Chapter 2: Q21DQ (page 538)
If you wait at a railroad crossing as a train approach and passes, you hear a Doppler shift in its sound. But if you listen closely, you hear that the change in frequency is continuous; it does not suddenly go from one high frequency to another low frequency. Instead the frequency smoothly (but rather quickly) changes from high to low as the train passes. Why does this smooth change occur?
Short Answer
The frequency changes smoothly from high to low as the train passes because the change depends on the distance of the train from the observer, which is changing slowly.