I do agree that you are comforted somewhat by your conception/twist there.

Perhaps Frank would be kind and tell me at what velocity or at what substantive change in medium "electromagnetic waves" differentiate themselves from sound waves, transition from sound behavior, interaction with moving solid bodies.

(Don't forget-- the confounding light speed slowing/freezing in those Bose-Einstein condensates.)

So, is it really apples-oranges? If so, that distinction seems to be brusquely/cleverly/?diplomatically or slyly brushed aside in the available treatments that I reviewed. I even sacrificially bought a couple of physics texts at the thrift stores. (Yes, it's possible that textbook authors, like reporters also bluff.)

What ***are*** the respective formulas showing Doppler effects that work in all regimes? I saw added confusion whenever I tried to jump from the discussion/formulas in the sound wave regime to the relativistic theory that the maximum relative position rate of change was limited by the "speed of light" "barrier". Approaching from the other direction, I wish to ask: Is there a sharp change at some point where "sound" waves acquire particle-analogous features, as with electromagnetic waves/particles?

I surmise that the trick of making Einstein's formula(s) work is entwined in his treatment of the "time" phenomena. If you want your race car to go faster, namely, just get a slower running watch. Neat trick. But, maybe a trick.

Extra credit question: Why could I find little/no clear discussion and differentiation of formulas for sound wave behavior, Doppler effect from/on moving bodies and the presumed electromagnetic realm? The bright point of light was the Sci Am article I saw about 2 years ago, questioning conventional conceptions of relativity. That is, if the wave behavior/phenomena are really subject to different regimes, and the laws differ? The questions persist:
1)Why isn't "Doppler" rejected or at least considered for light speed bodies? The whole ball of wax looks a little crazy to me, sorry.
2) Do "we" know, can it be defined, where the distinctive difference between light and sound behavior lies?

Based in part on some understanding of tuned coaxial lines, and wave guides, thought experiments with airplanes and submarines, I found the Doppler effect formula that Barbarian offered just to be plain incredible when attempting to apply it to Mach 1 source/reflector regimes. Interestingly, (grin) I feel entitled to expect Doppler effects with radar and airplanes to match Doppler effects with sound.

You could be right, Frank, I am just needing to meet the right higher intelligence "genius" who cares to unravel these scenarios convincingly.

I would grandiosely estimate that maybe a fraction of a percent of physicists even appreciate and understand this sound-light Doppler behavior question, so far. It seems to be something brushed aside, for convenience, merely. The risk, as I see it, is that the sycophancy of "relativity-ists" is in jeopardy. Likewise, I think the public is getting sold an incomplete unbalanced "missing gaps in logic" "evolution" theory, in TT position statement and in the popular press. That is, without bringing out/together the arrogance-assisted blind spots.

To the credit of the Science article authors, they themselves make no such clear statement of certainty of chicken having a lineal decendancy from T. rex. Inconvenient choke point:

1) Where and how did those tiny front legs turn in to feathered flight-capable wings? That's not a tiny gulf to bridge, after all.

Comparable?: The NY Times headline of Dewey beating Truman, ?1948, or the Dan RaTHer 2003-4 blunder that is probably implicated in an accelerated non-radioactive decay/decline of C-B.S.

When ***will*** this ordeal end? :-)