Understanding the propagation of sound on molecular Scale

[Slimy0233]

TL;DR Summary

Compressions and Rarefactions on a molecular level and how they manage to keep their initial positions after propagating sounds.

I am actually an undergraduate in Physics but I didn't understand this basic phenomenon. I saw this youtube video today and I was wondering how molecule in air would be able to regain it's initial position after it has transferred it's energy to the adjacent particle. Is it like a rebound, it transfers it's energy and after it, it acts like a ball with has just hit a wall and has enough energy to regain it's initial position.

Also, once the propagation of waves (multiple waves has changed, would that leave the air molecules undisturbed (Assume ideal condition and no disturbances other than the sound wave).

I also was gonna ask about the fact that how water was able to propagate sounds or have water waves, if it was incompressible. But this Stack_Exchange thread answers that question.

 

[vanhees71]

The description of these phenomena on the level of atoms and molecules is pretty complicated as you can imagine. The best answer still is at the end to describe sound or water waves in terms of fluid dynamics (aero and hydrodynamics). There is a chain of approximations you can make starting with fundamental quantum many-body theory to derive hydrodynamics, but that's pretty challenging: You need to learn (in this case non-relativistic) quantum field theory and then its application to non-equilibrium phenomena. The most elegant formalism is the so-called Schwinger-Keldsyh real-time contour description and socalled Green's function techniques based on it, also leading to a kind of Feynman diagram formulation similar to the Feynman diagrams in high-energy physics.

The next step towards a classical description then is the derivation of (semi-classical) transport equations, where you already average out the rapid quantum fluctuations to describe the motion of macroscopic fluid cells in terms of non-equilibrium phase-space distribution functions, also leading to dissipation and the H-theorem with the notion of a "thermodynamic arrow of time".

The last step then is to describe a situation close to local thermal equilbrium, where you assume that each fluid cell is in thermal equilibrium or pretty close to it, which then leads to the fluid dynamical description in various approximations like ideal fluids (Euler equations) and a systematic inclusion of off-equilibrium effects like viscosity and heat transfer (Navier-Stokes equation).

Sound waves can be understood as linearized approximations of the Euler equations together with an adequate equation of state (usually adiabatic changes of state).

 

[A.T.]

I am actually an undergraduate in Physics but I didn't understand this basic phenomenon. I saw this youtube video today and I was wondering how molecule in air would be able to regain it's initial position after it has transferred it's energy to the adjacent particle.

First thing to realize is that the particles are moving and bouncing around all the time. So most particles do not return to their initial position. But the center of mass of a packet of air behaves somewhat like the dots in the animation.

 

[Slimy0233]

First thing to realize is that the particles are moving and bouncing around all the time. So most particles do not return to their initial position. But the center of mass of a packet of air behaves somewhat like the dots in the animation.

thank you!

 

[Slimy0233]

The description of these phenomena on the level of atoms and molecules is pretty complicated as you can imagine. The best answer still is at the end to describe sound or water waves in terms of fluid dynamics (aero and hydrodynamics). There is a chain of approximations you can make starting with fundamental quantum many-body theory to derive hydrodynamics, but that's pretty challenging: You need to learn (in this case non-relativistic) quantum field theory and then its application to non-equilibrium phenomena. The most elegant formalism is the so-called Schwinger-Keldsyh real-time contour description and socalled Green's function techniques based on it, also leading to a kind of Feynman diagram formulation similar to the Feynman diagrams in high-energy physics.

The next step towards a classical description then is the derivation of (semi-classical) transport equations, where you already average out the rapid quantum fluctuations to describe the motion of macroscopic fluid cells in terms of non-equilibrium phase-space distribution functions, also leading to dissipation and the H-theorem with the notion of a "thermodynamic arrow of time".

The last step then is to describe a situation close to local thermal equilbrium, where you assume that each fluid cell is in thermal equilibrium or pretty close to it, which then leads to the fluid dynamical description in various approximations like ideal fluids (Euler equations) and a systematic inclusion of off-equilibrium effects like viscosity and heat transfer (Navier-Stokes equation).

Sound waves can be understood as linearized approximations of the Euler equations together with an adequate equation of state (usually adiabatic changes of state).

You scare me sir/madam! I was just trying to understand standing waves more completely, no one told me I have to study this before getting a full understanding of waves. But ik, you are right. Thank you! I will keep this in the back of the mind while studying, one day I will be able to understand it properly. Thank you for your help!

 

[A.T.]

I was just trying to understand standing waves more completely,

If you want to understand waves on the microscopic level, you should start with solids like metals, where the atoms do return to their initial position.

 

[Slimy0233]

If you want to understand waves on the microscopic level, you should start with solids like metals, where the atoms do return to their initial position.

any books you would recommend for this? I probably would not be reading it (as I am swamped), but I ask you anyway...
Thank you again!

 

[vanhees71]

You scare me sir/madam! I was just trying to understand standing waves more completely, no one told me I have to study this before getting a full understanding of waves. But ik, you are right. Thank you! I will keep this in the back of the mind while studying, one day I will be able to understand it properly. Thank you for your help!

No, I precisely told you that you don't need to study quantum many-body theory but fluid dynamics to understand sound waves! Only if you want to understand it on "a molecular scale", you have to go through the (difficult) steps to derive the fluid dynamics as an effective theory of the underlying microscopic theory.

 

[hutchphd]

I was just trying to understand standing waves more completely

You also need to remember that a standing wave is a steady state phenomenon. I would also recommend looking at Feynman Lecture 1-47