(a) 646.9 Hz
The formula for the Doppler effect is:
where
f = 600 Hz is the real frequency of the sound
f' is the apparent frequency
v = 345 m/s is the speed of sound
is the velocity of the observer (zero since it is stationary at the station)
is the velocity of the source (the train), moving toward the observer
Substituting into the formula,
(b) 20.1 m/s
In this case, we have
f = 600 Hz is the real frequency
f' = 567 Hz is the apparent frequency
Assuming the observer is still at rest,
so we can re-arrange the Doppler formula to find , the new velocity of the train:
and the negative sign means the train is moving away from the observer at the station.