User:John R. Brews/Sample: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>John R. Brews
imported>John R. Brews
Line 8: Line 8:
</ref> is the change in [[frequency]] of a [[wave]] for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a [[siren (noisemaker)|siren]] or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.
</ref> is the change in [[frequency]] of a [[wave]] for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a [[siren (noisemaker)|siren]] or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.


The relative increase in frequency can be explained as follows. 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. Therefore the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wavefronts 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 wavefronts is increased, so the waves "spread out".
The relative increase in frequency can be explained using the figure. Waves blowing ashore with velocity ''c'' are spaced a distance ''&lambda;'' apart. The frequency with which a crest appears at a fixed location is ''f<sub>w</sub>'':
:<math>f_w = c / \lambda  \ . </math>
The boat going to sea is running in the opposite direction to the waves at velocity ''v''. Consequently the boat moves relative to the crests at a speed ''v+c''. That means a crest is met at intervals of time &tau;'':
:<math>\lambda=(v+c)\tau \ .</math>
In other words, the frequency with which the boat bumps over a crest ''f<sub>b</sub>'' is:


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.
:<math> f_b= \frac{1}{\tau} = \frac{1}{\lambda / (v+c)} = f_w \frac {v+c}{c} = f_w \left( 1+\frac{v}{c} \right) \ . </math>
 
so evidently ''f<sub>b</sub>'' is a higher frequency than the frequency ''f<sub>w</sub>'' of the waves themselves. This increase in frequency is the ''Doppler effect'', and it is often expressed as the shift in frequency ''f<sub>d</sub>'', the ''Doppler shift'', namely:
 
:<math> f_d = f_b-f_w = f_w \frac{v}{c} \ . </math>
 
Of course, if the boat runs inshore with the wave, the opposite happens: it takes the boat longer between crests, and the frequency with which the boat bumps over a crest is lower than the actual frequency of the waves.


==Notes==
==Notes==
<references/>
<references/>

Revision as of 13:49, 12 April 2011

Doppler effect


(PD) Image: John R. Brews
Boat traveling against waves experiences Doppler effect.

The Doppler effect (or Doppler shift, or Doppler's principle), named after Christian Doppler who proposed it in 1842,[1] is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

The relative increase in frequency can be explained using the figure. Waves blowing ashore with velocity c are spaced a distance λ apart. The frequency with which a crest appears at a fixed location is fw:

The boat going to sea is running in the opposite direction to the waves at velocity v. Consequently the boat moves relative to the crests at a speed v+c. That means a crest is met at intervals of time τ:

In other words, the frequency with which the boat bumps over a crest fb is:

so evidently fb is a higher frequency than the frequency fw of the waves themselves. This increase in frequency is the Doppler effect, and it is often expressed as the shift in frequency fd, the Doppler shift, namely:

Of course, if the boat runs inshore with the wave, the opposite happens: it takes the boat longer between crests, and the frequency with which the boat bumps over a crest is lower than the actual frequency of the waves.

Notes

  1. ↑ C Doppler (1843). "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (On the colored light of the binary stars and some other stars of the heavens)". Abhandlungen der koniglich bohmischen Gesellschaft der Wissenschaften vol 2,: pp. 465-482.
Retrieved from "https://citizendium.org/wiki/index.php?title=User:John_R._Brews/Sample&oldid=817484"