Final answer:
Using the Doppler effect, the train's speed can be calculated from the change in frequency of its whistle as it passes an observer. The train is moving at a certain speed that causes the observed frequency to be 19.0% lower after it passes compared to when it approaches.
Step-by-step explanation:
The train's change in whistle frequency due to the Doppler effect indicates its velocity. When after the train has passed you, you hear that the whistle frequency is 19.0% lower than its frequency while the train was approaching, we can calculate the speed using the formula for the Doppler effect. The frequency of the whistle decreases because the train is moving away from you.
Let f0 be the original frequency and f be the frequency observed after the train passes. The observed frequency is 19.0% lower, so f = 0.81f0. The relationship between the frequencies and the velocities can be written as:
f = f0 ( vi / (vi + vs) )
Where vi is the speed of sound and vs is the speed of the train. We can rearrange this equation to solve for vs, taking into account that the speed of sound is approximately 343 m/s (1,234 km/hr) at room temperature.
Calculating the train's speed in m/s and then converting to km/hr, we can answer the student's question, how fast is the train moving? express your answer in km/hr.