The Relativistic Doppler Effect Relativistic Doppler Effect The

The Relativistic Doppler Effect

Relativistic Doppler Effect The Doppler Effect for EM Waves (Light): The Doppler effect is a shift in detected frequency due to relative motion of the source & observer It happens for all traveling waves. • For example, it happens with sound waves, water waves & other mechanical waves. It happens when the source & the observer are moving with respect to each other with relative velocity v. • The Doppler effect for EM waves depends on only the relative velocity, v, between source & detector, as measured from the reference frame of either.

Relativistic Doppler Effect The Doppler Effect for EM Waves (“Light”): • Let f = the proper frequency of the source—that is, the frequency measured by an observer in the rest frame of the source. • f´ = the frequency detected by an observer moving with velocity v relative to that rest frame. The relation between f & f´is given in the boxed equation. • For low speeds ( = v/c << 1), this equation can be expanded in a Taylor series in & approximated as f´ f[1 - + (½) 2]

Relativistic Doppler Effect • A consequence of time dilation that we’ve briefly talked about last class is the frequency shift found for light emitted by atoms in motion as opposed to light emitted by atoms at rest. • If a light source & an observer approach each other with a relative speed, v, the frequency f measured by the observer is shifted to f´. where v/c as usual

Relativistic Doppler Effect v/c as usual • f is the frequency of the source measured in the rest frame. The shift depends only on the relative velocity, v, of the source & observer. • ƒ' > ƒ when the source & the observer approach each other. An example is the red shift of galaxies, showing that most galaxies are moving away from us.

The Doppler effect is a shift in detected frequency for traveling waves. It is observed for ALL wave phenomena • It doesn’t have to be light (EM) waves. Sound waves, etc. exhibit this effect. • The Doppler effect for electromagnetic waves depends only on the relative velocity, v, between source & detector, as measured from the reference frame of either.

Change in notation f´ f, f f 0 , = v/c Assume << 1

Transverse Doppler Effect In terms of period of oscillations: Where To is the proper period.