# How sparse does air have to get before the speed of sound slows dramatically? Or ceases altogether?

Supposedly, at low altitudes, the increase in the speed of sound due to the increased pressure of air (and therefore, compressibility?) almost exactly cancels out the decrease in sound velocity due to increased density....

But the temperature goes down with increasing altitude, slowing sound velocity somewhat, dropping to about 85% of sea-level-velocity at the top of MT. Everest...

But what about in the exosphere? Does acoustic velocity change appreciably due to extremely low pressures and densities, differently than at lower altitudes? Is there a nonlinear effect?

The speed of sound is a complicated topic exoatmospherically. At some point the wave equations at the heart of the concept of a sound wave cease to be a good model of how things actually behave. Instead, we have to us rarefied atmosphere models, which approach things different.

As for whether the speed of sound is nonlinear, Wikipedia's page on the Speed of Sound has a picture which shows that it is most decidedly nonlinear:

For an interesting look into the oddity of rarefied gasses, one can look at Turbomolecular Pumps, which are used to generate high vacuums in vacuum chambers. At those pressures, the usual rules for gasses don't quite work because the assumptions of there being enough collisions to "propagate a wave" get questionable. For example, you start getting different behaviors based on the molecular weight of the molecules.

• is there an intuitive answer for the nonlinearity? why the cutoff at 10km? Aug 7 at 23:31
• You can see that the speed of sound follows the temperature. None of the parameters varies linearly with height. I won't call this a "nonlinear" behavior of the speed of sound.
– nasu
Aug 8 at 0:27
• @nasu it follows, but not exactly. The atmosphere is not a simple bulk of ideal gasses, so there are places where it diverges from the ideal gas assumptions. Aug 8 at 4:56
• @Leviathan The change at 10km is the tropopause. That's basically the edge of the boundary layer above the earth's surface. Above that, the surface of the earth has much less of an impact on the atmosphere's behavior. Aug 8 at 4:58
• @Leviathan Yeah. There's enough day-of variation that, if anyone needs better data than a few points on a graph, they tend to send out a airplane or rocket to go measure the speed of sound. Aug 8 at 23:13