What is the difference between the equations for Doppler effect and relativity?

In summary, the two equations for relativity and Doppler effect differ in the definition of the unit vector for the direction of the EM wave. One formula is for the source frame and is used for stellar aberration, while the other is for the observer's frame and is used for the Doppler effect. A more detailed explanation can be found in "Classical theory of Electric and Magnetic Fields" by Good and Nelson on page 456.
  • #1
Xeniebop
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Homework Statement



Hello, I'm researching about relativity and Doppler effect, most text and book gives the equation for it as

586dcd8c3f118083cc846e9d7e0b9fd8.png
(term with square root is on the numerator, and the term w/o is on the denominator)


while on some text, has the reverse of the fraction part (which is the term with the square root is on the numerator

img107.gif


Are they both equal to each other? I can't seem to express/derive the other one from the other one.
Can you explain what are the difference in both equations.

thanks
 

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  • #2
The two expressions differ in how the unit vector giving the direction of the EM wave is defined. Your first formula is for the direction in the source frame, and is used for stellar aberration. Your second formula defines the unit vector in the observer's frame, and is used for the Doppler effect. A good discussion of this is on page 456 of "Classical theory of Electric and Magnetic Fields" by Good and Nelson.
 

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. This effect is commonly observed with sound waves, such as the change in pitch of a siren as an ambulance passes by.

2. How does the Doppler effect relate to relativity?

According to the theory of relativity, the speed of light is constant regardless of the motion of the observer or the source of the light. This means that the Doppler effect for light waves is not caused by the relative motion between the source and observer, but rather by the changing distances between them.

3. How is the Doppler effect used in astronomy?

Astronomers use the Doppler effect to measure the motion of celestial objects, such as stars and galaxies. By analyzing the redshift or blueshift of the light from these objects, they can determine their velocity and direction of movement.

4. Can the Doppler effect be observed in everyday life?

Yes, the Doppler effect can be observed in many everyday situations. For example, the change in pitch of a passing car's horn, the change in frequency of a train's whistle as it approaches and then moves away, and the change in frequency of a police siren as it speeds by.

5. How has the Doppler effect influenced technology?

The Doppler effect has played a significant role in the development of technology, particularly in the fields of radar and sonar. These technologies use the Doppler effect to measure the speed and direction of objects, such as airplanes or submarines, by detecting changes in the frequency of the waves reflected off of them.

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