Sound waves: why do air molecules oscillate?

[haushofer]

Dear all,

"Why do air molecules start to oscillate and influence each other such that a wave is forming when you hit e.g. a drum?"

High school students asked me this, thinking the air molecules collide like marbles, creating a longitudinal wave. How would you explain this interaction-wise? Any links? Good analogies? Many thanks!

 

[HallsofIvy]

It's pretty straight forward. If you "beat" a drum, the air molecules next to the membrane are pushed back and forth by the membrane. And molecules close to those are pushed back and forth by them, etc.. If you want to get into details of the "push" then you would need to talk about magnetic fields, etc.

 

[Drakkith]

High school students asked me this, thinking the air molecules collide like marbles, creating a longitudinal wave.

Other than the fact that they are very much spaced out and moving mostly in random directions, don't they otherwise behave very much like marbles colliding with one another?

 

[anorlunda]

I used to think the same thing about interstellar nebula. They are so diffuse that the molecules almost never collide; right? Wrong. I learned here on PF that they not only collide, but that there is a speed of sound in nebula and there are shock waves, as visible in the image below.

Here is a thread from 2013, where I asked almost the same question as yours, but applied to space.

https://www.physicsforums.com/threads/interstellar-speed-of-sound.683322/#post-4334974

 

[vela]

High school students asked me this, thinking the air molecules collide like marbles, creating a longitudinal wave. How would you explain this interaction-wise?

I'm inferring from your post that you think the marble analogy is wrong in some way, but it's not clear what you're objecting to. Or are you asking why the molecules don't simply pass through each other? I'm not really sure what you're looking for here.

 

[Bystander]

Here is a thread from 2013, where I asked almost the same question as yours, but applied to space.

Don't know whether you've satisfied yourself or not, but consider mean free path lengths for very low pressures and compare those lengths to light-year distances. Or, conversely, what pressures are implied by mean free path lengths that are measured in light years; i.e., gas densities measured in atoms per cubic kilometer rather than cubic meter, or less.

 

[jbriggs444]

To me, the correct way of understanding is to build the continuum approximation (density, pressure, momentum, average velocity, flow rate, etc) based on the marble analogy and then build sound waves on top of the continuum behavior.

It is a matter of managing complexity by separating a complex behavior into simple and orthogonal components.

 

[haushofer]

I'm inferring from your post that you think the marble analogy is wrong in some way, but it's not clear what you're objecting to.

The way the air moleculew influence each other. Students think these molecules collide like marbles, having direct contact with each other.

 

[haushofer]

So, I mean: these (elastic) collissions, like here,

http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/longipatm.gif
are really "electromagnetic interactions", the molecules "pushing each other away" are really the electrons of the molecules repulsing each other by rheir electromagnetic fields, right? But do you explain that to (16 year old) students, or do you stick with the "direct contact marble model"?

 

[sophiecentaur]

I'm inferring from your post that you think the marble analogy is wrong in some way, but it's not clear what you're objecting to. Or are you asking why the molecules don't simply pass through each other? I'm not really sure what you're looking for here.

In air at atmospheric pressure, the mean free path is 68nm - that's how far a molecule is likely to travel before it hits another one. Pressure from one place to another will be 'communicated' at the speed of sound (330m/s) so it's reasonably intuitive that sound will propagate pretty easily because in, say 1m, there will be millions of collisions between the 'marbles' to achieve it.
With such vast numbers involved, it's easier (and valid) to treat the whole business as if there were a continuum, rather than lots of individual particles. The whole of thermodynamics works successfully using that assumption.

 

[haushofer]

But the "collision" really is an electromagnetic interaction, right?

 

[Ibix]

But the "collision" really is an electromagnetic interaction, right?

Yeah, but that's true of actual marbles, too. They're made of atoms too...

I'd be inclined to say the marbles model is fine qualitatively, but the reality is that they bounce due to EM interactions between their electron clouds - as does everything else.

Edit: I seem to get i instead of either o or u about 75% of the time on this phone keyboard. And I never spot it proofreading until after I post "atims" and "die to EM interactions".

 

[vela]

But the "collision" really is an electromagnetic interaction, right?

It's my understanding that the repulsion at short distances is a consequence of the Pauli exclusion principle, not the electromagnetic interaction.

 

[Delta2]

I like this thread because it asks for a deeper understanding of the internal mechanism of material waves(like sound waves, or waves in a water pool e.t.c).
I mean we know that the internal mechanism of EM-waves is Maxwell's equations and more specifically Gauss's law, Maxwell-Faraday's law and Maxwell-Ampere's law.
For material waves the internal mechanism seems to be the collisions between molecules. But we know that a collision is not indeed a collision it is either EM-interaction (thus we go again back to Maxwell's equations) or consequence of PEP (Pauli Exclusion Principle)

 

[anorlunda]

Jumping from sound in air to inter-atomic interactions is a huge leap. Are you sure that you want to cover all that in one thread? The reason I ask is that you can spend a whole lifetime understanding the interactions between just two atoms.

The theory that successfully describes such interactions is Quantum Electrodynamics QED. If that is your interest, then I recommend this famous book.

QED: The Strange Theory of Light and Matter by Richard P. Feynman

 

[haushofer]

It's my understanding that the repulsion at short distances is a consequence of the Pauli exclusion principle, not the electromagnetic interaction.

Do you have any reference for this? I know it plays a role, but I don't understand why it would be the only effect, and e.m. interactions don't playna role.

 

[sophiecentaur]

Do you have any reference for this? I know it plays a role, but I don't understand why it would be the only effect, and e.m. interactions don't playna role.

You need to be careful when you attempt to find out what 'what really happens and why'. Fields imply Forces which are nicely intuitive things; better still, the situation can be treated in terms of Potential Energy. The PEP is just a rule that tells you about not sharing quantum numbers. If you try to apply Pauli to two colliding neutral particles then could you really expect to identify which sets of quantum numbers of these particles is affecting their position and 'producing' a separating force? At the end of the day, you could, perhaps analyse such a situation in terms of the PEP but would it really get you very far?

Thermodynamics is another example where 'what really happens' when a gas does work on a piston could be put down to Statistics, rather than to forces and potential.

 

[Mister T]

"electromagnetic interactions", the molecules "pushing each other away" are really the electrons of the molecules repulsing each other by rheir electromagnetic fields, right? But do you explain that to (16 year old) students, or do you stick with the "direct contact marble model"?

You wouldn't want to pass up this wonderful opportunity to teach them that collisions don't require contact. Have two carts collide on a track. Then repeat with magnets attached to the carts in such a way that the carts exert forces on each other but never come close to touching each other. You can demonstrate that the interaction between the carts is similar whether they make contact or not. And of course, as has already been pointed out in this thread, the collision involving contact is not fundamentally different in that it also involves an interaction where, on the atomic level, there is no "contact". Thus when the drum set rests on the floor it doesn't really make contact with the floor!

 

[vela]

Do you have any reference for this? I know it plays a role, but I don't understand why it would be the only effect, and e.m. interactions don't playna role.

Kittel discusses it a little in his book Introduction to Solid State Physics. I have the sixth edition, and the discussion starts on page 61.

Also, the Wikipedia article on the exclusion principle says:

A more rigorous proof was provided in 1967 by Freeman Dyson and Andrew Lenard, who considered the balance of attractive (electron–nuclear) and repulsive (electron–electron and nuclear–nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle.

 

[anorlunda]

You are confusing intra-atomic (within an atom) with inter-atomic (between atoms) effects.

If you really want to discuss quantum mechanics, it should not be under classical physics. If that is what you want, I suggest starting a new thread under Quantum Mechanics, this thread is too confused.

 

[Nugatory]

Dear all,

"Why do air molecules start to oscillate and influence each other such that a wave is forming when you hit e.g. a drum?"

High school students asked me this, thinking the air molecules collide like marbles, creating a longitudinal wave. How would you explain this interaction-wise? Any links? Good analogies? Many thanks!

The air molecules aren’t oscillating, the air pressure is oscillating. Their first step could be understanding how in a static situation (container of gas obeying the ideal gas law) pressure is emergent from the random movement of the molecules. Once that is understood, it’s a lot easier to form an intuitive picture of how adjacent regions of high and low pressure will interact.

 

[Delta2]

The air molecules aren’t oscillating, the air pressure is oscillating. Their first step could be understanding how in a static situation (container of gas obeying the ideal gas law) pressure is emergent from the random movement of the molecules. Once that is understood, it’s a lot easier to form an intuitive picture of how adjacent regions of high and low pressure will interact.

My intuition tells me that if the pressure of a fluid is oscillating at a point then there must be some sort of oscillating movement of the molecules of the fluid around and at that point. The only way I see right now to back it up with a formal argument is to apply Bernoulli's principle for the oscillating pressure then under certain conditions oscillating pressure at a point implies oscillating velocity of the fluid at that point. But of course i am not sure whether Bernoulli's principle can be applied for sound wave pressures.

 

[haushofer]

Ok,many wonderful replies and ideas. Thanks a lot everyone! First time I teach this stuff having a PhD in quantum gravity, so I have to think more conceptually and didactically. So every input is useful!

 

[haushofer]

You are confusing intra-atomic (within an atom) with inter-atomic (between atoms) effects.

If you really want to discuss quantum mechanics, it should not be under classical physics. If that is what you want, I suggest starting a new thread under Quantum Mechanics, this thread is too confused.

No, it's ok, I think I have a clearer picture now !

 

[Drakkith]

My intuition tells me that if the pressure of a fluid is oscillating at a point then there must be some sort of oscillating movement of the molecules of the fluid around and at that point.

Have you taken into account the fact that the air molecules are already bouncing around MUCH faster than the speed of sound? It's basically an oscillation of a bulk behavior, like how electric current is the slight net motion of a chaotic mix of electrons moving in random directions in a conductor.

 

[vela]

You are confusing intra-atomic (within an atom) with inter-atomic (between atoms) effects.

No, I'm not.

 

[jtbell]

So, I mean: these (elastic) collissions, like here,

http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/longipatm.gif
are really "electromagnetic interactions", the molecules "pushing each other away" are really the electrons of the molecules repulsing each other by rheir electromagnetic fields, right? But do you explain that to (16 year old) students, or do you stick with the "direct contact marble model"?

I don't think the exact nature of the interaction matters, if the range of the interaction is short enough (much shorter than the average distance between molecules), and the collisions are elastic.

 

[hutchphd]

Have you taken into account the fact that the air molecules are already bouncing around MUCH faster than the speed of sound?

This is surprisingly not true. For an ideal gas$$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}} \qquad ,$$where ${v_m}$ is the rms speed and ${\gamma}$ is the ratio of specific heats

 

[Drakkith]

This is surprisingly not true. For an ideal gas$$\frac{v_s}{v_m}=\sqrt{\frac{\gamma}{3}} \qquad ,$$where ${v_m}$ is the rms speed and ${\gamma}$ is the ratio of specific heats

That is surprising. I thought they'd be going faster than roughly the speed of sound at room temp. That's what I get for not doing the math myself.

 

[Delta2]

Have you taken into account the fact that the air molecules are already bouncing around MUCH faster than the speed of sound? It's basically an oscillation of a bulk behavior, like how electric current is the slight net motion of a chaotic mix of electrons moving in random directions in a conductor.

I wasn't talking about the microscopic thermal motion of the molecules, i was talking about their macroscopic net speed which i believe it is also oscillating when the pressure is oscillating.

 

[sophiecentaur]

The air molecules aren’t oscillating, the air pressure is oscillating.

The molecules have a huge range of velocities; it's just the average of all the molecules' motions in a local region that's the density (pressure) and motion in the macroscopic sense.

 

[Nugatory]

The molecules have a huge range of velocities; it's just the average of all the molecules' motions in a local region that's the density (pressure) and motion in the macroscopic sense.

Yes. We plot the pressure at a point and we get a nice sinusoidal function of time, but that is a macroscopic phenomenon that emerges from averaging the much less orderly movement of the molecules. That orderly sinusoidal pressure oscillation does not imply a similar oscillation of the air molecules; they aren’t swaying back and forth in unison like a line of dancers with locked arms.

 

[anorlunda]

Yes. We plot the pressure at a point and we get a nice sinusoidal function of time, but that is a macroscopic phenomenon that emerges from averaging the much less orderly movement of the molecules.

Electric current is an even stronger analogy. The electrons move in every direction and bounce off the atoms, but the average of all their motions gives the direction and magnitude of current. Even in AC current, the electrons do not wiggle back and forth in unison.

 

[DrDu]

Actually, I think the marble analogy is quite a good one. There is this famous model of balls in a container whose bottom vibrates rapidly so that the balls jump around wildly. Would be interesting to see whether you can even simulate a wave when also one of the side walls is made to oscillate albeit more slowly.

 

[sophiecentaur]

Actually, I think the marble analogy is quite a good one. There is this famous model of balls in a container whose bottom vibrates rapidly so that the balls jump around wildly. Would be interesting to see whether you can even simulate a wave when also one of the side walls is made to oscillate albeit more slowly.

There are some good school models of kinetic behavior in gases but there are also some really poor ones with motors and rubber diaphragms which clatter a lot but their ‘wave’ patterns are mainly in one’s imagination. I suspect that small ball bearings in a container, excited and kept up by a high power piston / actuator using pink noise, would work well. But it would cost more than a budget level school demo.