In this lesson, we will learn how to calculate the change in the frequency and wavelength of electromagnetic radiation due to relative motion of the source and observer.

Q1:

A spaceship is traveling from Earth to Epsilon Eridani. Every hour, the spaceship sends a transponder signal back to Earth. At what speed would the spaceship have to be traveling relative to Earth for the transponder signal to have a frequency in the rest frame of Earth that is 13 of the frequency of the signal in the rest frame of the spaceship?

Q2:

In the spectrum of light coming from a star, the Hα emission line is found to be shifted toward the red end of the spectrum. In the rest frame of the source object, the H𝛼 line has a frequency of 4.57×10 Hz. In the rest frame of Earth, the H𝛼 line appears at 4.35×10 Hz. If all of this redshift is due to relativistic motion of the star relative to Earth, how fast is the star moving away from Earth? Give your answer to 3 significant figures as a multiple of the speed of light.

Q3:

An emission line in the spectrum of the light from a star is at a frequency of 2.00×10 Hz in the rest frame of a laboratory on Earth. The star is moving away from Earth at a speed of 0.02𝑐. What was the frequency of the emission line in the rest frame of the star? Ignore the effect of cosmological redshift. Give your answer to 3 significant figures.

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