Why Does Sound Propagate?

[crashsite]

Concept

But he claims the vector is the result of averaging. The length of such an average vector is not the same as the radius.

Unless it's important at this juncture, for a conceptual understanding, I don't want to get the thread too balled up in the numbers and calculations. As, Kenny Rogers sang..."There'll be time enough for counting when the dealing's done".

At this point, is the basic premise that the speed of sound is directly related to the speed of the molecules and that it can be calculated by their temperature and vectors (though apparently, not by direct averaging or summation...but, related)?

Can it be said that if there is a small bias impressed on the molecules by some source of sound energy, that it is added to the much larger movement, due to heat, that the sound energy will be propagated from molecule to molecule with a nominal average speed of Mach 1 (when the math is done correctly), because the molecules themselves are moving at that speed?

Sorry, kids...but, when you're a math moron like me, we can't just skim over big blocks of concept with equations and formulas. We need the blanks filled in.

 

[crashsite]

Molecule by Molecule

This small average velocity serves to change the number of molecules in a unit volume resulting in the compressions and rarefactions.

This is a point where we have a substantial conceptual difference of what's happening. You have the actual air molecules "oscillating" with resulting compressions and rarefactions. I think about it completely differently.

This was pretty much the post I was going to send to user, 3v0 but...

Just to keep it simple, let me pick a number out of the air. Let's say that, due to the air density and temperature, there is a uniform time that it takes one molecule to bump a neighbor of 10 picoseconds.

If we put something like a piston in the air and move it, the piston will interact with the air, either compressing it or rarefying it (as the piston moves back and forth). The piston is moving subsonically. The piston couples its energy to the air molecules adjacent to its surface only. Additional action and interaction is between the air molecules themselves.

There's a short range effect of the gross movement of air by the piston (similar to what you'd find by blowing out a breath of air). There is also an effect that propagates away from the piston at Mach 1. Since this thread is about sound propagation we'll just concentrate on the second one.

An air molecule that impinges on the piston encounters a moving mass and, either picks up a little energy from the piston (piston moving outward) or gives up a little to it (piston moving inward).

How much time is the piston in contact with the molecule? Well, the entire time it takes for a molecule to traverse the space from one molecule to the next (in our hypothetical example) is only 10 ps. The amount of time the piston would be in contact with the air molecules must be only a fraction of a ps. How far will the piston move in the amount of time it's contacting the molecule and transferring its energy?

When the next molecule encounters the piston, it also gains or loses a bit of energy from it.

The molecules that have encountered the piston, return to the random mix of molecules but, carrying the energy bias. As they collide with other molecules, they carry that bias away from the piston at Mach 1.

There was a post way back when that I expounded on why I thought the sonic effect only propagates away from the disturber.

So, there is no "oscillation" (at least not in the sense of some wavelike action of compression and rarefaaction). Instead there is a very slight, near instantaneous energy bias impressed on the molecules at the interface of the piston. As the affected molecules collide with other air molecules, that bias gets moved along from molecule to molecule.

Of course, over time, the piston moves a significant distance and the local pressure effects can be observed and/or measured but, by that time the "sound" has already propagated well out into the environment.

I know this is difficult to envision and I find that I must concentrate at each step to keep it in perspective, myself.

 

[skyhawk]

Unless it's important at this juncture, for a conceptual understanding, I don't want to get the thread too balled up in the numbers and calculations. As, Kenny Rogers sang..."There'll be time enough for counting when the dealing's done".

I believe that you were the one that brought up averages. As I understood your claim it was that the speed of sound is the rms speed of molecules times sin 45 due to some kind of averaging. I felt that I was dealing with concepts, the concept of an average, i.e. add together N objects and divide by N.

BTW I do think that averaging is an important concept when discussing the propagation of sound. I believe that what you describe as the bias corresponds to what is normally called the material or bulk velocity of the air. I don't know for sure since you are kind of fuzzy with your useage. The material velocity is obtained by averaging the velocity of a large number of molecules in a small region of space. It averages out the random motion and leaves a much smaller velocity that represents the directed or bulk motion of the gas. For reference note that at atmospheric pressure and room temperature there are 2.5x10^7 molecules in a cubic micron of gas.

At this point, is the basic premise that the speed of sound is directly related to the speed of the molecules and that it can be calculated by their temperature and vectors (though apparently, not by direct averaging or summation...but, related)?

Yes. The relation is by way of the kinetic theory of gases. Bernoulli in his book Hydrodynamics published in 1738 showed that pressure = (nmv^2)/3 where n is the number of molecules per unit volume, m is the mass of a molecule, and v is the rms molecular speed. The "springiness" of a gas is related to the speed of the molecules and to the speed of sound.

Can it be said that if there is a small bias impressed on the molecules by some source of sound energy, that it is added to the much larger movement, due to heat, that the sound energy will be propagated from molecule to molecule with a nominal average speed of Mach 1 (when the math is done correctly), because the molecules themselves are moving at that speed?

A lttle fuzzy, but it sounds about right.

Sorry, kids...but, when you're a math moron like me, we can't just skim over big blocks of concept with equations and formulas. We need the blanks filled in.

Fair enough, but don't reply to honest efforts with snarky comments like:

There are probably some mathematical gyrations that show that there are variations to skew what seems like a pretty obvious answer. I recall reading something once that it's been proven (mathematically) that 2+2≠4.

I'm not using a trick to prove 0= 1. I'm trying to do honest math and letting the chips fall where they may. I'm not trying to perpetrate a fraud.

 

[skyhawk]

This is a point where we have a substantial conceptual difference of what's happening. You have the actual air molecules "oscillating" with resulting compressions and rarefactions. I think about it completely differently.

I am not saying that individual molecules oscillate. Individual molecules undergo random motion, zig zag paths if you will. I am talking about the bulk motion that results when you average the random motions of literally millions of molecules. The frequency of molecular collisions is orders of magnitude higher than the frequency of ordinary sound. In fact when the frequency of sound reaches the order of magnitude of the collision frequency of the molecules the propagation of sound ceases to be a meaningful concept.

The molecules that have encountered the piston, return to the random mix of molecules but, carrying the energy bias. As they collide with other molecules, they carry that bias away from the piston at Mach 1.

Yes, but why does this small bias (to use your terminology) move at Mach 1? That is the question.

 

[crashsite]

Bits and Pieces

am talking about the bulk motion that results when you average the random motions of literally millions of molecules.

Whether it's one molecule or millions (billions or trillions) I don't see them oscillating. Just picking up that energy bias and moving outward. And then reconverting that energy bias to some receptor, as a copy of the original...minus losses and smearing, at another location.

Yes, but why does this small bias (to use your terminology) move at Mach 1? That is the question.

I'm thinking the reason the bias (to use my term) moves at mach 1 is essentially what's shown in my graphical example. The disturbance rides on the molecules that are moving at 1100 mph and the bias moves at the appropriate percentage of that (you mention the rms value...is that it?).

More of a question in my mind is why, if they are riding on randomly moving molecules, do they propagate only away from the point of disturbance? I do feel like I have a sense of this (I should go find the post I wrote about it for additional review of the concept).

 

[skyhawk]

Whether it's one molecule or millions (billions or trillions) I don't see them oscillating. Just picking up that energy bias and moving outward. And then reconverting that energy bias to some receptor, as a copy of the original...minus losses and smearing, at another location.

Cute! What I said was:

I am not saying that individual molecules oscillate. Individual molecules undergo random motion, zig zag paths if you will. I am talking about the bulk motion that results when you average the random motions of literally millions of molecules.

I am using the term oscillate in a mathematical sense that the bulk motion is described by a mathematical function that varies periodically in time. For instance

u = Usin(ωt)

where u is the bulk velocity, U is the amplitude, ω is the angular frequency, and t is time. I am convinced that part of your problem is that you misinterpret what people say because of your ignorance of math. You impose your interpretation on subjects rather that investigating what the author intended. You are very quick to do this. You seem to have a need to prove others wrong and yourself right.

I'm thinking the reason the bias (to use my term) moves at mach 1 is essentially what's shown in my graphical example. The disturbance rides on the molecules that are moving at 1100 mph and the bias moves at the appropriate percentage of that (you mention the rms value...is that it?).

Why don't you define bias. It seems to be a slippery term that can mean different things at different times. An honest discussion requires a clear definition of terms. Your graphical example has shown nothing. The projection of one vector onto another at 45 degrees results in a factor of√2/2. So what? That's garden variety vector algebra. What physical principle is at work? As I have stated the factor is wrong. The factor depends on gamma of the material.

More of a question in my mind is why, if they are riding on randomly moving molecules, do they propagate only away from the point of disturbance? I do feel like I have a sense of this (I should go find the post I wrote about it for additional review of the concept).

I may have missed it, but at this point I don't know what you believe to be propagating.

What precisely is propagating? Until you define that this is just hand waving.

 

[3v0]

So, there is no "oscillation" (at least not in the sense of some wavelike action of compression and rarefaaction). Instead there is a very slight, near instantaneous energy bias impressed on the molecules at the interface of the piston. As the affected molecules collide with other air molecules, that bias gets moved along from molecule to molecule..

A speaker cone periodically sends out a pulse of energy. We agree on that.

Between each energy pulse it is retracting. You get a series of energy pulses.

If we examine the air a few feet from the speaker we will see the energy pulses go by. The air is oscillating. There is an air density difference between the energy pulse and the air between pulses.

3v0

 

[crashsite]

Words fail me...but, so does math...

You impose your interpretation on subjects rather that investigating what the author intended. You are very quick to do this. You seem to have a need to prove others wrong and yourself right.

I've learned (the hard way) that, in a forum like this, you do not get an answer by asking a question. You can ask if there's a cloud in the sky and the next ten posts will be theories of cloud formation, tropical monsoons, lab experiments of boiling water (with YouTube video), and, of course, the operating principle of the obligatory gadget that grows hair or gives better gas mileage or converts nuclear waste to food for third world nations.

The tack that seems most successful in keeping a thread on topic is to advance a theory and give people specific things to pick apart.

Do I like being right? Sure. Do I need to be "right"? I'd rather be accurate.

In this case, I have a desire to know the answer and I know what level I want it and what my limitations are that force me to get it at that level. If I allow the thread to gravitate to Professor Peabody's Math Lab (which it surely will, if not aggressively kept in check), I just fall out of the loop. That's why I'm being such a poop about pushing past the math to get to the concept.

It's been a lot of work trying to keep this thread on topic and moving forward.

Let me append this. I really do appreciate everybody's views on this and I've probably learned as much or more from the posts I disagree with. I like it that we can disagree without taking it personally. There are a LOT of forums on the internet where even the smallest disagreement is perceived as a personal attack on someone.

The fact is, that I can definitely be the bad guy and I've been that guy in this thread.

Why don't you define bias. It seems to be a slippery term that can mean different things at different times.

I may have missed it, but at this point I don't know what you believe to be propagating.

What precisely is propagating? Until you define that this is just hand waving.

I've been thinking about this and, conclude that I also have been guilty of some wrong thinking. I was thinking about the compression cycle adding some energy and the rarefaction cycle subtracting some. Now, I think that both are adding energy to the molecules.

If the molecules are moving around at some speed, in a random manner, and they encounter a moving piston, the "bias" that's put on them is actually a change in direction and that requires that energy be expended to change the direction. That energy is absorbed by the molecule. So, the logic is that whether the change is toward the compression or rarefaction direction doesn't matter. It's still energy added to the molecule. I'm still considering the ramifications.

What's propagating is still the result of molecules colliding with one another but the direction is skewed by the motion that the piston impressed onto the molecules. I'm sorry. I don't know any words that are more descriptive for the effect.

 

[crashsite]

Gross Effects vs. Molecular Interactions

A speaker cone periodically sends out a pulse of energy. We agree on that.

I'm not sure we agree on that. Integrated over enough time, I guess you could say that it's true. But, when integrated over that much time it's at a scale that has nothing to do with the propagation of sound.

 

[3v0]

I'm not sure we agree on that. Integrated over enough time, I guess you could say that it's true. But, when integrated over that much time it's at a scale that has nothing to do with the propagation of sound.

Think about sound. We specify it it cycles per second and values like 200, 1000 are common and well within our range of hearing.

I understand you want to look at the molecular level and that is fine but both are part of the same happening.

If we ever worked it from little to big or big to little I think we would see that.

3v0

3v0

 

[crashsite]

It's a small world afterall...

If we ever worked it from little to big or big to little I think we would see that.

Okay, let's think big to little to big.

Typically, our sound source is big (vocal cords, a speaker, a hand clap, a car engine, thunder, etc.). As such, it interacts with a lot of air. Zillions of molecules. So, there is a lot of averaging and interaction going on at that level. Too much and at a scale that's overwhelming except by thinking "big".

In the big world, we see the speaker cone vibrating and feel the air vibrating and think of things in a very wave-like way.

In the big world, we also yell across a canyon and hear our echo come back to us and make some observations about speed and distance. We can then use that info to do things like estimate the distance of lightning strikes.

But, there's really no good explanation for the sound delay in the big world. Still, there's a natural tendency to try to explain it with what we know and what we know is "waves". It must have something to do with compression waves and restoring forces and potential and kinetic energy. Wave stuff.

In fact, the desire to think of it that way is so strong that the Wiki article on sound describes it that way and uses a bunch of really impressive looking equations to back it up.

But, I'm so bad at math, I can't look at it that way. What I do look at is how it logically must work and I saw problems. Either I was wrong or everybody else was.

As we progress in this, I think we can all see (optimistic cuss, eh?) that the Wiki version has some problems. And, it's while trying to sort out those problems that you keep getting down to more and more fundamental aspects of what's going on. you work your way down to the little world.

In the little world, we can examine what is happening with the very molecules and ask if we need to go even lowere and tinier. I've resolved, in my mind, that the molecular level is good.

Now, I'm not only no mathematician, I'm also no molecular physicist. But, I can (in my rather coarse way) come up with some hypotheses about what logically must be happening. What I see not happening is "waves".

While I don't have the credentials or skills to work out the proofs in the manner that's been developed by the scientific commmunity, I do feel like I'm on the right track.

Once the little world is resolved to some degree of satisfaction, then all those little events again need to be brought back to the big world again. But, this time the big world needs to be more critical. It's no longer adequate to observe big things and pronounce them to be the way it works. Now the big world needs to follow all the rules of both the big and little worlds.

Does any or all of that seem reasonable?

 

[3v0]

We can look at what is happening on the large scale then ask what happens on the small scale to cause the large scale action to happen.

When we know that we could ask what is happening at the next level. Repeat rinse.

You have to stop at some point due to choice or lack of ability. But it makes a lot of sense to start with the large.

3v0

 

[crashsite]

Regroup

But it makes a lot of sense to start with the large.

Okay, that sounds like a good plan. The floor is yours. The topic is, "How does sound propagate?".

 

[j.friend]

I gather that the question about the oscillation of the particles is one of the main problems here. I tend to go with crashsite on this one. If you were to send one pressure wave out I don't believe there would be much, if any rarifaction, as the energy has just been transferred between molecules. However in the presence of a sound source that is playing different sounds there will be oscillation to a certain degree as the waves created by different pressures spread out.

In this respect I dont think you can split wave analogy from sound. An wave of negative pressure propagates in the same way and speed as a wave of positive pressure. if you agree that sound propagates due to molecule - molecule interactions I dont think that you can deny the oscillation of molecules in the medium through which sound is passing throuhg

 

[j.friend]

whoops didn't see the other posts :S

i would just like to refine the speaker emitting pulses of energy statement...
just as the speaker emits a pulse of positive pressure where molecules are more likely to be directed away from the speaker. This is your diagram on whahever page it is.

However, on the return stroke it also 'emits' a pulse of negative pressure, meaning particles are more likely to be directed towards the speaker. this is due to the average distance they will travel due to 'extra space' on the side towards the speaker.

This may be a little unclear... I'll try to find a graphical representation.

 

[3v0]

Okay, that sounds like a good plan. The floor is yours. The topic is, "How does sound propagate?".

I would like to start with the classic notion that a speaker will send out a series of energy pulses in the form of compression waves.

The following link is a power point slide set for a UCSD physics lecture. Math is described to quantify as needed but there are also abundant diagrams to illustrate what is happening. If you can not or choose not to follow the math the pictures provide a nice trail of logic.

Keep in mind that this is a level one sort of thing and we will what and maybe some how but not a lot of why.

https://www.physics.ucsd.edu/~tmurphy/phys8/lectures/10_sound.ppt

If you object the content of a slide mention it's name and what you do not agree with. It that happens on slide one we will start there.

3v0

 

[crashsite]

The following link is a power point slide set for a UCSD physics lecture. Math is described to quantify as needed but there are also abundant diagrams to illustrate what is happening. If you can not or choose not to follow the math the pictures provide a nice trail of logic.

Keep in mind that this is a level one sort of thing and we will what and maybe some how but not a lot of why.

https://www.physics.ucsd.edu/~tmurphy/phys8/lectures/10_sound.ppt

If you object the content of a slide mention it's name and what you do not agree with. It that happens on slide one we will start there.

That presentation agrees pretty much down the line with the Wiki descriptions. We can ignore the first panel (cover page) and slides from about 10 to the end as they are related to the physiology of hearing and dissecting waveforms and speaker construction. That leaves slides 2 through about 9 or 10 to consider.

That presentation is also the way this stuff was taught to me.

I can see that I was wrong. That presentation shows me that it's not going to work to start out "big". The first sentence of slide 2 (What IS Sound) immediately requires dropping down to the molecular level to even begin to discuss it.

The author does make some correct statements on the, Speed of Sound slide when he says that the speed of sound is related to the motion of the molecules and that they move at 500 m/s while the sound itself propagates at about 345 m/s. But, you're right, he doesn't put it together how it works. Worse, by the time he gets to the, Sopeed of Sound slide, he's already got the subject completely polluted by longitudinal waves and slinky springs and wave analysis.

I don't think we can start with that Power Point presentation and have any hope of coming to an understanding of sound propagation. Everything I've complained about the way it's taught in the schools is in that presentation...in spades. There must be a more representative description of how it works out there...somewhere...

 

[j.friend]

So you are still totally against the idea of waves then?
I'm going to write down the logical sequence for me... then you can point out at which point you think the wave theory falls down:

-Sound is the propagated due to molecular interaction.

-The speed of the propagation of sound is dependent on the velocities of the gas molecules (or thermal energy as you may call it)

-A force applied by a sound source causes a the movement of air molecules to be aligned, resulting in the propagation of sound in the aligned direction.

-The 'down stroke' of the sound source causes an alignment of the direction of molecules in the opposite direction.
(more from a website on this at the end)

-These changes can be seen to be pressure 'fronts', as pressure is defined as force per unit area. By aligning the direction of the molecules you increase the force applied by these molecules per unit area at the front of the sound wave.

-As consecutive sound waves past a certain point, the pressure at that point will change.

-Therefore the change in pressure at a certain point can be modeled by a wave function.

-A wave is defined as : (physics) a movement up and down or back and forth

-The latter matches the general motion of the molecules within the medium through which the sound is being propagated. This would indicate that sound is propagated as a wave.



So I think that this is logical. Anyone feel free to pick it to bits.



In regards to the alignment of molecules, here is another way that I found it to be explained on a website:

You should be aware that the air is made up of molecules. Most of the characteristics we expect of air are a result of the fact that these particular molecules are very light and are in extremely rapid but disorganized motion. This motion spreads the molecules out evenly, so that any part of an enclosed space has just as many molecules as any other. If a little extra volume were to be suddenly added to the enclosed space (say by moving a piston into a box), the molecules nearest the new volume would move into the recently created void, and all the others would move a little farther apart to keep the distribution even.

If the piston were to move out suddenly, the volume of the room would be reduced and the reverse process would take place, again taking a hundredth of a second until everything was settled down. No matter how far or how quickly the piston is moved, it always takes the same time for the molecules to even out.

In other words, the disturbance caused by the piston moves at a constant rate through the air. If you could make the disturbance visible somehow, you would see it spreading spherically from the piston, like an expanding balloon. Because the process is so similar to what happens when you drop an apple into a bucket, we call the disturbance line the wavefront.

the website: **broken link removed**

 

[3v0]

That presentation agrees pretty much down the line with the Wiki descriptions. We can ignore the first panel (cover page) and slides from

I would like to start with the slide "What is Sound"

Either air is effected by sound as show by the scatter graph on the bottom and density graph on top or it is not.

I think that is something we can prove.

Or you can just blow it off.

It seems to me you just looked for what you disagreed with and dismissed the lot.

3v0

 

[crashsite]

Getting close, I think...

So you are still totally against the idea of waves then?

The first thing I want to note is that I really like that description from the web page you reference. At least right up to the very last sentence where the author tries to make an equation between the sound and the waves from dropping an apple into a bucket (even there, the "wave" is implied so, I'm not completely sure of his true intent).

Okay, now your logic. When you get to your step 3, you talk about the disturbing force "aligning" the molecules. This gets a little tricky but, I don't like the idea of thinking about them being "aligned". A better term might be, that the molecules are slightly skewed, from their entirely random motion, in the same direction as the disturber moves. and, when I say slightly, I mean slightly as in how far the disturber moves in picoseconds.

Here's where I think maybe some of the confusion lies. Each molecule picks up it's motion from the disturber and immediately carries it away and into the mass of molecules, imparting that bias to other molecules as it collides with them. In that sense, the propagation is taking place on a molecule-by-molecule basis. But, if you look at the process integrated over time, you see...well, not exactly a wave.

Consider this: you have a disturber moving in a sinusoidal manner with an excursion a lot larger than the size of air molecules. If the driving sine wave is near the zero crossing point, there is maximum movement vs. time for the disturber. That larger motion gets imparted to the molecules. As the sine wave reaches it's positive or negative peak, the disturber motion is essentially zero. And, that's what gets imparted to the molecules.

So, what you have is a train of molecules, carrying the bias of the movement picked up from the disturber (on a near instantaneous basis) traveling outward, away from the disturber.

If you could put your probe into the air and "see" what is coming by, you wouldn't see a sine wave. You'd see the slight pressure variations as the train of molecules passed by.

You'll see no periodic increase or decrease in the number of molecules (like you see in the pressure distrubution diagrams (scattergraphs)...often presented even in this thread). It's always the same number of molecules. It's just that they have a slight directional bias from their normal random motion that varies in accordance with the movement of the disturber. (I have to add this disclaimer for the fastideous ones...yes, there are pressure variations in the near field much like there's a pressure change when you blow a breath of air but, here I'm thinking of sound propagating a 'substantial' distance.)

When the sound gets to some point of impedance mismatch (such as an ear drum), the ear drum will vibrate. In effect, the ear drum is integrateing those instant-by-instant variations in the train of molecues reaching it.

The actual mechanism of the sound propagation is on a molecule-by-molecule basis but, integrated over time, you get the wave structure. That's what your ears or a microphone respond to.

The thermal energy of the air is providing the power to propagate the sound. The sound itself does add a tiny bit of that energy but, virtually all of it is the heat. As the air gets warmer and the molecules move faster, the rate that the sound propagates speeds up.

So, to answer your question. No, I'm not totally against waves. But, when thinking about sound propagation, you need to put them in their propper place in the context of what's actually happening.