I'm realizing there's another term besides "Doppler Effect" we can use to describe the sounds within the noise tracks.
If you find the Wikipedia entry for Flanger, they have an audio sample of the effect.
With my background as a DJ, I've been familiar with the sounds of flangers for many years. Most flangers are done with electronic FX machines, or are built into the mixers. But you can actually create flanger effects with 2 turntables and 2 copies of the same record. When you play the 2 records together and mix them, and then slightly adjust the delay between those records, you get an audible flanger effect. As the timing between the records changes, the pitch of the flanger will change.
The only thing is.... I've not been very good at picking out the flanger effect within pink noise using my ears. I believe the reason for this is because the amount of time delay for the flanger effect to be highly noticeable is probably a lot larger than the delay resolution of our DSPs. A .01ms delay won't create much flanging, especially at lower frequencies.
I'm going to try this method out again in a few weeks and see if I can't get my ears trained a little better now that I feel like I've got a stronger grasp on what to listen for.