Final answer:
The Doppler effect causes the frequency of sound waves to be higher when a train approaches and lower when it passes for a stationary person, whereas it remains the same for the train's engineer. A Sky Train arriving every eight minutes represents a uniform distribution of waiting times with an average of four minutes. For a bus route operating on a 15-minute schedule, four buses are needed in each direction.
Step-by-step explanation:
The frequencies observed by different observers when a train approaches and passes are examples of the Doppler effect in physics. Doppler effect describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It's applicable in many scenarios, including sound waves from a moving train.
(a) As a train approaches a stationary person, the frequency of the sound waves is higher than when the train is at a standstill because the waves are compressed. After it passes, the frequency appears lower because the waves are stretched out. On the other hand, (b) the frequency observed by the train's engineer remains constant because the engineer is moving with the source of the sound.
For illustrative purposes, if a Sky Train arriving every eight minutes follows a uniform distribution for waiting times, passengers may experience varying waiting times within that eight-minute interval, but the average time remains at four minutes.
Regarding bus schedules, the given example indicates that a one-hour one-way route with buses running every 15 minutes requires four buses in service at a time to maintain the schedule.