3.3 The Doppler Effect

For all Unit 3 pages:

• Unit 3 Master Packet
• Unit 3 Student Master
• Unit 3 Teacher Master

For Unit 3.1

• Unit 3.3 Student Guide
• Unit 3.3 Teacher Guide

Objective:

In this lab, students will measure and compare the peak intensity of 21 cm radio waves emitted from the gas and dust between three different objects.

Teacher Notes:

**Note: It is recommended that you complete Lab 1 and Lab 2 before doing this lab.

PARIPod 3.3 is still in development.

Background Knowledge

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. (Figure 2 and Figure 3) You hear the short, compressed wavelengths as a higher frequency and the stretched, longer wavelengths as a lower frequency.

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 that produce any type of wave (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:

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, starlike objects, all exhibit the Doppler Effect. If we measure the Doppler shifted and rest frequencies, then we can find the speed of the source.

Procedures

1. Login to Smiley. If you need any assistance with Smiley refer to to Unit 2: Smiley Basics.
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 TARGET Coordinates with the CURRENT Coordinates and using Hand Paddle.
5. Go into Spectrum mode to begin measuring intensity. Set your PLOT RATE to 1x, your IF GAIN to around 19, your Base Frequency to 1.42 GHz and click on Begin Scan.

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!

6. Click on Save Scan and name the scan. Then click on Open Data File, find the scan you saved and list the data points.
7. Record the Doppler shifted frequency of your scan and calculate the velocity of the source in the table below.
8. Repeat procedures #2 –8 for two more objects.