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Lab 3: The Doppler Effect

Introduction:

We highly recommend that you have completed Lab 1 and Lab 2 before doing this lab. In Lab 1 you explored space between the stars and in Lab 2 you explored the electromagnetic spectrum. 

Next time you are at a lake, watch the boats speed by. As they approach you the water waves are compressed in front of the boat and the waves behind the boat are spread out.  In other words as the boats approach wavelengths of the water waves are short, but the wavelengths behind the boats are long.

The same effect occurs with sound. Listen to a train go by. Blowing its whistle, the pitch is high as it approaches you.  When it goes past, and away from you, the pitch is lower. Sound waves from the whistle are compressed as the train approaches and stretched out as the train recedes from you. You hear the short compressed wavelengths as a higher frequency and the stretched longer wavelengths as a lower frequency.

Click on either image to hear a train.

Like water and sound, light can be described as waves. The same principle of compressed and stretched wavelengths of light from moving light sources applies! This principle is called the Doppler Effect.  The Doppler Effect applies to objects producing any type of waves (sound, water, light). In terms of light emitted by a moving object, the Doppler Effect states that the observed frequency of emitted light from a moving object depends on the speed of the moving object.  The equation for the Doppler Effect is below:

fDop/fRest = v/c

where fDop is the Doppler shifted frequency, fRest is the rest frequency, v is the velocity of the source and c is the speed of light (3.00 x 108 m/s).  After some algebra, the Doppler shift equation can be written as:

v = c(fDop/fRest)

Now we have an equation that we can use to find the speed of a source if we know the Doppler and the rest frequencies of the light emitted from the source.

Radio waves and visible light waves are all part of the electromagnetic spectrum, radio waves just happen to have a longer wavelength and lower frequency than visible light.  Thus an object emitting radio waves will also produce the Doppler Effect, if that object (or the observer) is moving. In fact many astronomical objects emitting radio waves show the Doppler Effect. For example supernova remnants, relatively dense interstellar clouds of neutral hydrogen and quasars all exhibit the Doppler Effect. If we measure the Doppler shifted and rest frequencies then we can find the speed of the source!

In this lab we will determine how fast an astronomical radio source is traveling!

Procedure:

  1. Login to Smiley.  If you need any assistance with Smiley refer to the Smiley Users Manual.
  2. In Map mode, pick one of the objects.  We suggest Cygnus A, Virgo A, the Crab Nebula, or the Galactic Center depending on which of these are above the horizon. Each of these sources is emitting 1.42 GHz radio waves, but when these objects are moving their 1.42 GHz radio waves are shifted due to the Doppler Effect when they arrive at earth.
  3. After you have picked an object click on GO.
  4. Once Smiley has reached the target make sure Smiley is close to the target by comparing the NEW Coordinates with the CURRENT Coordinates and using HandPaddle.
  5. Go into Spectrum mode to begin measuring intensity.
  6. Set your PLOT RATE to 1x, your IF GAIN to around 19, your Base Frequency to 1.42 GHz and click on Begin Scan.
  7. Watch the scan.  The x-axis is the frequency and the y-axis is the intensity.  The center of the x-axis is the 1.42 GHz frequency (right click on the graph and click on show grid to see the x and y axises). Lower frequencies are left of the center and higher frequencies are to the right of the center. Notice that the peak in intensity does not occur at exactly 1.42 GHz, because of the Doppler Effect!

Here is an example of a spectrum scan showing a Doppler shifted frequency from 1.42 GHz.

The rest frequency is 1.42 GHz (1.42 x 109 Hz) and the Doppler shifted frequency is 160 KHz (160 x 103 Hz).  Below is a screenshot of the listed points for the graph above showing they value of the peak intensity.

Now to calculate the Doppler shift we use the equation:

v = c(fDop/fRest)

or

v = (3.00 x 108 m/s)[(160 x 103 Hz)/(1.42 x 109 Hz)]

Thus v = 3.38 x 104 m/s
  1. Record the Doppler Effect shifted frequency of your scan and calculate the velocity of the source.

Challenge Question:  Convert the velocity of the source from m/s to km/hr and compare it to the speed limit on a typical highway (100 km/hr).  Also, is the source moving towards or away from us?