Lorentz transformation of frequency

In summary, the law for frequency change when a plane wave reflects from a mirror moving along the X-axis with speed V, with the wave orthogonal to the mirror, is that the frequency of the incoming wave in the lab frame is converted to the frequency in the mirror's frame, and then back to the lab frame using the absolute invariant of wave phase. All observers will agree on the frequency of the reflected wave.
  • #1
Maximtopsecret
19
0

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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  • #2
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.
 
  • #3
MarcusAgrippa said:
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.
IMG_20150602_184117.JPG


Should it be like that?
 
  • #4

What is the Lorentz transformation of frequency?

The Lorentz transformation of frequency is a mathematical formula that describes how the frequency of light or other electromagnetic radiation changes when observed from different reference frames in special relativity.

Why is the Lorentz transformation of frequency important?

The Lorentz transformation of frequency is important because it is a fundamental concept in special relativity, which is a crucial theory in modern physics. It helps to explain how the observed frequency of light changes with the relative motion between the observer and the source of light.

How does the Lorentz transformation of frequency differ from the classical Doppler effect?

The Lorentz transformation of frequency takes into account the effects of time dilation and length contraction, which are not considered in the classical Doppler effect. It also applies to all forms of electromagnetic radiation, while the Doppler effect only applies to sound waves.

What is the formula for the Lorentz transformation of frequency?

The formula for the Lorentz transformation of frequency is f' = (f (1 ± β))/(1 ± β cos θ), where f is the observed frequency, f' is the frequency in the rest frame of the source, β is the relative velocity between the observer and the source, and θ is the angle between the direction of motion and the direction of the emitted light.

How does the Lorentz transformation of frequency affect the color of objects in motion?

The Lorentz transformation of frequency can cause a shift in the color of objects in motion, known as the relativistic Doppler effect. This means that objects moving towards an observer will appear more blue, while objects moving away will appear more red. This effect is especially noticeable for objects moving at high speeds, close to the speed of light.

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