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Lorentz transformation of frequency

  1. Jun 1, 2015 #1
    1. The problem statement, all variables and given/known data
    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.
    2. Relevant equations
    I know Lorenz transformation for frequency.
    3. 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?
     
  2. jcsd
  3. Jun 2, 2015 #2

    MarcusAgrippa

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    Convert the frequency [itex] \omega_1 [/itex] of the wave in the lab frame to [itex] \omega_1' [/itex] in the frame of the mirror. The, as you correctly state, the reflected wave has [itex] \omega_2' = \omega_1' [/itex]. Convert the frequency [itex] \omega_2' [/itex] 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.
     
  4. Jun 2, 2015 #3
    IMG_20150602_184117.JPG

    Should it be like that?
     
  5. Jun 2, 2015 #4

    MarcusAgrippa

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