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The Doppler Effect is a wave phenomenon that all of us have encountered in our everyday experiences. Dutch physicist Christian Doppler first studied it in relation to sound waves, and that is where most of us have encountered it. If a source of noise (say, an ambulance siren) is coming towards you, the noise sounds high-pitched. However, once the object passes you by, the pitch of the noise drops. Only for a split second (say, when the ambulance is right beside you) do you hear the sound the way it "truly" is (that is, the way the ambulance driver hears it). How is the Doppler Effect explained? Let's stick with the sound wave example first. Remember that what we call "pitch" is really just the frequency of a sound wave: the more frequently sound waves hit our eardrum, the higher pitched the sound wave sounds. If we are headed towards the source of sound waves (or it is headed towards us), the soundwaves hit our eardrums more frequently that they would if we were both standing still. This makes the sound higher pitched to our ear. Conversely, if we were headed away from the sound (or it away from us), the soundwaves would hit our eardrum less frequently, and the sound would be higher pitched. The Doppler Effect is an "illuision," caused by the fact that we are moving relative to the source of sound. Consider another example with water waves. Imagine that you are standing on a beach, feet barely in the water. Waves come lapping into the shore at a rate of, say, one every five seconds, over your toes. If you dive in, and start swiing out to sea, you are travelling into the waves. Therefore, as you swim out to sea, waves will hit you more frequently, say one every 3 seconds. If you are in a speedboat, that could even increase to one per second! The rate of waves has not changed to someone standing still on the beach, but the rate at which you encounter them has changed. If you then turn around and swim or motor back to shore, waves strike you less frequently as you head away from the waves. Astronomy is primarily concerned with how this phenomenon applies to light waves. In the illustrations below (not yet available), we have two objects: one object (the "source") is giving off light, while the other (the "observer") is receiving it. Note in the first situation, the distance between observer and source is not changing. This can be due to one of two situations: both objects could be completely stationary, but we must also entertain the possibility that both objects are travelling at the exact same speed. Two cars travelling at 70 miles per hour remain the same distance apart until someone changes speed! Regardless of which situation prevails, we call this situation "at rest" (a somewhat unfortunate name). Light travels between the source and observer with a certain wavelength, which is called "lambda-rest" or (my preference) "lambda-zero." In the second situation, the distance between the source and observer is decreasing; the two are getting closer. This can be because the source is in motion, the observer is in motion, or both. What matters is that the two objects are getting closer together. Notice how the light waves get "scrunched up" by this motion. If the observer is a human eye, then the light waves strike the eye more frequently, causing the eye to see a slighly different color. The wavelength of the obseved light (called simply "lambda") appears shorter than the wavelength the light would have if the objects were "at rest" (called "lambda-zero"). We call this situation a "blueshift" although the new color may not necessarily be blue (and yes, science is full of poorly chosen names like that). In the third situation, the distance between the source and observer is increasing; the two are getting farther away. As before, this can be because the source is in motion, the observer is in motion, or both. What matters is that the two objects are getting farther apart. Now the light waves are getting "stretched out" by the motion. If the observer is a human eye, then the light waves strike the eye less frequently, causing a "redshift," an apparently longer wavelength than if the objects were "at rest" ("lambda" is greater than "lambda-zero"). Notice that a Doppler shift only occurs when objects are heading towards or away from each other. This is called line-of-sight motion. "Sideways" motion, called transverse motion does not cause a Doppler shift, as you can see in Text Figure 3.16. Only very rarely does an object have purely transverse or purely line-of-sight motion. The Doppler Effect helps us find out the size of that portion of an objects motion which is line-of-sight. Christian Doppler experimented with sound to determine exactly how the Doppler Effect worked. By listening carefully to the sounds made by a band as it played on moving platform, he determined that the size of the "Doppler shift" depends on how fast the two objects are coming together or moving apart. The Doppler Shift, in other words, depends on the line-of-sight velocity. Doppler summarized this in a formula: Where
Notice that this equation looks different from the one given in the text. They are equivalent, but I think the one above is easier to use. Just take it in steps:
Police officers use the Doppler Effect to determine the speed of your car. Their "radar gun" sends out a radio wave of a known wavelength. If your car were just sitting there, the radio wave would return to the "gun" unchanged. But since your car is moving, a shift in wavelength will result as the radio wave bounces off your car. A computer in the device can then calculate your velocity from the shift. We can use a similar method to gauge the line-of-sight velocities for stars. Sometimes, when we examine the lines seen in the absorption spectra of stars, we note that the dark lines are not always at the exact wavelengths we expect them to be. For example, the unmistakable line at 6563 Angstroms caused by hydrogen electrons that we see in the Sun could be seen at 6564 Angstroms in another star. We see the line at its "rest" wavelength in the Sun because we have no really significant motion towards or away from the Sun. In the case of the other star, the line appears to be at a slightly longer wavelength because we are separating from the star: either the star is headed away from us, or we are headed away from the star, or both. In this manner we can use the spectral lines of stars as "signposts" to measure the line-of-sight velocities of heavenly bodies. We know from experiments in the laboratory or with the Sun what the wavelength of a spectral line should be. If the wavelength of that spectral line in the star is different from what we expect, then the star likely has some line-of-sight velocity compared to us. This really only works with the big, prominent spectral lines, though (such as those of hydrogen, sodium, or calcium), so that few mis-identifications are made.
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 Updated
8/27/99
By James
E. Heath
Copyright Ó 1999 Austin Community College |