What IsThe Doppler Effect ? what are its applications
The Doppler effect (or Doppler shift) is |
| What IsThe Doppler Effect ? what are its applications |
the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842 in Prague. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.
When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the observer than the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are travelling, the distance between successive wave fronts is reduced, so the waves "bunch together". Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves "spread out".
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What IsThe Doppler Effect ? what are its applications
For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered.
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| Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0 . |
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| The same sound source is radiating sound waves at a constant frequency
in the same medium. However, now the sound source is moving with a speed
υs = 0.7 c (Mach
0.7). Since the source is moving, the centre of each new wavefront is
now slightly displaced to the right. As a result, the wave-fronts begin
to bunch up on the right side (in front of) and spread further apart on
the left side (behind) of the source. An observer in front of the source
will hear a higher frequency
f = c + 0/c - 0.7c f0 = 3.33 f0 and an observer behind the source will hear a lower frequency f = c - 0/c + 0.7c f0 = 0.59 f0 . |
 |
| Now the source is moving at the speed of sound in the medium (υs = c,
or Mach 1). The wave fronts in front of the source are now all bunched
up at the same point. As a result, an observer in front of the source
will detect nothing until the source arrives where
f = c + 0/c - c f0 = ∞ and an observer behind the source will hear a lower frequency f = c - 0/c + c f0 = 0.5 f0 . |
 |
| The sound source has now broken through the sound speed barrier, and is traveling at 1.4 c
(Mach 1.4). Since the source is moving faster than the sound waves it
creates, it actually leads the advancing wavefront. The sound source
will pass by a stationary observer before the observer hears the sound.
As a result, an observer in front of the source will detect
f = c + 0/c - 1.4c f0 = -2.5 f0 and an observer behind the source will hear a lower frequency f = c - 0/c + 1.4c f0 = 0.42 f0 . |
The Doppler Effect
Suppose that there is a happy bug in the center of a circular water puddle. The bug is periodically shaking its
legs
in order to produce disturbances that travel through the water. If
these disturbances originate at a point, then they would travel outward
from that point in all directions. Since each disturbance is traveling
in the same medium, they would all travel in every direction at the same
speed. The pattern produced by the bug's shaking would be a
series of concentric circles as shown in the diagram at the right. These
circles would reach the edges of the water puddle at the same
frequency. An observer at point A (the left edge of the puddle) would
observe the disturbances to strike the puddle's edge at the same
frequency that would be observed by an observer at point B (at the right
edge of the puddle). In fact, the frequency at which disturbances reach
the edge of the puddle would be the same as the frequency at which the
bug produces the disturbances. If the bug produces disturbances at a
frequency of 2 per second, then each observer would observe them
approaching at a frequency of 2 per second.Now suppose that our bug is moving to the right across the puddle of water and producing disturbances at
the
same frequency of 2 disturbances per second. Since the bug is moving
towards the right, each consecutive disturbance originates from a
position that is closer to observer B and farther from observer A.
Subsequently, each consecutive disturbance has a shorter distance to
travel before reaching observer B and thus takes less time to reach
observer B. Thus, observer B observes that the frequency of arrival of
the disturbances is higher than the frequency at which disturbances are
produced. On the other hand, each consecutive disturbance has a further
distance to travel before reaching observer A. For this reason, observer
A observes a frequency of arrival that is less than the frequency at
which the disturbances are produced. The net effect of the motion of the
bug (the source of waves) is that the observer towards whom the bug is
moving observes a frequency that is higher than 2 disturbances/second;
and the observer away from whom the bug is moving observes a frequency
that is less than 2 disturbances/second. This effect is known as the Doppler effect.What is the Doppler Effect?
The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding. It is important to note that the effect does not result because of an actual change in the frequency of the source. Using the example above, the bug is still producing disturbances at a rate of 2 disturbances per second; it just appears to the observer whom the bug is approaching that the disturbances are being produced at a frequency greater than 2 disturbances/second. The effect is only observed because the distance between observer B and the bug is decreasing and the distance between observer A and the bug is increasing.The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or emergency vehicle was traveling towards you on the highway. As the car approached with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency) was high; and then suddenly after the car passed by, the pitch of the siren sound was low. That was the Doppler effect - an apparent shift in frequency for a sound wave produced by a moving source.
The Doppler Effect in Astronomy
The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.Sources
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