Suppose a futuristic spaceship is moving toward a space colony at a velocity of 100,000 km/h. The spaceship is equipped with a communication system that emits a signal of 50 GHz frequency.
a) Calculate the frequency detected by the space colony observer as the spaceship approaches.
b) Calculate the frequency detected by the space colony observer after the spaceship passes by.
a) In order to calculate the frequency detected by the space colony observer as the spaceship approaches, we need to take into consideration the concept of Doppler effect. The equation used to calculate the observed frequency is given by:
observed frequency (fo) = emitted frequency (f) * (speed of sound + velocity of observer) / (speed of sound + velocity of source)
In this case, the emitted frequency is 50 GHz and the velocity of the spaceship is 100,000 km/h. The speed of sound is not given, but since the spaceship is moving in space, we can assume that the speed of sound is not significant. Therefore, the equation simplifies to:
fo = f * (velocity of observer) / (velocity of source)
For the observer, the velocity is zero since they are stationary in the space colony. Therefore, the equation becomes:
fo = f * (0) / (velocity of source) = 0
The frequency detected by the space colony observer as the spaceship approaches is 0 Hz.
b) Similarly, to calculate the frequency detected by the space colony observer after the spaceship passes by, we use the same equation, but now the observer is still stationary and the source (spaceship) has a velocity of 100,000 km/h (since it is moving in the opposite direction). Therefore, the equation becomes:
fo = f * (0) / (velocity of source) = 0
The frequency detected by the space colony observer after the spaceship passes by is also 0 Hz.