The spaceship shown in the figure below is traveling at a speed of 15,000 km/s to the left while it sends out a signal with a wavelength of 4 meters. If astronomers living on planets A and B measure the radio waves coming from the space ship, what wavelengths will they measure?
A) Planet A measures 6 meters, and planet B measures 2 meters.
B) Planet A measures 2 meters, and planet B measures 6 meters.
C) Planet A measures 4.2 meters, and planet B measures 3.8 meters.
D) Planet A measures 3.8 meters, and Planet B measures 4.2 meters.
E) Both Planet A and Planet B measure 4 meters.

Question

The spaceship shown in the figure below is traveling at a speed of 15,000 km/s to the left while it sends out a signal with a wavelength of 4 meters.  If astronomers living on planets A and B measure the radio waves coming from the space ship, what wavelengths will they measure?
A) Planet A measures 6 meters, and planet B measures 2 meters. 
B) Planet A measures 2 meters, and planet B measures 6 meters. 
C) Planet A measures 4.2 meters, and planet B measures 3.8 meters. 
D) Planet A measures 3.8 meters, and Planet B measures 4.2 meters. 
E) Both Planet A and Planet B measure 4 meters.

Quizplus · Accepted Answer

The wavelengths observed by planets A and B can be calculated using the formula:
λ_observed = λ_emitted / (1 ± v/c)
where λ_emitted is the wavelength emitted by the spaceship, v is the velocity of the spaceship, c is the speed of light, and the ± sign depends on whether the spaceship is moving towards or away from the observer.
For planet A, the spaceship is moving towards it, so we use the minus sign:
λ_A = λ_emitted / (1 - v/c) = 4 / (1 - (-15000 km/s)/3e8 km/s) ≈ 3.8 meters
For planet B, the spaceship is moving away from it, so we use the plus sign:
λ_B = λ_emitted / (1 + v/c) = 4 / (1 + (-15000 km/s)/3e8 km/s) ≈ 4.2 meters
Therefore, the correct choice is D.

The Spaceship Shown in the Figure Below Is Traveling at a Speed