How do you find relative velocity of an electromagnetic wave?
for example: Intelligent beings in a distant galaxy send a signal to earth in the form of an electromagnetic wave. The frequency of the signal observed on earth is 1.1% greater than the frequency emitted by the source in the distant galaxy. What is the relative velocity of the galaxy relative to the earth?
for example: Intelligent beings in a distant galaxy send a signal to earth in the form of an electromagnetic wave. The frequency of the signal observed on earth is 1.1% greater than the frequency emitted by the source in the distant galaxy. What is the relative velocity of the galaxy relative to the earth?
1 Answer
where
Explanation:
There is difference between the question heading and the main question.
We are required to find the relative velocity of the galaxy to the earth given is the frequency of the signal emitted by the source in the distant galaxy while observed on earth.
It is a question of application of Doppler effect as applicable to electromagnetic radiations.
We know from the postulate of Special Relativity that speed of light
As such Doppler effect is observed in case of movement of source with respect to the observer as shown in the figure below which depicts Doppler redshift and blueshift.
It is given in the problem that The frequency of the signal observed on earth is
We know that for relativistic Doppler effect, observed frequency
where
We have
Squaring both sides and solving for
where