Problems on the Relativistic Doppler Effect
Problem 1.1:
A train is moving directly towards you at
2×108 m/s. The (monochromatic) light on the front of
the train has a wavelength of 250 nanometers in the frame of the train. What wavelength do you observe?
[Solution]
Problem 1.2:
Light that is assumed to be from the 22.5 cm microwave Hydrogen line is measured at a frequency of
1.2×103 MHz. How fast is the galaxy from which this light was emitted receding from the earth?
[Solution]
Problem 1.3:
Consider two ultra-high-speed drag racers. One drag racer has a red stripe on the side and overtakes the
other drag racer at a relative speed of
c/2. If the red stripe has wavelength 635 nanometers, what
color is the stripe as observed by the other drag racer (that is, what is the wavelength) at the exact instant
the overtaking occurs as measured in the frame of the racer-being-overtaken?
[Solution]
Problem 1.4:
In the previous problem, what is the observed color of the stripe at the instant the overtaken drag racer
observes herself being overtaken?
[Solution]
Problem 1.5:
Explain (qualitatively if you like) why an observer moving in a circle around a stationary source observes the
same Doppler effect as one of the transverse cases discussed in Section 1.
Which one and what is the frequency shift? Use the fact that if an inertial observer observes the clock of an accelerating
object, it is only the instantaneous speed which is important in calculating the time dilation.
[Solution]
c/2. If the red stripe has wavelength 635 nanometers, what
color is the stripe as observed by the other drag racer (that is, what is the wavelength) at the exact instant
the overtaking occurs as measured in the frame of the racer-being-overtaken?
[Solution]
