Lorentz transformation of frequency

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Homework Help Overview

The discussion revolves around the Lorentz transformation of frequency in the context of light reflecting off a moving mirror. The original poster is trying to understand how to apply the Lorentz transformation to determine the frequency change of a wave reflecting from a mirror that is moving along the X-axis.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conversion of frequency between different frames of reference, specifically from the lab frame to the mirror's frame and back. There are questions about the correctness of the assumptions regarding the frequencies of the incoming and reflected waves.

Discussion Status

Some participants have provided guidance on the steps to convert frequencies between frames, noting the invariance of wave phase. There seems to be a general agreement on the approach, but the original poster is still seeking confirmation on their understanding.

Contextual Notes

The discussion includes assumptions about the relationship between the frequencies in different frames and the behavior of the wave phase as an invariant across observers. There may be constraints related to the specific conditions of the problem, such as the angle of incidence and the speed of the mirror.

Maximtopsecret
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Homework Statement


Light (plane wave) reflects from the mirror moving along X-axis with speed V. The wave is orthogonal to the mirror (φ=0°).
Write the law for frequency change.

Homework Equations


I know Lorenz transformation for frequency.

The Attempt at a Solution


All I do not know is how to apply the mentioned equation. I suppose if we denote ω'1 is the frequency of a falling wave in the mirror's system, ω'2 is the frequency of a reflected wave in that system, ω'1 = ω'2. Also I suppose ω'2 will be equal to the frequency of reflected wave in the stationary system. Am I wrong?
 
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Convert the frequency \omega_1 of the wave in the lab frame to \omega_1' in the frame of the mirror. The, as you correctly state, the reflected wave has \omega_2' = \omega_1'. Convert the frequency \omega_2' of the wave in the mirror frame back to the lab frame. The conversion is done by noting that the wave phase is an absolute invariant - all observers agree on what is a crest and a trough.
 
MarcusAgrippa said:
Convert the frequency \omega_1 of the wave in the lab frame to \omega_1' in the frame of the mirror. The, as you correctly state, the reflected wave has \omega_2' = \omega_1'. Convert the frequency \omega_2' of the wave in the mirror frame back to the lab frame. The conversion is done by noting that the wave phase is an absolute invariant - all observers agree on what is a crest and a trough.
IMG_20150602_184117.JPG


Should it be like that?
 

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