Relativistic Doppler Shift for Transverse Movement

In summary, the conversation discusses a sodium light source moving in a horizontal circle at a constant speed while emitting light at a specific wavelength. The wavelength shift of the emitted light is calculated using the doppler shift equation for transverse movement. The resulting shift is approximately 2.97 nm.
  • #1
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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  • #2
Looks right to me. (I get 2.97 nm for the shift.)
 

1. What is relativistic doppler shift?

Relativistic doppler shift is a phenomenon in which the observed frequency of electromagnetic waves (such as light) is changed due to the relative motion between the source of the waves and the observer.

2. How is relativistic doppler shift different from regular doppler shift?

Relativistic doppler shift takes into account the effects of special relativity, such as time dilation and length contraction, which can significantly affect the observed frequency at high speeds. Regular doppler shift only considers the relative motion between the source and observer.

3. What causes relativistic doppler shift?

Relativistic doppler shift is caused by the changing distance and time intervals between the source of the waves and the observer due to their relative motion. This results in a shift in the observed frequency.

4. How is relativistic doppler shift used in science?

Relativistic doppler shift is used in a variety of fields, including astronomy, remote sensing, and telecommunications. It allows scientists to accurately measure the motion and distance of objects in space, as well as to transmit and receive signals from moving objects.

5. Can relativistic doppler shift be observed in everyday life?

Yes, relativistic doppler shift can be observed in everyday life, although it may be imperceptible to the naked eye. For example, GPS satellites use relativistic doppler shift to accurately calculate the position of receivers on Earth. Additionally, the red and blue shift of light from stars and galaxies is also a result of relativistic doppler shift.

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