The most difficult aspect of this project was applying the doppler shift to a frequency-varying source; this required the use of frequency modulation, which follows this expression for a sinusoidal baseband signal:
Where indicates the modulation depth and indicates the modulation rate. More information about frequency modulation at Wikipedia.
A binaural representation of the scenario in Problem 1 and Problem 2.
NOTE: For problem 4, the inter-aural distance of 17 cm didn't result in a very audible difference in the stereo signal. For these examples, the inter-aural distance has been deliberately exaggerated by a factor of 4, to a distance of 68 cm.
Audio example (P1):
Audio example (P2):