For practical engineering purposes, it is only dependent on temperature, proportional to the square root of the temp.
A mediocre intuition is that the speed of sound is governed by the speed of the individual gas molecules. Higher pressure and density mean there are more molecules hitting each other more often, but the speed of any individual molecule is the same and defined by temperature only. (it's only a mediocre intuition because the statistical dynamics that relate bulk properties to individual molecule interactions are complicated)
I'm curious if the practical approximation still roughly holds in the thermosphere at very high temps and very low densities, do you know?
So according to the above graph, supersonic speed in the ionosphere is ~280-300 m/s, lower than at sea level. Temps are lower on average too. But a plasma jet punching through the ionosphere at 10k C would mean the plasma itself is creating the condition for supersonic speeds on the order of 2000 m/s. (Not sure if the research is saying this, or saying the jets are moving at supersonic relative to the surrounding atmosphere...)
I had forgotten about speed of sound being primarily governed by temperature until @djaychela reminded me. But I still find it completely unintuitive, even with your explanation... which is really interesting!
Hot near-vacuum gases often need molecular approaches to make models. "Sound" itself needs careful definition in such atmospheres. They're talking about jets of air pushed around by huge electric fields. "Speed of sound" is just a good way to indicate scale, it probably doesn't have much other useful meaning.
> "Speed of sound" is just a good way to indicate scale, it probably doesn't have much other useful meaning.
Yeah, that's pretty much what I'm getting out of the article... the problem is I still have no idea what that scale is, do you? I'm sure the term 'supersonic' was meant to impress and sound fast, but there's at least an order of magnitude uncertainty.
> "Sound" itself needs careful definition in such atmospheres.
I could hazard a guess, but I doubt the scientists have particularly precise measurements (and if they did they'd be better found in a paper rather than my guessing). Having a number and concentrating on it misses the forest for the trees, it's a big number, but not the most interesting part by far.
Well. In layman terms, 1) Gas's thermal energy is:
E=kT, k -some constant, T is a temperature in Kelvins
2) that thermal energy is roughly a kinetic energy at molecular level, i assume :), hence it is something like
E = (mv^2)/2, m - molecule mass, v - its speed
3) so we have kT = (mv^2)/2 ==>
==> v = sqrt(2kT/m)
this way it maybe more intuitive
Thermal energy is stored as kinetic energy in the form of vibration, rotation, and translation. That k will depend on the makeup of the gas. Monatomic gas can't store any energy in rotation whereas diatomic and larger molecules can. (This is why humidity matters, water has three atoms and thus different thermal energy characteristics)
How much thermal energy ends up as kinetic energy in translation effects the proportion of T to speed of sound.
The storage also depends on temperature, how much energy goes into each degree of freedom (rot, trans, vib) changes with temperature but is fairly static around the human experience scale of things.
A mediocre intuition is that the speed of sound is governed by the speed of the individual gas molecules. Higher pressure and density mean there are more molecules hitting each other more often, but the speed of any individual molecule is the same and defined by temperature only. (it's only a mediocre intuition because the statistical dynamics that relate bulk properties to individual molecule interactions are complicated)