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- Doppler effect for $v \ll c$: $$\frac{\Delta \omega}{\omega} = \frac{v}{c} \cos\theta,$$ where $v$ is the velocity of the source, $\theta$ is the angle between the source's motion direction and the observation line.
- Doppler effect in the general case: $$\omega = \omega_0\frac{\sqrt{1-\beta^2}}{1-\beta\cos\theta},$$ where $\beta = v/c.$
- If $\theta=0$, the Doppler effect is called radial, and if $\theta = \pi/2$, transverse.
- Vavilov-Cherenkov effect: $$\cos\theta = \frac{c}{nv},$$ where $\theta$ is the angle between the radiation propagation direction and the velocity $v$ of a particle.
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