Caption: The Doppler effect for electromagnetic radiation (EMR) in vacuum, where the phase velocity (i.e., velocity of wave propagation) is the invariant vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns.
For the second panel in the image, instead of "wavelength longer" read "wavelength shorter".
In vacuum, the Doppler effect for EMR is always the (extreme limit) relativistic Doppler effect.
Explication of the Doppler effect for electromagnetic radiation (EMR) in vacuum:
So phase velocity is the invariant for all observers (no matter how they are moving) unlike the classical Doppler effect for mechanical waves where the invariant for all observers is wavelength. Note we will NOT expand on the weird effects of special relativity here.
The upshot of the foregoing is that the behavior and formulae are different for the relativistic Doppler effect for EMR.
If you consider EMR in a medium, you have to deal both with frame-dependent phase velocity and relativistic effects.
But we will avoid this tricky case.
Note air is approximately a vacuum for most purposes.
If you move in the wave propagation direction, the frequency decreases (i.e., there is a redshift). If you move opposite the wave propagation direction, the frequency increases (i.e., there is a blueshift).
The Doppler shifts are illustrated in the image.
If you move perpendicular to the wave propagation direction, there is a relativistic Doppler effect transverse Doppler effect, but it is very small usually and we will NOT consider it further.
We only explicate them here for motion along or opposite the wave propagation direction for simplicity.
First, for the classical Doppler effect for mechanical waves, except to 1st order in small observer velocities, the Doppler shift in frequency between two observers depends on their individual velocities. But for relativistic Doppler effect (in vacuum), it depends only on the relative velocity between the two observers.
Second, for the classical Doppler effect for mechanical waves, the Doppler shift in wavelength depends only on source velocity relative to the medium. But for relativistic Doppler effect (in vacuum), it depends again on (and only on) the relative velocity between any two observers (one of whom may also be a source).
In fact, the relativistic Doppler effect (in vacuum) is simpler to understand given the vacuum EMR phase velocity formula fλ=c: any increase/decrease in frequency correponds to an inverse decrease/increase in wavelength. So, in fact, one does NOT need to always refer to both frequency and wavelength Doppler shifts since one kind of Doppler shift implies the other.
A Doppler shift---or any other kind of wavelength shift---that decreases wavelength is called a blueshift because blue is at the short wavelength end of the visible band.
The blueshift and redshift astro-jargon is used for all EMR, NOT just visible light.
But why NOT violetshift instead of blueshift? After all, violet is the shortest wavelength visible light.
Probably, because violetshift does NOT trip off the tongue.
The formula for wavelength shift is
where the vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns, v is the velocity along the line of sight of observer 2 relative to observer 1. Note v is positive/negative for recession/approach.
The frequency formula is derived from the wavelength shift formula using the phase velocity formula fλ=c. It is
If |v| << c , then we have the 1st order Doppler effect formula
where Δλ is the change in wavelength and λ is either of the observer 1 wavelength or observer 2 wavelength or an average thereof since their difference is insignificant.
The corresponding frequency formula is
which is exactly analogous to the Doppler effect formula for mechanical waves in the case of low velocities for two observers relative to the phase velocity of the medium.