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The basic formula for the speed of sound in a gas $c=\sqrt{\left(\frac{\partial p}{\partial \rho}\right)_s}$ assumes that it is uniform, and thus that sound waves travel through the gas at one speed. Suppose a gas is composed of multiple components with very different masses (e.g. a 50/50 mix of hydrogen and carbon dioxide).

Is there ever any case where it is more accurate to model the transmission of sound through this gas as happening at two distinct speeds instead of one?

Specifically if the gas were confined to a thin two-dimensional film between two solid boundaries, and it is thinner than the mean free path in the gas, then sound waves transmitted by the gas molecules will be better approximated as happening at two speeds than one. If that's the case, you could do lots of fun things with thin-film style interference of the sound waves.

That said, when dimensions are that small, even talking about "sound waves" is dubious. That's why I'm curious about whether this idea works, especially whether experiments like this have been tried.

Sean E. Lake
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    I think it's along the lines of partial pressures, i.e., the pressure in the typical sound speed equation can be summed as it is a moment of the velocity distribution function, which are additive. In an electron-ion plasma where each population has a different polytrope index, the sound speed can be approximated as shown at https://physics.stackexchange.com/a/179057/59023. – honeste_vivere Aug 13 '19 at 13:14
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    I don't have an answer, but there was a similar question about the properties of sound travelling through very thin sheets of metal a while back (https://physics.stackexchange.com/questions/341732/wall-thickness-and-acoustic-impedance). You say, "when dimensions are that small, even talking about sound waves is dubious". I, too,would like to improve my understanding of propagation through thin layers or mixtures of layers. It seems like digging into the properties of acoustic metamaterials would be an informative study. – Halyn Betchkal Aug 22 '19 at 16:49

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