Relativistic Doppler Shift for Transverse Movement

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SUMMARY

The discussion centers on calculating the relativistic Doppler shift for a sodium light source moving in a horizontal circle at a speed of 0.100c, emitting light at a proper wavelength of λ0=589 nm. The relevant equation used is the transverse Doppler shift formula, ƒ = ƒ0√(1-β²), where β represents the speed as a fraction of the speed of light. The calculated wavelength shift is Δλ = 2.95 nm, with a slight variation noted at 2.97 nm. This confirms the accuracy of the calculations presented.

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  • Understanding of relativistic physics concepts
  • Familiarity with the Doppler effect in light
  • Knowledge of wavelength and frequency relationships
  • Basic proficiency in algebra for solving equations
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  • Study the derivation of the relativistic Doppler shift equations
  • Learn about the implications of transverse versus longitudinal Doppler shifts
  • Explore applications of Doppler shift in astrophysics
  • Investigate the effects of relativistic speeds on light properties
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Students and educators in physics, particularly those focusing on relativity and wave phenomena, as well as professionals in fields requiring an understanding of light behavior under relativistic conditions.

L_landau
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Homework Statement


A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of λ0=589 nm. Wavelength l is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift λ-λ0?

Homework Equations


Since the light source is always moving tangent to the center of the circle, I figured that I should use the doppler shift for transverse movement ƒ = ƒ0√1-β2.

The Attempt at a Solution


Using the above and solving for λ, Δλ = 2.95nm. Is this correct?
 
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Looks right to me. (I get 2.97 nm for the shift.)
 

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