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

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SUMMARY

The discussion clarifies the differences between the equations for the Doppler effect and relativity. The first formula, used for stellar aberration, defines the unit vector in the source frame, while the second formula, applicable to the Doppler effect, defines the unit vector in the observer's frame. Both equations are not equivalent due to their differing reference frames. For further understanding, the text "Classical Theory of Electric and Magnetic Fields" by Good and Nelson is recommended for deeper insights.

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  • Understanding of the Doppler effect in physics
  • Familiarity with relativity concepts
  • Knowledge of unit vectors in different reference frames
  • Access to "Classical Theory of Electric and Magnetic Fields" by Good and Nelson
NEXT STEPS
  • Study the derivation of the Doppler effect equations
  • Explore the concept of stellar aberration in detail
  • Review the definitions of unit vectors in various reference frames
  • Read "Classical Theory of Electric and Magnetic Fields" by Good and Nelson for comprehensive understanding
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Students and educators in physics, particularly those studying relativity and wave phenomena, as well as anyone interested in the mathematical foundations of the Doppler effect.

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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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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.
 

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