Which speed should be used in calculating the mach number?

[Natstrackalpha]

IAS,RAS,TAS,CAS,EAS

I thought IAS was what you see on the airspeed indicator dial - subject to position error / mechanical error (of all the things that make the a/s indicator . . .work). Take these out in your calcs and you get
RAS (which you did not mention) So RAS is IAS with all the errors taken into consideration
So far then its
IAS
RAS

So with your RAS you then work out your temperature (OAT/Ambient - i.e., the air around you, only) and Pressure i.,e your altitude. So at 5,000ft it will be less pressure than at Sea Level, as you know full well.

On your computer / whizz wheel you just stick the temp against the altitude you want to fly at. you, get, your, TAS, which is found against your RAS - see?

So far then its
IAS
RAS
TAS

then take that true airspeed and adjust on your computor for commpressability error? This gives you CAS [and for some reason the Yanks go to CAS all the time - which is which is there way of doing it and is fine]
IAS
RAS
TAS
CAS

Now, the air going into the tube [pitot] is going to cause a rise in temperature of the air - obviously we don`t bother about this flying a little old puddle-jumper, but when flying along at some 450 kts - this will happen. . . So, we . . .adjust the speed we have to accommodate the temperature rise (we are still in the briefing room) at that alt and that speed by the method used to obtain EAS (see your little book that came with your big fat CRP5 -don`t leave home without it) to get our EAS therefore we get

IAS
RAS
TAS
CAS
EAS

e` voila! However, if they are teaching you in America-land to do it straight from CAS - then do it.

Just when you thought it cool to pop a valium, hang on a sec. The question is - now, do we use the EAS speed or TAS for Mach calcs?

Well, a super sonic aircraft flying through the air at the LSS or shall we say Mach one is going to break the sound barrier - which will be a different airspeed when it is cold outside to when it is hot!

In minus 35 deg C the Speed of Sound is 600 kts
at +35 deg C its 683 kts

Even though the air popping down the tube is compressing or rising in temp
(due to compressibility and temperature rise) the fast aeroplane is moving through the atmosphere at, the, speed, of, sound, based on temperature of that air.