PH604 – Special Relativity (Ass. 2)
1. [30]
Hand in before 11:05am Thurs WK6
A fast pulsar emits light pulses at 1000 Hz in its own rest frame.
1000 Hz Pulsar


v
An observer in a space ship moving at a velocity, v  0.8 c , relative to the pulsar
perceives the light coming from the pulsar to be inclined at an angle,   , as measured with respect to the
relative velocity direction (as shown). What Doppler-shifted frequency will be detected on board the
space ship when
a) θ  0
b) θ  90
c)
At what angle, θ , will the pulsar frequency be unshifted.
d)
In case c), if O’ reflects the signal back along what he sees as its incident direction, what frequency
would an observer in the pulsar’s rest frame, O, observe on looking at this reflected beam?
2. [10] A particle of rest mass, m, has a total energy of 2 m c 2 , what is its kinetic energy? Deduce
speed.
its
3. [20]A police radar beam working at f 0  10 GHz records an upward shift of 1 kHz in the frequency
of the reflected signal when pointed at an oncoming car. Show that the relationship between the
oncoming car’s velocity, v car , and the frequency shift of the radar beam, f  f 0 , is given by
f - f0
2 v car
,

f0
c  v car
What is the approach speed of the oncoming car? Convert your answer to m.p.h.
(miles per hour).
v 
O
O
4.[40] Using 4-momentum conservation law to solve the following questions:
a) An elementary particle of rest mass M decays from rest into a photon and a new particle of rest
mass M/3, Find its velocity.
b) Show that a gamma photon cannot decay to produce a pair of electron and positron without
involvement of other particles.