Why Does Sound Propagate?

[crashsite]

Stating the Obvious

This post will concentrate solely on the executive toy.


This is the problem with your reasoning. The steel balls in the model represent molecules and they are touching by virtue of the scale. Even if you move then a wee bit apart they are still many magnitudes closer then molecules in air.

You can not use this flawed model. If you wanted to model air molecules with these balls you need to place them quite far apart. Even then you still have the problem with the wrong kind of forces.

3v0

Obciously, there's not a direct one-for-one corrolation between the toy and air molecules. I never meant to imply that the toy is functionally an exact model of air molecules. You bring up a valid point that the scales are completely different.

What the toy does is show, in a practical way, the concept of propagating a disturbance through an intervening mass of something and seeing how it acts. But, then you need to analyze what you discover.

There was a French machinist who made a scale model of a Ferrari (1/6 scale if memory serves me). He made every single part to scale. The trouble was, the engine didn't run very well. The Ferrari engineers took an interest and told him that the problem was that the jets in the carburetors and the manifold and engine valves were now the wrong size for air and fuel molecules. So, he had to go back and re-design the parts.

Likewise, there are differences between the toy and actual air molecules that can't be easily duplicated. So, the model is used to show what the model shows and the stuff that can't be physically modeled, on a scale we can see, must be deduced. That doesn't invalidate the model...it just means that you have to use it as a guide and take from it what it offers.

One deduction is that air molecules are tiny and light and can absorb heat energy and move quickly. Steel balls are heavy and massive. Molecules can also change directions in picoseconds. The molecules operate in any direction, not just in a row. They also have a large random motion relative to the directional bias (even for loud sounds). But really, you already know all this so, I'm just covering bases.

 

[3v0]

You bring up a valid point that the scales are completely different.

I do. Fix the model by moving the balls (molecules) apart to make them scale and watch how it works.

What the toy does is show, in a practical way, the concept of propagating a disturbance through an intervening mass of something and seeing how it acts.

What grounds to you have to make the claim that it does. Pool balls are a better choice, they also suffer from not having the correct forces acting between them, but at least you can get a more correct distance between them.

It does not relate to a gas like air. If your balls are molecules you will have to visit the vicinity of a black hole to find anything that dense as the spacing in the toy.

You have you money on the wrong horse.

3v0

 

[3iMaJ]

Why not define a "wave" as "function" or phenomenom that exhibits movement or propagation as a function of time? Isn't that really what a "wave" is any "function" or phenomenom that changes position with respect to time.

 

[crashsite]

Models

I do. Fix the model by moving the balls (molecules) apart to make them scale and watch how it works.

You can't "fix" it by moving the balls apart. As stated, the model has its purpose. It brings some of the concepts down to a very basic level and puts them on a scale that allows them to be directly observed.

The toy allows you to see how a moving mass can be coupled to another mass and have the effect of that movement be propagated through without there having to be gross movements or oscillations to accomplish it. It also shows how the movement can then be restored on the other end. It also does a good job of showing how impedance changes lead to reflections.

But, being such a simple model, it also fails substantially. For example, it's a one-dimensional model. Pool balls are at least 2D and the real thing is 3D. The toy is static. It doesn't start with the balls already in motion and moving in a substantial and random manner relative to the scale of the model. The speeds associated with the toy are highly simplified and don't match the speeds associated with sound very well.

If I build a model of a, Messerschmit ME-109, it can serve a purpose. It can be used to train RAF pilots to recognize Nazi aircraft. It can be used for wind tunnel testing (with the appropriate scaling factors employed). It can be used for visualizing how to attach armaments such as machine guns and rockets and bombs. But, through it all, it has to be considered that the real ME-109 is not constructed of balsa wood or styrene plastic and assembled with Testor's model airplane cement. But, for modeling, it works fine...just as does the toy.

I think you will agree that the executive toy does provide some modeling of the concepts of propagation although, you seem to be less impressed with it's contribution than I am.

 

[crashsite]

Waves

Why not define a "wave" as "function" or phenomenom that exhibits movement or propagation as a function of time? Isn't that really what a "wave" is any "function" or phenomenom that changes position with respect to time.

I think we're all agreeing that a wave involves "movement" at least to the extent that it's associated with some sort of change. That change may be pressure variations or electrical variations or mechanical shifts in position.

But, we are in substantial disagreement as to how the waves relate to movement through space (propagation). In my case, I don't happen to believe that "waves" are either a requisite or the mechanism of propagation.

You'll need to refine your definition. What do you mean by, "changes position"?

 

[3v0]

I think you will agree that the executive toy does provide some modeling of the concepts of propagation although, you seem to be less impressed with it's contribution than I am.

That is an understatement.

The speed of sound is important.

You think the model shows how sound can move without waves. All I see is newtons 3rd law of motion at work. There is nothing more and it does not work for sound in a gas.

It is the wrong model and you need to scrap it and go back to the drawing board.

3v0

 

[crashsite]

That is an understatement.

The speed of sound is important.

You think the model shows how sound can move without waves. All I see is newtons 3rd law of motion at work. There is nothing more and it does not work for sound in a gas.

It is the wrong model and you need to scrap it and go back to the drawing board.

3v0

It appears that the, "drawing board" may need to be the actual space, time and physical configuration of the environment of sound. The executive toy and the pool balls are merely simplified models that show some small bit of the concept of it.

You really and truly don't see any value in or corrolation to the executive toy and sound propagation??? That in itself is rather interesting.

Perhaps it's unfortunate but, as I've said, there a lot of factors that must be simultaneously considered when thinking of the concept of sound propagation and, just because you happen to be concentrating on one specific facet of it, you still need to keep, in perspective, the other facets of it, too. I wonder if the ability of people to keep all the different parts of it in context and in mind while assembling the pieces might be one of the big problems of being able to grasp how it all works...

The next thing I was going to present is a graphical representation of the vectors. But, now I'm a little nervous of how it will be received. After all it attempts to distill the concept down from a spherical model, with sound propagating all directions, down to a 2D graph (and, even that is truncated to a single quadrant). But, I suppose I'll just have to take my chances since I don't really have the time, inclination or ability to build a large-scale, 3D, full motion model (and, even if I could it would still be as complex and difficult to comprehend as the real thing).

 

[3v0]

You really and truly don't see any value in or corrolation to the executive toy and sound propagation??? That in itself is rather interesting.

I do not for the reasons stated earlier.

I wonder if the ability of people to keep all the different parts of it in context and in mind while assembling the pieces might be one of the big problems of being able to grasp how it all works...

I wonder how you can imagine that the scientific community does not know how sound travels. Why you get upset at the mention of compressed air or waves ? Then there is your total rejection of math.

The problem with the 1/16 scale cars carburetor would not have existed in a theoretical model using 1/16 scale gasoline molecules. Making 1/16 scale gasoline is not possible.

The little airplanes pilots use to illustrate their maneuvers are useful for the intended purpose. They are illustrative props with no realism beyond their outward appearance, shape and color.

The first is not an excuse for a model not to work in theory. The second is not an excuse to use a model that does not apply.

3v0

 

[skyhawk]

I wonder how you can imagine that the scientific community does not know how sound travels. Why you get upset at the mention of compressed air or waves ? Then there is your total rejection of math.


3v0

Yes, it's kind of funny. Yesterday I went to our technical library and checked out a book called "Microscopic Thermodynamics". It's 400+ pages plus appendices. The first part of the book uses rigorous mathematics to start with individual molecular collisions and go through an averaging process to obtain the macroscopic, continuum equations we normally use for fluids. From these come the usual acoustic equation with the analytic form for the speed of sound. The book was written by a mechanical engineering professor in 1968, which shows how well developed this field is. Long ago it had moved from the realm of pure science to engineering application.

 

[skyhawk]

The issue of scaling is well understood in engineering.

**broken link removed**)

Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat the laborious task of dimensional analysis and formula derivation. Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application.

Similitude can be used to predict the performance of a new design based on data from an existing, similar design. In this case, the model is the existing design. Another use of similitude and models is in validation of computer simulations with the ultimate goal of eliminating the need for physical models altogether.

Another application of similitude is to replace the operating fluid with a different test fluid. Wind tunnels, for example, have trouble with air liquefying in certain conditions so helium is sometimes used. Other applications may operate in dangerous or expensive fluids so the testing is carried out in a more convenient substitute.

Some common applications of similitude and associated dimensionless numbers;

Incompressible flow (see example above)- Reynolds number, Pressure coefficient, (Froude number and Weber number for open channel hydraulics)
Compressible flows - Reynolds number, Mach number, Prandtl number, Specific heat ratio
Flow excited vibration Strouhal number
Centrifugal compressors - Reynolds number, Mach number, Pressure coefficient, Velocity ratio

 

[crashsite]

It's like pulling teeth!

The first part of the book uses rigorous mathematics to start with individual molecular collisions and go through an averaging process to obtain the macroscopic, continuum equations we normally use for fluids. From these come the usual acoustic equation with the analytic form for the speed of sound.

The general methodology sounds a lot like what I'm trying to figure out except that it was done with, "rigorous mathematics" rather than, "conceptual reasoning".

Individual molecular collisions? Who else in this thread has accepted that except me? Where does the Wiki guy talk about how individual molecular collisions move the sound along?

Averaging to obtain the macro view? Once you accept that the process is predicated on individual molecular collisions, the averaging process is a logical extension. The graphical analysis I mentioned a couple of posts ago (that I'm concerned about how it will be received) is all about exactly this; the averaging of how to get from the molecule-to-molecule view to the macro view. Except that my analysis is by conceptual reasoning rather than by rigorous mathematics.

The chart is done and my first cut at the description is done. After some clean up, I'll present it. May still be a few days.

Actually, I've already posted my, averaging analysis but, without the graphic and it was completly ignored...but, will try it again (with the picture).

The book was written by a mechanical engineering professor in 1968, which shows how well developed this field is. Long ago it had moved from the realm of pure science to engineering application.

So, how is it that in 2000+, some guy can write an article in Wiki about longitudinal waves and springs and the interchange of potential and kinetic energy and how the medium oscillates...and nobody questions it?

And, then when somebody does question it, for the physics comminity not be able to come up with a nominally understandable answer that doesn't involve throwing out a bunch of math and a weak apology for being a, "math Nazi" and with an admonition that, "if you don't understand the math you can't understand the concept"?

Then, I watch a remdial science show on the NASA channel on sound and, Dr. D is demonstrating sound by flying gas-powered model airplaines and waving slinkies around.

 

[crashsite]

Usually, we only go back to square 1...this time it's square -1

I wonder how you can imagine that the scientific community does not know how sound travels.

Boggles the mind, doesn't it.

Why you get upset at the mention of compressed air or waves ? Then there is your total rejection of math.

I don't totally reject math. But, I do object when somebody feels like they understand some phenomena because they've learned some equations and formulas that allow them to calculate some values...especially, when they seem unable to show sufficient understanding to explain the concept of how it works. Or when somebody waves a slinky spring around and explains that's how sound propagates. Or when somebody says the answer is in, traveling waves or longitudinal waves or traverse waves but, then never gets around to explaining how those waves manage to travel at Mach 1 (oscillating the medium as they go) but, instead launch into a spate of equations to "explain" it.

Things are happening but, I don't buy into the notion that the concept of them can only be understood by the application of mathematics.

 

[3iMaJ]

So, how is it that in 2000+, some guy can write an article in Wiki about longitudinal waves and springs and the interchange of potential and kinetic energy and how the medium oscillates...and nobody questions it?

And, then when somebody does question it, for the physics comminity not be able to come up with a nominally understandable answer that doesn't involve throwing out a bunch of math and a weak apology for being a, "math Nazi" and with an admonition that, "if you don't understand the math you can't understand the concept"?

Then, I watch a remdial science show on the NASA channel on sound and, Dr. D is demonstrating sound by flying gas-powered model airplaines and waving slinkies around.

I think for starters one should never take what is written on wikipedia at face value. It is useful for a quick reference, but the reader must do sanity checks of their own because the wikipedia articles are not rigorously reviewed. However, a book that has been published and accepted HAS been put through a heavy peer review process and is a far more credible source. It is not that I don't question wikipedia, I just don't really believe what wikipedia says with out some further checking of my own.

I also think that there is some confusion on "what came first?" Experimental, conceptial work preceeds the description of some physical process through the use of mathematics. Those mathematics can then be used as a tool to further describe more complex physical processes (this is called research). At each step of the extension of understanding physical experimentation takes place to verify that the mathematics do indeed describe the physical process, if it turns out that the model does not accurately describe the process then the expression is refined. This iterative process of experimentation and refinement continues to take place until an accurate (or reasonably accurate) model is found.

So to deride a book that contains "complex mathematics" simply because the author describes the physical processes in language of math is not helpful. The "complex mathematics" cover possibly hundreds of years of experimentation and the author is cutting to the chase because the reader has nor the time or the inclination to review 100s of years of research on thermodynamics when there is a book that provides an accurate, competent summary of the history of thermodynamics that has been heavily tested and verified (and thus accepted) by the scientific community.

Now to turn to a previous question, I think in this case a picture is worth 1000 words.


The sinusoid is plotted as a function of position against some abstract "amplitude" quantity. Each of the different curves are shown at a different time snapshot and plotted against position. You can see the sinusoid changes position (physical position, like moving in a room) as a function of time. That is there exists some nonzero partial derivative dz/dt, where z is our "position variable." There are three curves plotted each at a different time snapshot such that t1>t2>t3.

This plot shows what I earlier defined as a "wave." A wave is a phenomenon that changes position with respect to time. That to follow the crest of a sinusoidal wave in this particular instance one has to change position as a function of time. As time changes one has to move in position to follow the peak of the sinusoidal wave.

 

[skyhawk]

Here's an excellent demonstration of the elasticity of air from MIT.

MIT TechTV – Air Spring with Oscillating Steel Ball

When the steel ball is at the lowest point all of its kinetic energy has been converted into potential energy. The air subsequently expands converting potential energy back to kinetic energy.

The potential energy is not the result of the inter-molecular potential, but rather from the increase in the density of the gas so that air molecules are impacting the ball more often resulting in a larger upward force. Because the compression is adiabatic the rms velocity of the molecules is also increased resulting in a higher momentum transfer for each molecular impact.

 

[crashsite]

Springs and Things

Here's an excellent demonstration of the elasticity of air from MIT.

MIT TechTV – Air Spring with Oscillating Steel Ball

When the steel ball is at the lowest point all of its kinetic energy has been converted into potential energy. The air subsequently expands converting potential energy back to kinetic energy.

The potential energy is not the result of the inter-molecular potential, but rather from the increase in the density of the gas so that air molecules are impacting the ball more often resulting in a larger upward force. Because the compression is adiabatic the rms velocity of the molecules is also increased resulting in a higher momentum transfer for each molecular impact.

That's not a steel ball. Probably a ping pong ball, judging from the ease with whick the guy can "pump" it up to the top of the column. But, regardless, it does show what you say it does.

But, I don't believe it relates to the sound propagation issue (see the next post).

 

[crashsite]

This plot shows what I earlier defined as a "wave." A wave is a phenomenon that changes position with respect to time. That to follow the crest of a sinusoidal wave in this particular instance one has to change position as a function of time. As time changes one has to move in position to follow the peak of the sinusoidal wave.

What you seem to be trying to demonstrate is the way a traveling wave, such as you might find in sound, works. But, you are doing so on a wave-by-wave basis rather than on an instant-by-instant basis.

We know it is not the air but rather the energy provided by the sound source. The sound energy moves through the air, the medium through which it travels.

Can we agree that a working definitions as the words are used in physics.

oscillate

Quote:
To vary between alternate extremes, usually within a definable period of time.

I was trying to reconcile both of these comments in the context of sound propagation through air. Here's what I came up with:

Just as, "waves" need to be carefully defined, when talking about sound propagation, "oscillation" also needs to be carefully defined.

Certainly, in the classical sense, as demonstrated by a pendulum, oscillation is not related to the definition that must be used with sound propagation. That would be the notion that the air disturber pushes some air, as one would give a tot a push on a swing and the whole mass of air, from the hand to the eardrum sweeps out and back like the entire swing and tot do. In other words, the mass of air does not oscillate.

We can make a case for a special definition of "oscillation" but, it's pretty hinky at best.

If I have an MP3 player and I download a music file from the internet to it and then play the file, is the MP3 player an oscillator? One could say that, as it reads the music file it's outputting varying audio signals. At some times, as during a flute solo, it may even be outputting a fair rendition of a sine wave.

What if the audio file is a sine wave? Or a repeating square wave or sawtooth. If that file is played, is the MP3 player an oscillator? Or, is the MP3 player simply sequentially reading out the bytes in its memory?

If you couple some energy to the air from a speaker connected to the MP3 player does that set up an "oscillation" in the medium?. Is the air oscillating in sympathy with the speaker cone as it zips away from it at Mach 1? The answer is no. There is no mechanism in that scenario to make the sound move at mach 1.

The speaker does move a local mass of air and, at some point in physics, that action needs to be discussed. But, when the issue is sound propagation, what needs to be understood is that the air disturbance from the speaker gets coupled to the adjacent air molecules on an instant-by-instant basis and that the molecules themselves are randomly moving at some speed (average of about 1100 mph in air under standard conditions). I really need to get my graphic post up to explain that.

Anyway, the upshot is that a vector bias is put on the air molecules and that's what propagates away from the speaker at Mach 1. But, during the compression cycle of the speaker cone, the bias is to add a wee bit of energy to the air molecules. During the rarefaction cycle it takes away a wee bit of energy. Integrated over time, we can define that as compressing and rarefying the air as the waveform from the speaker moves outward at Mach 1 as a traveling wave.

Is the air oscillating? I think it's a stretch to say it is. I think the best you can say is that it's following the original disturbance, pressure-wise, as it moves along.

The other thing about all this is that the traveling wave (as I've said) is just an artifact of the sound propagation process. The sound is propagated on a moelcule-by-molecule basis. To "develop" a wave from it requires you to create a scenario that's unrelated to the actual propagation of sound.

If you ask what makes a railroad train go and I comment that it has lots and lots of cars...I haven't lied...I just haven't addressed the question. If I ask why sound propagates and you reply that it's because there's longitudinal traveling waves in an oscillating medium......wellllll.....

 

[3v0]

You are not going to like this.

oscillate:
To vary between alternate extremes, usually within a definable period of time.

It says noting about oscillators, what it is oscillating, or why it is oscillating. Only what it means to oscillate. It is a good definition.

Certainly, in the classical sense, as demonstrated by a pendulum, oscillation is not related to the definition that must be used with sound propagation. That would be the notion that the air disturber pushes some air,

The cone tries to push air. But the air is not solid so there is movement that results in compression.

We know it is not the air but rather the energy provided by the sound source. The sound energy moves through the air, the medium through which it travels.

This does not mean the air is unaffected. The speaker alternatly compress and rarefies air (air pressure oscillates). This air's oscillation is the mechanism for the energy transfer.

It is the speakers energy, transferred to, and oscillating the air pressure near your ear that causes you to hear. The original air oscillates in front of the speaker, it does not travel to your ear. It causes pressure oscillations that move out from the source at mach 1.

What if the audio file is a sine wave? Or a repeating square wave or sawtooth. If that file is played, is the MP3 player an oscillator? Or, is the MP3 player simply sequentially reading out the bytes in its memory?

If anything that causes oscillation is an oscillator. I would have to say YES to all.

Certainly, in the classical sense, as demonstrated by a pendulum, oscillation is not related to the definition that must be used with sound propagation. That would be the notion that the air disturber pushes some air, as one would give a tot a push on a swing and the whole mass of air, from the hand to the eardrum sweeps out and back like the entire swing and tot do. In other words, the mass of air does not oscillate.

You have neglected the fact that air is compressible and elastic. It is like tapping the side of a slab of jello. It makes waves! The jello moves little but the energy makes it all the way to the other end. Jello is a far better model then the executive toy.

Is the air oscillating? I think it's a stretch to say it is. I think the best you can say is that it's following the original disturbance, pressure-wise, as it moves along.

Given that oscillation is moving between alternate extremes (compressed and rarefied in this case), is oscillating !

 

[crashsite]

Let the dough rest and rise...

It says noting about oscillators, what it is oscillating, or why it is oscillating. Only what it means to oscillate. It is a good definition.

Okay, we have a lot to disagree this in your post. I'm going to hold back for a little while to try to give some other people a chance to weigh in on our last two respective posts.

My next post will be the one with the graphic regarding getting to the speed of sound.

I hope there will be some good comments come in from others during this lull.

 

[3iMaJ]

What you seem to be trying to demonstrate is the way a traveling wave, such as you might find in sound, works. But, you are doing so on a wave-by-wave basis rather than on an instant-by-instant basis.

It is an instant-by-instant basis. It is a single wave shown to be propagating (changing position) as a function of time, which if you'll look to my previous post is what a "wave" was defined to be. You asked what I mean by changes position, so I showed you that a "wave" changes position as a function of time. There are not multiple waves in my plot, there is a single wave shown at different times.

 

[crashsite]

Remedial vs. Advanced Topics

It is an instant-by-instant basis. It is a single wave shown to be propagating (changing position) as a function of time, which if you'll look to my previous post is what a "wave" was defined to be. You asked what I mean by changes position, so I showed you that a "wave" changes position as a function of time. There are not multiple waves in my plot, there is a single wave shown at different times.

I got that it was a single wave that was moving along. My concern is that it clouds the water of how the sound propagates by adding the extra layers of having to conceptualize the integration of the molecule-to-molecule actions into the wave and then, after analyzing the motion of the wave, on some macro level, re-conceptualizing things back to the molecule-by-molecule level where the propagation is actually taking place.

I have no objection to doing all that...but, at a more advanced level than when trying to figure the basic principles of how sound itself propagates.