DOPPLER EFFECT – MOTIVATION
Doppler effect is phenomenon of frequency changing during the motion of the source of frequency. If the source is coming closer to observer, the frequency is increasing, if it is coming away from the observer, the frequency is decreasing. This phenomenon is observable for sound or electromagnetic waves or for another periodical process. Now we are going to talk about non-relativistic Doppler effect which was derived by Christina Andreas Doppler (1803–1853) in 1842. Doppler worked for some time on the predecessor of today's Czech Technical University. His name is placed under the windows of National Museum in Prague and one of the the Prague high schools is named after him.
Christian Andreas Doppler
Example One: Imagine that buses run in a one-way street in regular intervals. If you go on a bike in the opposite direction (against motion of the buses), you will meet buses more frequently than if you go in the direction of the motion of the buses. The observed frequency change is caused by the Doppler phenomenon.
Example Two: Rain is not exactly periodical process, but Doppler effect can be also applied. If you run against diagonally falling rain, the frequency of the falling drops will be higher and you'll be more wet than if you run in the direction of the rain.
Example Three: Car makes a wide range of sounds when it's running. When it will pass around you, the heard frequency during coming closer will be higher than when it moves away. This characteristic change in the sound everybody knows. Try to remind it from prepared audio files:
Example Four: The light emitted by the stars can be decomposed into spectrum. The spectrum contains spectral lines, that shift to higher frequencies, when the star is approaching, and to the lower frequencies when it moves away. If the star rotates, the spectral lines will be extended. Spectral lines from the approaching edge have frequency shifted to the blue end, lines from receding edge have frequency shifted to the red end of the spectrum.
Relations for Doppler effect are derived in detail in the instructions for the task. The result is formula for the frequency and ot is easy to remember:
| f = f0(1±v/c), resp. ω = ω0(1±v/c), | (1) |
where f is observed frequency, f0 is frequency of source, v is the joint velocity of movement of the source and the observer andc is velocity of propagation of the peridical process (e.g. waves). Relations in this simple form are valid under the condition v << c. The plus sign applies to approaching the observer and the source, minus to receding. The second relationship is given for the angular frequencies. After multiplication we can arrange both relationships for relative frequency change.
| Δf /f0 = (f−f0)/f0 = ±v/c, resp. Δω/ω0 = (ω−ω0)/ω0 = ±v/c. | (2) |
Doppler effect is used to measure the speed of moving objects (e.g. police radar), in medicine for the diagnosis of moving organs in the body (such as heart), in astronomy to map the surface of planets, determining the motion of astronomical objects or view inside the Sun. Certain applications can be found in section „Advanced reading“.
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Tyto materiály vznikly v rámci projektu OPPA CZ.2.17/3.1.00/33306 Inovace předmětů a studijních materiálů pro e-learningovou výuku v prezenční a kombinované formě studia.
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