A source of radio waves, rest frequency 188 MHz, is moving at a speed of 0.717c transverse to the line of sight to a detector. We have to find the angle to the line of sight of a second source, rest frequency 162 MHz, moving also at 0.717c, for the frequencies of the two sources as received at the detector to be equal.
|
Solution: Click For PDF Version If a source of light moving with velocity
with respect to an inertial observer in a frame S
emits light of frequency
measured in the stationary frame of the source and its frequency
is measured in the frame S when
the line of site makes an angle
with the velocity
,
the frequencies
and
are related by the relativistic Doppler effect equation
The frequency of the radio waves, rest frequency 188 MHz, emitted by a source moving with speed 0.717c at right angles to the line of site will be
We have to
find the angle to the line of sight of a second source, rest
frequency 162 MHz, moving also at 0.717c,
for the frequencies of the two sources as received at the detector
to be equal. Let the angle between the line of site of the second
source and its velocity be
The condition that
gives the equation
|
.
