Don't Make It Too Complicated
Ryan:
EAS is usually so similar to CAS or IAS that it isn't worth mentioning. V-speeds have to do with dynamic pressure, as you stated.
r1830:
The speed of sound in any gas depends on one thing only: Temperature. The colder it gets, the slower the speed of sound.
Two things happen as you climb: temperature goes down, so the actual Mach-1 speed of sound goes down.
Second: since air density goes down, your Indicated speed starts to be significantly less than your True Air speed through that medium.
So as you climb, at lower indicated speeds, your true speed through the medium is a bigger percentage (Mach nnumber) of a speed of sound that has decreased with altitude.
And the critical Mach of an airfoil (wing or prop) cares only about the ratio of true speed and actual speed of sound.