# Velocity of two different species in a gas with propagating sound wave

1. Jun 25, 2013

### bohrpi

I have a theoretical question which I would like to brainstorm, and would appreciate any assistance.

Let's say sound waves are propagated through a gas, with two types of atoms with very different mass, different by say a factor of ten. The number of particles per unit volume is equal, as are there temperatures. The gas is collisional. I would like to know if the sound wave causes one species to go faster than the other, and if so, how much faster?

2. Jun 26, 2013

### bohrpi

Anyone?

3. Jun 28, 2013

### Bobbywhy

Your question is not specific: when you say “the sound wave causes one species to go faster than the other” are you referring to the motion of the individual gas molecules? If yes, then that’s not the way particle motion caused by sound pressure and rarefaction waves is characterized. Normally a "parcel of the gas" is described. For instance, this from Wiki:

“Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.” http://en.wikipedia.org/wiki/Particle_velocity

Naturally, a more massive molecule would not accelerate as much as a less massive one. This page should add to your understanding of the mechanisms involved: “In classical mechanics, acceleration is related to force and mass (assumed to be constant) by way of Newton's second law:”
http://en.wikipedia.org/wiki/Particle_acceleration

“A particle of the medium undergoes displacement according to the particle velocity of the wave traveling through the medium, while the sound wave itself moves at the speed of sound, equal to 343 m/s in air at 20 °C.”
http://en.wikipedia.org/wiki/Particle_displacement