htm. Perform the tasks
outlined for you and answer the corresponding questions. Feel free to experiment and learn as you go.
Try new things and record on the back of this paper what you tried and what you learned.
Honking Horn Section:
Movie #1: Is it coming from inside the car or outside the car? If outside the car, where?
Movie #2: Is it coming from inside the car or outside the car? If outside the car, where?
Explain your answer:
Please circle the answer for the next two questions:
Did the horn in Movie 3 sound the same as the horn in Movie 1 or Movie 2?
How about the horn in Movie 4? Is it more like Movie 1 or Movie 2?
If the object is coming toward you how do you expect the pitch to change?
If the object is moving away from you how do you expect the pitch to change?
Please skip the Doppler Ball Section, you’ve already done it.
Wave Exploration Section:
(Please note: Do not play with the relativistic function here. It doesn’t work well and
won’t teach you anything.)
Let's investigate. Leave the button on Classical and using the "speed" slider set the
speed of the object at 0. Press the "start" button.
Adjust the "speed" slider to 0.5 and press the "start" button. Notice the pattern of waves
that is produced.
How would you describe the resulting wave pattern?
Would the pitch of the sound produced by the object be equivalent on all sides?
What do you think will happen to the sound waves preceding the object when you set the speed
of the object equal to the speed of sound?
What pattern of waves do you predict when you increase the speed of the object to higher than
the speed of sound?
What would the object sound like as it is approaching you?
What would the object sound like when it passes you?
We know airplanes experienced violent buffeting when they approached Mach 1, so what do
you think happened to the planes when they broke the "sound barrier?"
Sonic Boom Section:
Based on what you have learned about the Doppler Effect, can you give a possible explanation
as to what is happening in this picture?
STOP HERE AND WATCH A COOL SONIC BOOM VIDEO WITH THE CLASS.
Homework:
Assessment Questions (5):
1. The car below emits sound waves, represented by red circles, that are heard by an
observer. Based on the pattern of sound waves, what is the direction and speed of the car?
o
A. Towards the observer, faster than the speed of sound.
o
B. Towards the observer, slower than the speed of sound.
o
C. Away from the observer, faster than the speed of sound.
o
o
D. Away from the observer, slower than the speed of sound.
2. Based on what you have seen, what is the best definition of the Doppler effect?
o
A. A change in the frequency of a wave caused by the motion of the source
relative to the observer.
o
B. The increase in volume of a sound as the source approaches an observer.
o
C. A low-pitched, very loud noise produced by aircraft moving at or above
the speed of sound.
o
D. The pattern of louder and quieter regions caused by the interference of
sound waves.
3. Assuming the speed of sound is 340 m/s, what is the most likely speed of the jet shown
below?
o
A. 200 m/s
o
B. 500 m/s
o
C. 100 m/s
o
D. 340 m/s
4. What type of motion is illustrated in the diagram below?
o
A. Oscillating motion faster than the speed of sound.
o
B. Oscillating motion slower than the speed of sound.
o
C. Circular motion faster than the speed of sound.
o
D. Circular motion slower than the speed of sound.
5. The Doppler effect applies to light waves as well as sound waves. Astronomers use this
to measure the motion of stars and galaxies. In 1929, Edwin Hubble discovered that light
from distant galaxies was shifted away from the blue end of the spectrum and towards the
red end of the spectrum. Red light has a longer wavelength (and a lower frequency) than
blue light. What could Hubble conclude about these galaxies?
o
A. The distant galaxies are growing smaller.
o
B. The distant galaxies are growing larger.
o
C. The distant galaxies are moving towards the Earth.
o
D. The distant galaxies are moving away from the Earth.
Assessment Questions (5):
1. The car shown below is approaching the observer at a speed of 40 m/s. The car honks its
horn at a frequency of 1,000 Hz, and the speed of sound in air is 340 m/s. What is the
frequency that the observer will hear?
o
A. 882 Hz
o
B. 960 Hz
o
C. 1,118 Hz
o
D. 1,133 Hz
2. A plane flies at 200 m/s, emitting a 600 Hz roar. Assuming a 340 m/s speed of sound,
what will be the frequency of sound waves heard by a stationary observer directly behind
the plane?
o
A. 247 Hz
o
B. 260 Hz
o
C. 378 Hz
o
o
D. 400 Hz
3. A train traveling 30 m/s blows its whistle at 8,000 Hz as it passes by an observer.
Assuming the speed of sound is 340 m/s, how much of a frequency change will the
observer hear?
o
A. 1,412 Hz
o
B. 1,423 Hz
o
C. 1,485 Hz
o
o
D. 1,551 Hz
4. Driving your Ferrari through the Italian countryside at a speedy 88 m/s, you approach an
opera diva singing a high C (1,046 Hz). What note will you actually hear as you
approach? (Assume a speed of sound of 340 m/s.)
o
A. C-sharp (1,108 Hz)
o
B. D (1,174 Hz)
o
C. E-flat (1,244 Hz)
o
D. E (1,318 Hz)
5. An observer measures a 100 Hz Doppler shift as an ambulance goes by. At rest, the
frequency of the ambulance's siren is 2,000 Hz. What is the speed of the ambulance?
o
A. 8.5 m/s
o
B. 12.4 m/s
o
C. 16.1 m/s
o
D. 20.0 m/s