Hi mea05key,
Nice description! One detail I want to point out: your first part of the description, where the Concorde is approaching (I’m assuming by Concorde you mean an airplane travelling toward you that is flying at hypersonic speed), from your vantage point (being in another airplane), you would not hear any sound.
I found an interesting link that takes into account the Doppler effect, however, at hypersonic speeds, the sound will never reach you as the Concorde travels away from your aircraft either.
http://www.kettering.edu/~drussell/Demos/doppler/doppler.html
My theory (guess) is, all you would encounter as the two aircraft pass each other is a single sonic boom (from the pressure), but thereafter, you would not hear the Concorde sound (as you indicated).
In the case of subsonic sound, your ambulance analogy describes Doppler shift, however, the dip in the pitch of the sound is attributed to the added velocity of the approaching ambulance (the sound wave’s frequency is shifted up), and a dip in the frequency as the ambulance travels away (the sound is shifted lower by the subtractive effect of the escape velocity, offsetting the speed of sound). The factor is that the object creating the sound (the ambulance) is not travelling above the speed of sound, thus, the sound is heard, but shifted. Also, the description of the ambulance is somewhat different, if we assume our vantage point is stationary. If we make a similar comparison, maybe it would be that if we were on a road in a car, traveling in the opposite direction of the approaching ambulance, the Doppler effect would still be in effect, but we would be able to hear both the approaching and departing sound because we’re subsonic.
my brain hurts now, and I have to drive home 90 minutes from work
Nice pontificating with you :)