Why Does Sound Propagate?

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Germain? In this thread? LOL

It is sort of like talking to a kid that say why after every answer. No answer is sufficient.

3v0

 
The Nittiness and Grittiness

dknguyen said:
I'd normally say no, but from the way you've been pushing this topic, probably.
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I really would like to set a precident with this topic.

Initially, I just wanted to get an explanation of how/why sound propagates but, I can see that the answer also not only answers other question I have about things it also points out the crying need for some good, basic conceptual descriptions about how these things work.

I propose, as an example, some of your own delvings into flight. I have to admit that I almost winced when you started talking about Reynolds numbers. Reynolds numbers are exactly the problem with learning about this kind of stuff. Reynolds numbers are to understanding the basic principles of flight as Ohm's Law is to understanding the principles of electricity. Just as Ohm's Law only quantifies the relationships of numerical values of electrical components, without making any effort to explain the concept of them, Reynolds numbers attempt to quantify aspects of airflow around objects but, without trying to explain the concepts of why the air does what it does.

Rather than looking at classical math and physics, the way it's taught in the classroom, to get your answer to how an airplane flies, maybe it's time to get down to the nitty gritty of just how air does interact with the airplane...at whatever level is needed to understand the concept of it. And, if that means the molecular level...well, so what?

For my part, I want to set the precident that some el-crappo, half-assed description or tossing out some formulas or equations, as a way to foist off an explanation of how something works just wont cut it with this kid. And, I apologize in advance but, I have other questions that need answers, too. And, they aren't going to be any less messy...

Even though it may be messy and exasperating at first, I truly believe that such simplified, conceptural descriptions can have a great benefit for people trying to understand these things as time goes on.
 
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Back to the initial question of how a pressure disturbance propagates using the basic laws of physics.

Let's assume that the continuum description of air is valid and see where that leads, and then examine where the consequences of those assumptions are valid.

Consider a small volume in space. For concreteness let it be a cubic box with top and bottom, back and front, and left and right faces. Let there be a disturbance propagating from left to right or right to left. Then the change in the amount of air in the box is dependent on the net amount of air flowing in or out through the right and left faces. If the velocity is the same at both faces then the amount of air in the box doesn't change, but if the velocity of the air is different at the two faces then the amount of air in the box will change. Since the box is fixed in size that means that the density is changing which in turn means that the pressure is changing. Thus, the conservation of mass implies that a spacial variation (mathematically called the divergence) of velocity results in a pressure varying in time.

Next apply Newton's second law to the air in the box. If the pressure on the left and right faces is the same, then there is no net force on the air in the box. But if the pressure on the left and right faces is different then there is a net force on the air in the box. By Newton' second law this results in an acceleration of the air in the box. In other words, the velocity of the air changes with time. Therefore, Newton's second law implies that a spacial variation of pressure (mathematically called the gradient) results in a velocity varying in time.

It is clear from the above statements that pressure and velocity changes are coupled, and that there is also a coupling between spacial and time variations. At this point proceeding further without the use of mathematics seems to be intractable. First, there are proportionality constants in the equations that scale the responses with respect to one another that need to be expressed. The constants contain information about the material properties. Second, the verbal manipulation these relations is more difficult to follow that the manipulation of the underlying equations. If one can't follow the math then one certainly can't hope to follow the words.

If one does the manipulations, one does in deed find an equation that looks like a wave equation. Am I saying that sound is a wave. I won't be so bold, but to paraphrase my favorite physics teacher, "If it looks like a duck, it has webbed feet like a duck, and it quacks like a duck, you might as well call it a duck."

We've assumed the continuum description of air and obtained waves. Now where might this assumption break down and invalidate our results?
 
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I need help from the math whizzes to bring this down to my level

I'm going to try to follow this as faithfully as I can.

skyhawk said:
Consider a small volume in space. For concreteness let it be a cubic box with top and bottom, back and front, and left and right faces.
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That would be a sealed cube (all 6 faces walled). This 2D view represents that but, with the font and back faces assumed.

**broken link removed**

skyhawk said:
Let there be a disturbance propagating from left to right or right to left.
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A piezo transducer is added to create the disturbance.

**broken link removed**

The transducer is connected to a pulse generator and pulsed. the pulse begins to travel from left to right.

**broken link removed**

Of course, the sonic wavefront shown is a stylized conception but, it is a short pulse that approximates an impulse.

skyhawk said:
Then the change in the amount of air in the box is dependent on the net amount of air flowing in or out through the right and left faces.
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Both (actually, all) faces are closed otherwise, it can't be defined as some "volume" in space.

skyhawk said:
If the velocity is the same at both faces then the amount of air in the box doesn't change, but if the velocity of the air is different at the two faces then the amount of air in the box will change.
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???????

If the box is sealed then, the amount of air inside the box will always be the same. There is no velocity of the air (not at least as an air mass). If the descriptions I've read are correct, with the pulse at the location shown, neither the left or right face has any inkling that anything is going on at all. The sonic wavefront hasn't reached the right face yet and due to the "isentropic process" (ref: Sound Wave Applet), the left face has already 'forgotten' that it occurred.

skyhawk said:
Since the box is fixed in size that means that the density is changing which in turn means that the pressure is changing.
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It makes sense that if a transducer, fixed to the wall, flexes, there will be a pressure change in the box (that will travel at Mach 1). If, instead of a transducer, attached to the side of the box, the disturber is a reed that flexes, withing the volume of the box, is there a net pressure change or only the presure spike, in different parts of the box, as the impulse passes by?

**broken link removed**

skyhawk said:
Thus, the conservation of mass implies that a spacial variation (mathematically called the divergence) of velocity results in a pressure varying in time.
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Sounds very technical. I have to wonder if the operative words may be, "in time". Sound propagation seems to be a pretty much instant-by-instant process.


It's not clear to me which I suppose mostly just makes me too darn stupid to warrant knowing it.


I sure hope that's not true...in fact, I can't believe that it's true or merely asking the question is ludicrous


I have to wonder if it's a good approach to generalize about pressures and pressure gradients within an enclosure to explain what's happening as relates to sound propagation.
 
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Well...think about how someone might answer if you were asking about Ohm's law the same way you are asking about sound propogation. What would someone say?

The flowing electrons crash into the nucleus which sucks energy out of them reducing the voltage (which is more or less the energy contained in a single electron, whereas the number of electrons is the current. THe electrons that don't have enough energy just don't make it through at all which reduces the current with higher resistance. Not quite right, but you the idea.

Now, if you ask WHY when you get this answer. BAM! You are smack dab into quantum mechanics (like the forces between subatomic particles. Sound familiar?

WHy does sound propogate?->Molecular Collisions make pressure waves->BAM!

What kind of question is this? Both the volume of the box and the air mass has remained the same. You tell me if there is a permanent net pressure change. THose animations I posted way back seem to make it pretty clear there isn't going to be a permanent change in pressure enclosed space or not.

Now the localized pressure in different parts of the box on the other hand...that depends if the box is perfectly rigid, conducts heat, etc. because that energy has to go somewhere.

crashsite said:
I have to wonder if it's a good approach to generalize about pressures and pressure gradients within an enclosure to explain what's happening as relates to sound propagation.
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I don't think so. Especially when you think of where the energy is supposed to go once it hits the other side. Reminds me of the problems of 2D infinite airfoils in wind tunnels vs real airfoils. Personally, I don't know what the problem is just using an open ended or infinitely long tube.

I can sort of see how you got that a gas existing at absolute zero would not conduct sound because it would still settle to the ground due to gravity. Well it would probably still conduct but more like a really light liquid or solid within its own mass where it settled. BUt where else are you trying to go with this now? To me it seems like if things hit other things (or repulse each other when close enough), the other things move. Where else are you trying to go?
 
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I'm going to try to follow this as faithfully as I can.
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Try to follow what I mean rather than imposing your own ideas.

Both (actually, all) faces are closed otherwise, it can't be defined as some "volume" in space.
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Sounds very technical. I have to wonder if the operative words may be, "in time". Sound propagation seems to be a pretty much instant-by-instant process.
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The words "in time" are only there to distinguish what kind of variation I'm talking about. If something is not constant it can vary from place to place or time to time (or both). Here I'm focusing on how something changes as time passes at a point fixed in space.

I have no idea by what you mean by an instant-by-instant process. Do you mean some quantity has one value at one time and another value at a later time? That's what we mean when we say something varies in time. And what do you mean by "pretty much"?

The faces don't have to be closed to define a volume, and its clear by my usage that they aren't. Its a reference system. Even if you don't agree with my terminology why don't you play along (by substituting some other word for the concept of a fixed but open region in space) and see where the argument leads. Obviously you aren't trying to understand. This is standard terminology and hundreds of thousands of freshman and sophomore students grasp these ideas every year in the university in their physics and calculus courses. I've taught this to junior level chemical engineering students and even the poorest students in the class had no problem grasping the concept. I don't think you want to understand because you are too wrapped up in your own ideas. Your mind is closed. I give up.
 
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Control volume
From Wikipedia, the free encyclopedia

In fluid mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference, it is a fixed volume in space through which the fluid flows. The surface enclosing the control volume is referred to as the control surface.

At steady state, a control volume can be thought of as an arbitrary volume in which the mass of the fluid remains constant. As fluid moves through the control volume, the mass entering the control volume is equal to the mass leaving the control volume. At steady state, and in the absence of work and heat transfer, the energy within the control volume remains constant.

Overview

Typically, to understand how a given physical law applies to the system under consideration, one first begins by considering how it applies to a small, control volume, or "representative volume". There is nothing special about a particular control volume, it simply represents a small part of the system to which physical laws can be easily applied. This gives rise to what is termed a volumetric, or volume-wise formulation of the mathematical model.

One can then argue that since the physical laws behave in a certain way on a particular control volume, they behave the same way on all such volumes, since that particular control volume was not special in any way. In this way, the corresponding point-wise formulation of the mathematical model can be developed so it can describe the physical behaviour of an entire (and maybe more complex) system.

In fluid mechanics the conservation equations (Navier-Stokes equations) are by nature integrals. They therefore apply on volumes. Finding forms of the equation that are independent of the control volumes allows simplification of the integral signs.

Control volume - Wikipedia, the free encyclopedia
 
Less Literality

skyhawk said:
Try to follow what I mean rather than imposing your own ideas.
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I was trying to be as literal, at each step, as possible.

Okay, if the "volume" is open ended or even if the box doesn't exist at all and you are merely creating the disturbance somewhere in space and then measureing the pressures at some reference points, the things you say about the pressure and velocity of the air may be true. I know you may not like the, "may be".

If the disturbance is something like blowing air from a nozzle, it's definitely true. You can set up a couple of manometers and measure the pressures as the air either does or doesn't flow past them.

If the disturbance is a sonic impulse, it's not true. Even if you have a way to measure a fast event such as a sonic wave front passing by, what you'll measure at each point is ambient pressure. Then there is a sudden pressure change that returns immediately back to the ambient pressure at the first measuring point and then see it repeated a moment later at the second measuring point.

Put onto a more macro scale, if you have two people under, and in line with, the path of a supersonic aircraft but, a mile apart, the first person will hear the boom and then, a few seconds later the second person will hear it.

If what you are measuring is a low frequency signal that is changing slowly enough that you are actually measuring the pressure changes between your two measuring points, you can measure some variation of pressure and velocity changes of the air. But, you're not measuring anything related to sound propagation. You're measuring either traveling or standing waves. If need be, I can explain what I mean by this more fully.

skyhawk said:
I have no idea by what you mean by an instant-by-instant process....And what do you mean by "pretty much"?.
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If sound propagates by the process of one molecule colliding with the next and if that process occurs such that the sound will travel at high speed (about 1100 fps in air and faster in other things), the molecule to molecule action must take place in a matter of picoseconds. That's "pretty much" instantaneous.
 
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That's actually a good and valid question. And, it serves to show just how inadequate all of our methods of trying to define nature can be. We try to standardize on terminology and apply symbology and sometimes get frustrated and just make stuff up. But, it's the way we learn and part of the learning process is to find what works for yourself and try to use it as best you can.

Math is touted as the language of the universe. Who says that? The mathematicians. But, math is terrible. It's a clumsy way to try to quantify things to some level of decimal accuracy (which is always just awful compared to what's really needed), but, bad as it is, it's necessary.

Verbage is also just awful. Even when you learn the terminology of the technology, it seems like everone else has a different concept of what's meant by the words. That really shows up in forums such as these. But, lousy as it is, it's necessary.

Even the people who make stuff up (like science fiction writers...intentional and otherwise) often serve to get people thinking in odd directions and it often leads to some real science. The nut fringe may not be necessary but, they can serve to entertain and sometimes provide useful seeds.

Is the verbal, conceptural approach the "right" one for sound propagation? I think it is and for me, it's sort of the way I need to do it. I'm not convinced that it's not a pretty good approach for anybody who is trying to understand it (although I sometimes I kind of feel like the Lone Ranger on that position).
 
(although I sometimes I kind of feel like the Lone Ranger on that position).
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And some days I feel like Tonto. Surrounded by dumbass white people that think I am the uneducated one!
 
One mystery solved, anyway....


I was wondering why an enclosed (open ended) box suddenly showed up. This explains a lot.

I'm thinking that this method might not be a very good candidate for analyzing sound propagation.
 
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So you propose that any mathematics is inadequate to quantify anything accurately... you propose that the method of applying mathematics to a situation is so inadequate, but to what level?

reading through this debacle of a thread, it does seem that you are hell-bent on contradicting any form of understanding of principles that are generally accepted in modern society. Your query into the propagation of sound seems little more than an outlet into which you can be as difficult as possible. Are you attempting to be some form of revolutionary, or are you taking the ideology of questioning what you see to another painful level?

Whilst it is true that the people who have come up with new ways of explaining the nitty gritty aspects of the physical world have rejected the current way of thinking and developed a new theory (think the development of quantum mechanics). You seem to be trying to take this approach, albeit in all areas... modern understanding from sound to mathematics seems insufficient to sate your desire for perfection in comprehension of our natural world.

Your rejection of maths as the most viable way in which to explain most of these aspects is, as I see it it, ludicrous. Mathematics, whilst perhaps not being perfect in some aspects of calculations is one of the few ways in which the ways the physical world can be understood, to whatever level of detail you deem necessary. A workman can only work with what he has, a builder with only a small hammer to complete a dastardly job is not going to reject the use of the hammer for it's relative inadequacy for the job, for what else is he to use, his hands?

In the same way that you are rejecting mathematics as a viable way to understand and employ the physics of such things present in this thread is akin to a builder rejectingly the only tool that will enable him to complete his job. You can simply not undertstand most of the concepts of even trigonometry with words.

its just not going to happen.

Bottom line: How bout you bring something to this discussion instead of critisizing and shooting down anyone who is tring to give you a hand

Whilst it is true that revolutionaries have changed
 
Math, like a firearm, is okay...propertly used.

j.friend said:
So you propose that any mathematics is inadequate to quantify anything accurately... you propose that the method of applying mathematics to a situation is so inadequate, but to what level?
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Yes.

And, even to the relatively modest level where an aircraft company could feel comfortable enough with even a computer-assisted design of a conventional airplane that they would be willing to take it directly from the drawing board to the production floor. Or, that the weather man could calculate the conditions that would allow accurate weather predictions a month out without having to rely on statistical trends. Or, any of other countless ways that math falls short in defining the natural world and how to best interact with it.


Not at all. I too, have gone through life thinking I had at least a fair understanding of sound propagation (from learning about it in science class) and it seemed to match the generally accepted model; that it's all based on "waves". Then, I tried to apply it. I discovered that what I thought I knew just fell apart when even trying to take it down one small steip.

In this (debacle of a) thread, I discovered that nearly everyone else holds the same flawed views that I had. What I'm trying to do is find out how it really works. What's more, the problems are compensated for by the equations to make it seem right.


I don't have a bit of trouble with people changing the way physics is thought of or defined. It's expected that, as people learn more, that will be reflected in how they analyze things. But, when there'a a glaring problem and the "solution" is to append some mathematical constant to make it come out "right" (agree with experimental results), I do have a problem with it.


I, in no way, reject math. I even use it myself to some degree.

To use your analogy, what if the workman was a Thalomide baby and has no arms. Then no size of a traditional hammer is of much use. In that case the workman must employ other means. Perhaps a foot-operated device or driving in nails with some sort of screw mechanism he can turn with his teeth (once I had to resort to driving a horseshoe nail with a C clamp because it was in a location that could not be struck with a hammer).

That's what I face. I just don't "see" answers in math so I need to use other means to understand them. What I'm finding out more and more is that, on the subject of sound propagation, a lot of people are masking their lack of understanding of how it really works by using prefabbed formulas. In fact, it's rampant on the internet.

j.friend said:
You can simply not undertstand most of the concepts of even trigonometry with words.

its just not going to happen.
Click to expand...

Well, it also takes some charts and drawings. There's not one reason in the world why the concepts of trig can't be learned in a non-mathematical way. And, in a lot better way than it's conventionally taught (my opinion).

j.friend said:
Bottom line: How bout you bring something to this discussion instead of critisizing and shooting down anyone who is tring to give you a hand
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If you have read through the thread you will see that I have tried to come up with some scenarios that will explain the phenomena of sound propagation. I feel like I am on the right track but, continue to suffer the frustration of battling off the wave theorists; those who are convinced that sound is somehow (that they can't quite define) propagated by wave action.

I've asked the question, point blank a few times, of how waves do it. If you have the explanation, please feel free to share.
 
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Mathematics can easy show how and why a theoretical wing produces lift. Modeling an entire airplane is a much more complex problem.

The same sort of thing holds for weather. We can easily show what makes wind blow and rain fall. To create a model that accurately predicts the weather we input all the data for all variables that exist in the real system. An impossible task.

Scientists can accurately describe how sound works with math. Modeling the sound over the face of the entire earth, no.

3v0

 
If some one were to ask me how sound travels through any given medium I would indeed say it were to be through longitudinal waves. So in this way I must surely be in the group of wave theorists. If you were to look at what sound is i personally cannot go past the interaction and kinetic collisions of particles in a medium.

All this has probably already been mentioned but heck i'll say it again.

Firstly I would quite comfortably presume that you agree that the way in which we hear sound is due to pressure changes affecting our eardrums. Due to this it would be logical to assume that the sound we here is derived from the changes in pressure in our ear canal. The way in which these changes of pressure propagate seem to be the real issue being discussed.

The fact that sound is the change of pressure and/or pressure waves indicates that there is an interaction of the medium which is in contact with your eardrum. for your ear to detect sound there needs to be a change in pressure at your ear drum. This energy is caused, I believe, by the longitudinal waves travelling through the medium.

The fact that a greater pressure will result in a louder sound, whilst having "the same sound" indicates that sound itself can be in the least modelled by a wave/sine function (volume being the change in amplitude of a wave-corresponding to the force exerted due to pressure). Longitudinal waves can be seen on the macro level on such a simple scale as a newtons cradle. There are many applets that will show how a longitudinal wave will propagate throughout a medium.

Some of the characteristics of sound are most simplistically explained by longitudinal waves. The first being that sound cannot travel through a vacuum. This fact in itself indicates that that sound is a transferral of energy between the particles of a medium. The 'speed' of sound being proportionate to the density of the medium also indicates the longitudinal wave theory. The distance over which sounds travel in different mediums is also dependent on the relative movement of particles. This explains why sound travels much further and is louder underwater than in air.

If you want to go into other characteristics of sound such as the diffraction and such also indicates its wave like characteristics.

All this makes sense to me, however I acknowledge that it may indeed be wrong, after all at one point in time the world was thought to be flat.


In terms of my analogy with the builder it would be true that a person with no arms would find it very difficult to use a hammer, this however I do not feel is truly indicative of your situation. If it is how I see it, which may be completely wrong, you are not particularly proficient in mathematics (in no way am I saying that I am either). This seems to lead on to you not knowing how to apply it to the situation, an subsequent unwillingness to see it as a useful tool to utilise to solve the problem.

To put this once again in the builders analogy, a nail gun would be the best tool for the job. Lets then extend the parameters to someone who know how the nailgun itself works. not only can they use it but if something goes wrong they know how to fix it (or as it may be whether it can be fixed). A builder may only know that it does work and know how to use it (the people who appear smart through spouting or formulae?). Then there is the person who doesn't plug it in and doesn't know how it works and tries to go about finding other ways to stick in the nails (whether this be a hammer or a C-clamp).

If you do not know how to use something then how can you have a true understanding or appreciation of its capabilities to help solve a situation.


On another note can I ask as to what the simple experiment is that proves that sound is not propagated as a wave?
 
Square One...Again....

I've taken the liberty to bolden a couple of the points you make.


Okay, I agree with all that up to the point that you state that the speed of sound is proportionate to the density. It seems so intrisically obvious that would be correct that it's widely accepted. Unfortunately, it's just not true. And, that's where the wave analysis starts breaking down.

By using your logic, sound will propagate faster in colder and more highly pressurized air, (continuing to stick with air). It doesn't. Colder air is denser as is pressurized air. But, sound travels slower in colder air and the pressurization has little or no effect on the speed. There must be some other mechanism at work as regards sound propagation.

When you get to other media (liquids, solids, plasmas, other gasses) you have to rethink the whole thing anew. I've limited myself, thus far, to air but, knowing that the time will come when the other media will also have to be addressed.

j.friend said:
On another note can I ask as to what the simple experiment is that proves that sound is not propagated as a wave?
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I mentioned that part of the frustration of trying to get to the answer to this question is continually having to go back to square one to rehash the fundamental principles.

I can say that one 'experiment" is that a signal approximating an impulse propagates the same way as a wave continuum. But, that can just lead to getting into the semantics of what constitutes a "wave" and that discussion quickly masks the discussion of sound propagation.

So, what I'm going to do is refer you back to the post, in this thread, where I pretty much spelled out what I think is happening. Locate the post (I think it's the last one on page 14, titled, "Got It"). Also, read the few posts following by user, chconnor and myself. Then see what you think about it all.

Finally, after you think about it, go back to the wave analysis model and tell me how "longitudinal waves", generated by some subsonic disturber (such as vocal cords, a speaker or a steamship whistle) virtually instantly accelerate to Mach 1 and propagate at that speed.
 
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No Panacea

3v0 said:
Mathematics can easy show how and why a theoretical wing produces lift. Modeling an entire airplane is a much more complex problem.

The same sort of thing holds for weather.....
Click to expand...

No it doesn't. Math tells nothing of how or why...

Math can quantify some of this stuff in a very coarse way. Sometimes, with sufficient accuracy to be useful. But, it rarely, if ever, tells what's happening or why. It just crunches numbers and assumes that any conceptualization needs to be performed by people.

The best way to conceptualize is with words and pictures. Math results can be useful to aid the words and pictures by providing numeric values.
 
Math in not coarse. Think about calculating pi. 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 ...

Math is used to describe energy. motion, and all manner of forces, even dark energy.

I agree that human conceptualization is required but it works in conjunction with math.

how: Definition from Answers.com

how adv. In what manner or way; by what means: How does this machine work? In what state or condition: How is she today? To what extent, amount ...

why: Definition, Synonyms from Answers.com

why adv. For what purpose, reason, or cause; with what intention, justification, or motive: Why is the door shut? Why do birds sing? conj.
​
Lets talk about one rock striking another.

Why did the 2nd rock move? It moved because the 1st rock transferred energy to it. Math tells us how much energy and vorticity are involved.

Why did the rock move? Some would tell you it moves because the the laws of motion. You would correctly argue that the laws are based on observation and show how but not why. For years we have lived without knowing why. Some of that is now being determined. I have not seen much of it but expect it is mostly over my head due to the math.

3v0


 
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