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

In summary, the conversation discusses the effects of sound waves on a gas with two types of atoms with different masses. The question is whether the sound wave causes one species to move faster than the other and if so, by how much. The answer is that the speed of the wave is not the same as the particle velocity, and a more massive molecule would not accelerate as much as a less massive one. This is explained by Newton's second law and the concept of particle displacement.
  • #1
bohrpi
2
0
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?
 
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  • #2
Anyone?
 
  • #3
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
 

1. What is the significance of studying the velocity of different species in a gas with propagating sound wave?

The velocity of different species in a gas with propagating sound wave is an important parameter in understanding the dynamics and behavior of gases. It can provide insights into the thermodynamic properties of the gas and its interaction with sound waves.

2. How does the velocity of different species in a gas affect the propagation of sound waves?

The velocity of different species in a gas influences the speed at which sound waves travel through the gas. This is because the sound wave energy is transferred through the collisions between gas molecules, and the velocity of the molecules determines the frequency and wavelength of the sound wave.

3. Are there any factors that can affect the velocity of different species in a gas with propagating sound wave?

Yes, the velocity of different species in a gas can be influenced by factors such as temperature, pressure, and the molecular weight of the gas molecules. These factors can alter the average speed of the molecules, thus affecting the overall velocity of the gas.

4. How do different gas species with varying velocities affect the speed of sound in a gas mixture?

The speed of sound in a gas mixture is determined by the weighted average of the individual gas species' velocities. This means that gases with higher velocities will contribute more to the overall speed of sound in the mixture.

5. Can the velocity of different species in a gas with propagating sound wave be measured directly?

Yes, the velocity of different species in a gas with propagating sound wave can be measured directly using techniques such as acoustic interferometry or laser Doppler velocimetry. These methods allow for precise measurements of the velocity of gas molecules and can provide valuable data for scientific research.

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