Other Possible Motions of Source and Observer The Doppler shift for light depends on the relative velocity u of source and observer (it's relativity,įor motion towards each other. A derivation can be found in my Modern Physics The Doppler shift in this case requires special relativity. The argument above for the Doppler frequency shift isĪccurate for sound waves and water waves, but fails for light and otherĮlectromagnetic waves, since their speed is not relative to an underlying Opposite direction, the observed frequency is found by switching the sign of If either observer or source is moving in the īoth motions increase the observed frequency. Source and Observer Both Moving Towards Each Otherįor this case, the arguments above can be combined to give:į ′ = f 0 ( 1 + u obs / v 1 − u s / v ). Will measure between meeting successive crests isĪnd therefore the sound frequency she measures isį ′ = 1 τ ′ = u obs + v λ = v λ ( 1 + u obs v ) = f 0 ( 1 + u obs v ). It is evident from the diagram that the time interval she During this time, she moves u obs τ ′ , the wave crest moves v τ ′ coming to meet her, and between them they Suppose her time between meeting successiveĬrests is τ ′. Remember, the wave crests are λ apart in the air, and moving at v. So, she’s moving to meet the oncoming wave crests. Stationary Source, Moving ObserverĬonsider now an observer moving at speed u obs directly towards a stationary frequency f 0 source. We can approximate, f ′ ≅ f 0 ( 1 + u s / v ).)īy an exactly parallel argument, for a source moving away from an observer at speed u s , the frequency is lower by the corresponding factor:į ′ = f 0 ( 1 1 + u s / v ). (Note that for the common case ( u s / v ) ≪ 1 , Moving towards the observer at speed u s is:į ′ = v λ ′ = v λ − u s τ 0 = v λ ( 1 1 − u s τ 0 / λ ) = f 0 ( 1 1 − u s / v ). Frequency Detected by Stationary Observer of Moving Sourceįrom the above argument, the observed frequency for a source The source is moving directly towards him, he will hear a frequency f ′ = v / λ ′. Therefore, as these waves of wavelength λ ′ arrive at an observer placed to the left, so Of the source does not affect the speed of sound in air. The speed of sound v relative to the air -the motion These waves, having left the source, are of course moving at Therefore, the actual distance between crests At the same time, the previously emittedĬrest will itself have moved to the left a distance λ. Have moved to the left a distance u s τ 0. And it’s easy to understand why.ĭenoting the steady source velocity by u s , in the time τ 0 = 1 / f 0 between crests being emitted the source will Shorter wavelength than they would have if the same source were at rest. Waves emitted in the forward direction (to the left in the diagram) have a It is evident that, as a result of the motion of the source, Or, to be more realistic (from Wikipedia Commons): Particular, if the source is moving steadily to the left, the wave crests will Of the emitted circles of waves will be equally spaced along its path, Therefore, if the source is moving at a steady speed, the centers Wave crest emitted continues its outward expansion centered on where the source was when the crest was emitted, independent Provided the source is moving at less than the speed of the wave) the circular The Doppler effect arises because once a moving source emits a circular wave (and Traveled a distance λ , so, since it’s moving at speed v , If the source has frequency f 0 , the time interval τ 0 between wave crests leaving the sourceĪs a fresh wave crest is emitted, the previous crest has The circles are separated by one wavelength λ and they travel outwards at the speed of sound To set up notation, a source at rest emitting a steady note The moving object, ultrasound for blood in arteries, radar for speeding carsĭistant galaxies are measured using the Doppler effect (the red shift). Used to measure velocities, usually by reflection of a transmitted wave from Noise from a fast-moving emergency vehicle as it passes. Overhead, the note of the engine becomes noticeably lower, as does the siren Sound emitted by a source moving relative to the observer: as a plane flies The Doppler effect is the perceived change in frequency of Michael Fowler, University of Virginia Introduction
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