can you change the scenerio and the numbers of this question the story have to be completly different and original and creative: Suppose a fire truck is moving toward a stationary observer at 25.0 m/s. The frequency of the siren
on the fire truck is 800 Hz.
a) Calculate the frequency detected by the observer as the fire truck apporaches.
b) Calculate the frequency detected by the observer after the fire truck passess by.
Sure! Here's an original and creative scenario:
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.
Solution:
a) To calculate the frequency detected by the space colony observer as the spaceship approaches, we can use the formula for Doppler effect:
f' = f * (v + vo) / (v + vs)
Where:
f' = Frequency detected (unknown)
f = Frequency emitted by the spaceship (50 GHz = 50 * 10^9 Hz)
v = Velocity of the signal in space (speed of light = 3 * 10^8 m/s)
vo = Velocity of the observer (stationary = 0 m/s)
vs = Velocity of the source (spaceship approaching = 100,000 km/h = 100,000 * 1000 / 3600 = 27.8 m/s)
Plugging in the values:
f' = (50 * 10^9) * (3 * 10^8 + 0) / (3 * 10^8 + 27.8)
f' ≈ 49,999,999,072.12 Hz
Therefore, as the spaceship approaches the space colony, the observer detects a frequency of approximately 49,999,999,072.12 Hz.
b) To calculate the frequency detected by the space colony observer after the spaceship passes by, we use the same formula. However, in this case, the velocity of the source (vs) will be negative, indicating that the spaceship is moving away.
Using the same values as before:
f' = (50 * 10^9) * (3 * 10^8 + 0) / (3 * 10^8 - 27.8)
f' ≈ 50,000,000,928.28Hz
Therefore, after the spaceship passes by the space colony, the observer detects a frequency of approximately 50,000,000,928.28 Hz.