Download Einstein Postulates for Special Relativity

Lecture 5-1
The Doppler Effect
For Sound:
“The change in frequency for a given velocity v depends on whether it is the source or receiver that is
moving with that speed.” It depends on the medium, e.g. “air.”
vL
L
B
vs
vs
S
S
F
vst
L is listener, B is behind, F is front, S is source.
The wavelength Fin front of the source is:
The wavelength Bbehind the source is:
The waves approaching the moving listener L have a speed of propagation relative to him given
by:
The frequency fL at which the listener encounters these waves is:
which expresses the frequency fL as heard by the listener in terms of the frequency fs of the
source.
Lecture 5-2
Lecture 5-3
Transverse Doppler Effect
A light source travels with velocity v past a detector at D. The special theory of relativity predicts
a transverse Doppler effect as the source passes through point P, where the direction of travel is
perpendicular to the line extending through D. Classical theory predicts no such effect.
Lecture 5-4
Astronomical Doppler Effect
In astronomical observations of stars, galaxies, and other sources of light, the speed of sources can be
determined either receding, directly away from us, or approaching, directly toward us, by measuring the
Doppler shift of the light that reaches the Earth.
Suppose a star moves away from us with a radial speed v that is low enough so that  is small enough for
us to neglect 2 terms or
Because astronomical measurements involving light are usually done in wavelengths rather than
frequencies, replace  with c/ and p with c/p, where  is the measured wavelength and p is the proper
wavelength.
Lecture 5-5
Problem: How much energy would be required to accelerate a particle of mass m from rest to speed of (a)
0.5c, (b) 0.9c, (c) 0.99c? Express answers as multiples of the rest energy.
Lecture 5-6
Problem: At what value of u/c does the measured mass of a particle exceed its rest mass by: