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For a shock wave to form, the air must have a certain density. Surely in Thermosphere or even upper parts of Mesospheres the air is very thin. I was wondering if there is a formula related to the Mach Number and the probability of shock wave.

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    $\begingroup$ Your question does not make sense. There is no "probability of shock wave". You are either supersonic and get a shock, or not. The solar wind is supersonic w.r.t. the interstellar medium and it produces a shock (termination shock) in space (where the air is very thin). $\endgroup$
    – Bianfable
    Dec 14, 2020 at 17:48
  • $\begingroup$ @Bianfable: Yes, if you want to get tecnical, quite a ways beyond the orbit of Pluto :-) $\endgroup$
    – jamesqf
    Dec 15, 2020 at 4:02

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Shock waves form any time the speed of the airflow over or around a vehicle exceeds the speed of sound.

The local speed of sound varies with ambient temperature in a well-defined way; in general it goes down slightly as you climb higher.

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  • $\begingroup$ Every reference I've seen talking about mach # says it's purely a function of temperature and I've always wondered if and to what extent pressure comes into it. $\endgroup$
    – John K
    Dec 14, 2020 at 22:16
  • $\begingroup$ changing the temperature will change the air density, which will change the speed of sound. $\endgroup$ Dec 15, 2020 at 3:43
  • $\begingroup$ Yes but when you refer to "ambient pressure" it tends to infer altitude or barometric pressure. That needs to be clarified. If you said "temperature/density" that would be more accurate perhaps. $\endgroup$
    – John K
    Dec 15, 2020 at 5:13
  • $\begingroup$ @JohnK The speed of sound in an ideal gas is proportional to the square-root of the temperature, but not the pressure. Both temperature and pressure affect density, but only temperature affects speed of sound. Of course, at some point it does not make sense any more to model air as an ideal gas and this will no longer work, but for the altitudes aircraft typically fly at, it works quite well. $\endgroup$
    – Bianfable
    Dec 15, 2020 at 8:01
  • $\begingroup$ @Bianfable That has been my understanding of it. So to my point, should the post be corrected to remove the mention of "ambient pressure"? Someone reading that could infer the speed of sound is affected by altitude changes that are to one degree or another independent of temperature. $\endgroup$
    – John K
    Dec 15, 2020 at 13:32

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