A Doppler Shift Speed Gun

 


Reid Sherman

Kavli Institute for Cosmological Physics

Department of Astronomy and Astrophysics

University of Chicago

NSTA National Conference

St. Louis, MO

March 30, 2007

 

 


 

 

Abstract:

This is a fun and educational lab for students in middle school and above to learn about the Doppler shift, and about waves in general.  After reviewing the basic properties of waves, with some Socratic questioning students form their own hypothesis of what will happen to a sound wave when emitted by a moving object.  The students then construct their own instrument and test their hypothesis in both a qualitative and quantitative manner, with the final goal being to correctly measure the speed of an object using only the waves emitted from it.

 

Background:

The Doppler effect of sound is something that we are familiar with from our everyday experience. When something making a loud noise (e.g., a car horn, a fire truck siren or a train whistle) moves past us quickly, the sound changes because the sound waves reach us differently than if everything was sitting still. This effect happens with all types of waves, and is a very useful tool.

LetŐs think a bit more about why waves appear different if things are moving about. Imagine you are a lifeguard in a rowboat a bit off shore guarding all the swimmers at the beach, and that there are some waves evenly spaced apart, moving directly towards the beach. Every few seconds, your rowboat is rocked by a wave. What would happen if you started to row away from the beach, toward the incoming waves? Would the waves rock your boat more or less frequently? What if you were done working and you were rowing in toward shore? This is the essence of the Doppler effect: that waves will be more frequent if you are moving towards them or if the source of the waves is moving towards you, and they will seem less frequent if the source and the observer are moving apart.

The Doppler effect was first proposed by Christian Andreas Doppler, the man it is named after (pictured left). On May 25, 1842 at the Royal Bohemian Society in Prague he presented the paper ŇOn the Coloured Light of the Double Stars and Certain Other Stars of the Heavens,Ó where he first predicted that motion could effect the color or frequency of light (source info and photo http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Doppler.html). Doppler did not get all the details right, nor were the instruments of that era accurate enough to test his theory with light. However, his central idea was right and that is why over 160 years later we all recognize his name. One of the first experiments to test the Doppler effect involved having musicians play a certain note while sitting on a moving train and having another musician record what notes he heard as they approached and retreated.

 

The diagram above illustrates how our perception of light changes depending on whether the source of the light is stationary, moving towards us, or moving away from us. On the left side of the Figure we see that if the source is still, an observer will just see the light with the same wavelength and frequency as was emitted. However, on the right side of the Figure we see what happens if the source is moving. As the source moves towards the left, successive waves are crowded together. That is, each new wave begins a bit more to the left than if the source stayed in one place. To an observer on the side that the source is moving toward (the left side in our diagram), this behavior will make the sourceŐs wavelength appear shorter, which means its frequency will appear higher. This change to a higher frequency/shorter wavelength is called a blueshift. However, if the observer is on the side that the source is moving away from (the right side in our diagram), then the opposite will happen. The successive waves will be spread out and the light will appear to have a longer wavelength and a lower frequency. This change to a lower frequency/longer wavelength is called a redshift.

 

Materials:


Wiffle ball cut in half

Buzzer

9 volt battery

Battery clip

Switch

Wire strippers

Twist connectors

String

Meter stick

Tape

Stopwatch

Computer

Sound analysis software

Microphone


Procedure:

I – Build Doppler ball

Strip the red and black wires attached to the buzzer about a half of an inch, so that the battery clip and the buzzer wires can be twisted together. Stripping a wire means exposing the metal wire by removing the outer insulating cover without damaging the wire itself.

Once your circuit is complete and tested, secure the assembly and attach it to at least 1.5 meters of string. Remember to test the on/off circuit before you seal the ball up. Make sure the switch will still be accessible after sealing the ball.  Record the buzzerŐs nominal frequency in your notebook and mark it on the outside of the ball (e.g. 3,500 Hz).

II - Empirically Observe Doppler Shift of Sound (Swing and Listen):

Once all the Doppler balls/buzzers are assembled and working, go outside (or somewhere with plenty of room) to experiment with them. In a clear area with no one in the way, double check that everything is secure and then twirl the ball around your head. Once you are confident that the assembly will stay together turn the buzzer on and twirl the buzzer assembly around your head, with your partners standing several feet away. Try to swing it at a constant rate. What do you hear? What do they hear? Describe how the sound changes. Is the pitch/frequency constant? The volume? Try to swing it at a few different speeds. Record your observations. Make sure the person swinging in the middle has a chance to be on the outside and observe the sound change.  Also have two partners listening from two directions and see if they hear the pitch change in the same way and at the same time.

III - Getting Quantitative - the Need for Speed:

In this portion of the lab we will try to quantify the Doppler shift. We will do this in three steps:

1) measure the speed of the swinging buzzer

2) use calculations to predict what the actual Doppler shift is

3) directly measure the Doppler shift of sound

 

How would you determine the speed of the buzzer as is it swung around?

What do we need to measure? How would you measure it?

Pull the sting taut and use tape to mark it at multiple lengths away from the buzzer. Pick one of the marked lengths as your handhold and record the length (this will be your radius, r, for below). Practice swinging the assembly at a steady constant rate with your wrist held stiff in one position. Once the group feels that the buzzer can be consistently swung at a steady rate, swing the buzzer at that constant rate and time how long ten (10) complete cycles take. Record the observed times.

Now Calculate the Speed (Speed = distance/time):

You know the time it takes for the swinging buzzer to go around ten times, but what was the distance traveled in that time? (Note: The circumference, c, of a circle is equal to two š  times the radius, r. That is, c = 2š r). Now that you know the distance and the time, you can calculate the observed speed for each of the 3 trials and find the average speed. Show your calculations in your lab notebook and record the results in a data table.

Rope Length (radius, r) :_________________________ (meters)

Circumference (c) = 2š r :___________________________ (meters)

Distance for 10 rotations = 10 x 2š r = 10 x c : ___________ (meters)

Time for 10 rotations:_______________________________(seconds)

Speed of ball = Dist/time:____________________________(meters per second)

IV – Equations, Calculations, & Predictions:

Mathematically, the Doppler shift that you observed may be described by the following equations:

 

Source moving towards you: fŐ observed frequency

fŐ = f / [1 – (v/vs)]

 

Source moving away from you: fŐ observed frequency

fŐ = f / [1 + (v/vs)]

 

f = source frequency in Hertz (Hz)

fŐ = perceived frequency (Hz)

v = speed of source

vs = speed of sound

 

The speed of sound depends on the weather (both the temperature and the humidity), but for our purposes we will assume that the speed of sound is

vs = 350 m/s.


Calculate the expected perceived frequency of your buzzer by using the equations above and the average speed from your earlier measurements.

 

What is the calculated perceived frequency when the buzzer is

moving towards you?_________________________________

moving away from you?_______________________________

The human ear can hear sounds ranging from 20 Hz to 20,000 Hz.  It is most sensitive to frequencies between 500 and 4,000 Hz and can distinguish between sounds that are a few Hertz different.

 

Should a human with normal hearing be able to detect the frequency shift you calculated?_________________________

 

V – Computer measurements

Use sound analysis software to record the buzzer both at rest and while swinging it at constant speed.  The software will be able to measure both the intensity and frequency of sound waves.

 

Can you tell from the spectrum when the ball was moving towards the microphone and when it was moving away?

 

What is the frequency shift?

 

Compare the measured Doppler shift to the calculated one.  Do they agree?

 

Scientific applications:

The Doppler effect is one of the core tools of modern astronomy. Astronomers are most interested in shifts in electromagnetic radiation waves (e.g., visible light and radio waves), and not sound waves. Since the only thing astronomers can measure about distant objects is the waves of light that come from them, measuring the spectrum of those waves to find the Doppler shift is astronomersŐ only speed gun.  Frequency shifts just like the ones measured in this lab were used by Edwin Hubble to find the amazing fact that all distant galaxies are moving away from ours, leading him to claim that the Universe was expanding!

Beyond astronomy and sirens, there are many important ways that the Doppler effect is used in the world around us. Examples include: police radar, determining the speeds of baseball pitches and tennis serves, and Doppler weather radar. All of these examples use radio waves. For the sports events and the police, a very well defined frequency of electromagnetic radiation is sent out (typically x-band at 10.5 GHz). When the ball or the car is moving toward the radar gun, the radiation from the radar gun reflects off the object and picks up a little energy from the speeding object. The reflected radiation has a slightly higher frequency (more energy) compared to the emitted frequency. The amount of the blueshift is used to determine how fast the car or ball was moving.

Doppler weather radar is much more complex. It is used to look at much larger areas: tens or hundreds of square miles rather than hundreds of feet. It also provides us with much more information. In a manner very similar to the Speed of Light lab that you will do, Doppler weather radar determines how far away a storm is by how long it takes radio waves to travel to the storm clouds, reflect, and travel back. Based on how strongly the storm reflects the radio waves it is able to determine the composition of the storm (e.g. density, whether it is rain, hailÉ). Finally, Doppler radar uses the Doppler shift to determine in what direction and how fast a storm is moving. Visit http://www.crh.noaa.gov/radar/latest/DS.p19r0/si.klot.shtml to see the most recent Chicago Doppler radar measurements. Also see http://www.crh.noaa.gov/fsd/soo/doppler/doppler.htm for more information from the National Weather Service on Doppler weather radar.

 

Recommendations:

1)    This lab can also be done essentially in reverse, with the frequency shift being measured, and the speed being calculated from that frequency shift, then finding if the speed calculated from the Doppler shift matches the speed measured with stopwatch and meterstick.

2)    More advanced students might be able to derive the Doppler shift equations on their own with a little guidance and a good diagram.

3)    Any sound spectrum analyzer should do for this lab, as the measurement will not have to be terrifically exact.  Find the one that seems easiest for you and your students.  The one we used was called Spectra Plus, which is available for a free 30 day trial at http://www.spectraplus.com/

Conclusion:

This lab was developed as part of a larger curriculum on the nature of light.  The goal was to help students understand waves and how the wave nature of light can explain natural phenomena, even while observing and learning in another lab that only a light with a particle nature could explain the photoelectric effect.  We found this to be a generally productive and enjoyable lesson on its own.  It was taught to a group of students who ranged in age from 12 to 17, and the lesson seemed to work equally well for all ages.  We hope that it works well for you as well.

Special Thanks to Randy Landsberg for help in lab development, and to Walter Glogowski, Robert Friedman, and Sarah Hansen for help in teaching.

Please visit our other NSTA National Conference presentations, and our website:

http://cfcp.uchicago.edu/education/index.html