Are we science literates/ Doppler effect/ 31 july 2015.

Low velocity limit (v/c small)

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Relativistic Doppler effect

Doppler Effect, Electromagnetic Waves

The Doppler effect is observed with visible light and all other electromagnetic waves. Just as in the case of sound waves, the wavelength in the direction of the source motion is shortened to

where all quantities here are measured in the observer's frame. To relate this to the source frequency, it must be expressed in terms of by using the time dilation expression

This is used to get the frequency.

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Fractional Wavelength Change

For purposes of determining recession speed of stars and galaxies with the Doppler effect by observation of the red shift of spectral lines, it is convenient to express the Doppler effect in terms of the shift in wavelength compared to the source wavelength. For these purposes it is more convenient to define a receding velocity as positive in the wavelength relationship:

The fractional wavelength change is defined as the z parameter for characterizing red shifts:

In terms of the usual relativity symbols, this becomes

Derivation

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Relativistic Doppler effect

Doppler Frequency

From the Doppler shifted wavelength, the observed frequency is

Rearranging gives the convenient form

where the relative velocity v_s is positive if the source is approaching and negative if receding. In terms of the usual relativity symbols, this becomes

Comparison with sound

Low speed approximation

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