Mike wrote:
...
The sound waves will also be coming at you faster as the train comes
toward you, and slower as the train travels away from you.
...

No. The speed of sound, in the atmosphere, is fixed, it cannot be exceeded.

What is happening is that the horn is emitting a frequency, just for
example, say 2000HZ. But, the speed of the train is moving the horn
forward at some speed, what this is causing is a "shortening" of the
sound wave being emitted by the horn--while the tone is leaving the horn
at the speed of sound, the next instant of that tone wave is being
"jammed" at the beginning of the tone wave, and at the speed which the
train is traveling--this is effectively "shortening" the length of the
sound wave and raising the perceived frequency of the tone.

Or, in other words, if the train is going the speed of sound, it will
reach you at the same time the sound its horn is emitting will. This is
why you see some aircraft pass over before you hear their sound (sonic
shock wave)

Now, throw a rock from the train and (rock speed + throw speed = total
speed)--but, depending on train speed vs. wind friction--this speed will
decline quickly. Indeed, at some speed, wind friction will make it
impossible for you to throw the rock!

JS