Doppler Effect

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The wave nature of light means there will be a shift in the spectral lines of an object if it is moving. This effect is known as the doppler effect. You have probably heard the doppler effect in the change of the pitch of the sound coming from something moving toward you or away from you (eg., a train whistle, a police siren, an ice cream truck's music, a mosquito buzzing). Sounds from objects moving toward you are at a higher pitch because the sound waves are compressed together, shortening the wavelength of the sound waves. Sounds from objects moving away from you are at a lower pitch because the sound waves are stretched apart, lengthening the wavelength. Light behaves in the same way.

Motion of the light source causes the spectral lines to shift positions. An object's motion causes a wavelength shift = _new - _rest that depends on the speed and direction the object is moving. The amount of the shift depends on the object's speed: = _rest × V_radial / c, where c is the speed of light, _rest is the wavelength you would measure if the object was at rest and V_radial is the speed along the line of sight.

There is a lot of information stored in that little formula! First, it says that the faster the object moves, the greater the doppler shift . For example, a particular emission line of hydrogen from nearby galaxies is shifted by a smaller amount than the same line from faraway galaxies. This means that the faraway galaxies are moving faster than the nearby galaxies. The ``radar guns'' used by police officers operate on this principle too. They send out a radio wave of a set wavelength (or frequency) that reflects off a car back to the ``radar gun''. The device determines the car's speed from the difference in the wavelength (or frequency) of the transmitted beam and reflected beam.

Second, the term V_radial means that only the object's motion along the line of sight is important. If object moves at an angle with respect to the line of sight, then the doppler shift () tells you only about the part of its motion along the line of sight. You must use other techniques to determine how much of an object's total velocity is perpendicular to the line of sight.

Finally, which way the spectral lines are shifted tells you if the object is moving toward or away from you. If the object is moving toward you, the waves are compressed, so their wavelength is shorter. The lines are shifted to shorter (bluer) wavelengths---this is called a blueshift. If the object is moving away from you, the waves are stretched out, so their wavelength is longer. The lines are shifted to longer (redder) wavelengths---this is called a redshift.

This explanation also works if you are moving and the object is stationary or if both you and the object are moving. The doppler effect will tell you about the relative motion of the object with respect to you. The spectral lines of nearly all of the galaxies in the universe are shifted to the red end of the spectrum. This means that the galaxies are moving away from the Milky Way galaxy and is evidence for the expansion of the universe.

The doppler effect will not affect the overall color of an object unless it is moving at a significant fraction of the speed of light (VERY fast!). For an object moving toward us, the red colors will be shifted to the orange and the near-infrared will be shifted to the red, etc. All of the colors shift. The overall color of the object depends on the combined intensities of all of the wavelengths (colors). The first figure below shows the continuous spectra for the Sun at three speeds (zero, a fast 0.01c, a VERY fast 0.1c). The Hydrogen-alpha line (at 656.3nm) is shown too. Objects in our galaxy move at speeds much less than 0.01c. The doppler-shifted continuous spectrum for the Sun moving at 0.01c is almost indistinguishable from the Sun at rest even when you zoom in to just the optical wavelengths (second figure). However, the doppler shift of the spectral line is easy to spot for the slow speed. By zooming in even further, you can detect spectral line doppler shifts for speeds as small as 1 km/sec or lower (less than 3.334×10^-6 c).

Vocabulary

Formulae

1. Wavelength shift: = _new - _rest. _rest is the wavelength measured if the object is at rest and _new is the wavelength measured for the moving object.
2. Doppler effect: = _rest × V_radial/c, where V_radial is the object's speed along the line of sight and c is the speed of light.
3. If _new > _rest, the object is moving away (redshift).
4. If _new < _rest, the object is approaching (blueshift).

Review Questions

1. What two things can the doppler effect tell you about an object's relative motion?
2. Which galaxy is moving faster: one with lines red-shifted by 200� or one blue-shifted by 300�? Which one is moving away from us?
3. Would a star moving left to right with respect to you have a doppler shift? Why or why not?
4. There are two edge-on binary systems (orbiting in a plane along our line of sight) with the two stars separated by 2 AU. Which will produce the largest shifting of their spectral lines: the system with star masses 10 & 15 solar masses or the system with 1.5 & 2.0 solar masses? Explain why.
5. There are two binary systems with the two stars separated by 2 AU. Which will produce the largest shifting of their spectral lines: an edge-on system with star masses 1.5 & 2.0 solar masses or a face-on system (stars orbiting in a plane perpendicular to our line of sight) with star masses 10 & 15 solar masses? Explain why.
6. Why should you use spectral lines to measure velocities rather than the change in color of an object?

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last updated: 17 May 2001