Why Does Sound Propagate?

[crashsite]

More Wave Analysis to Explain Sound Propagation...

**broken link removed**

First, your link. The guy that wrote that page would have gotten along really well with the crowd here. He immediately launches into the holy grail of, "wave analysis" as a way to explain sound propagation.

How does this effect fidelity? Easy answer, it doesn't. The shape of the human ear itself has more effect on the perception of sound than the frequency dependent component. Last time I checked for true in your face fidelity the microphone has to actually be placed inside the ear canal, or in mock ear canal very similar to the individual and played back inside the ear canal to notice these effects, and they only alter spatial perception of audio.

That's a good point and it's true. But, how it sounds has nothing to do with how the true audiophile sizes up fidelity.

Back in the 70s, a stereo dealer did an experiment. He set up two hi-fi systems for people to try and judge. One was absolute, top of the line consumer equipment and the other a run-of-the-mill system. Customers were allowed to adjust the controls but, without knowing which was which. About hllf the people prefered the sound of the cheaper system.

Specs are everything. If the spec isn't there, the true audiophile will "hear the problem". It's like the tube vs. transistor amp thing. There are still augiophiles who will only use tube equipment because they can hear the distortion of transistors.

The fact is the, Sala Effect© exists and, now that there's a way to correct it, the true audiophiles should want to address it...even though they've been hearing that distortion all their lives without a murmur of complaint.

 

[Sceadwian]

If you feel comfortable feeding people snake oil go ahead, but personally I think it's morally reprehensible. The phase effects you're talking about only effects stereo perception. Many stereo equalizers and a lot of headset type devices have 'enhancement' modes that already do something like this by creating a subtle phase delays. Personally I find it annoying.

 

[crashsite]

Perception Isn't Always Logical

Personally I find it annoying.

Personally, I do too. But then, I've never been a hardcore audiophile. But, I've known a few so, I have some familiarity with their mindset. My own collection of audio hardware, gleaned over the years is, at best a hodge podge of mid-range consumer to low-end pro stuff.

But, far from snake oil, the, Sala Effect© (I believe) is a real, definable distortion. Admittedly, a small one and mostly affecting very high frequencies and louder sounds where the ear doesn't hear that sort of thing very well anyway. But, in the pursuit of audio perfection it must be addressed and corrected...or at least taken into account and dismissed as being so slight as to not be important enough to fix (ie: it's masked by other phase or time shifting effects in the signal's passage through an audio system that swamp it out).

Besides, is selling snake oil from the back of a covered wagon any more morally reprehensible than peddling a fantasy from a pulpit or love advice from a gypsy's crystal ball or daily expectations from a horoscope column? A lot of people seem to "need" those things and get comfort from them.

 

[Sceadwian]

A lot of people seem to "need" those things and get comfort from them.

A drug dealer could say the same thing, doesn't make it right.
Granted stupid high end audio gear isn't drugs, it serves the same purpose to some fools, only costs a lot more.
Being legal doesn't make it any more right.

 

[crashsite]

Ahem...

A drug dealer could say the same thing, doesn't make it right.
Granted stupid high end audio gear isn't drugs, it serves the same purpose to some fools, only costs a lot more.
Being legal doesn't make it any more right.

Believe me, being the argumentative cuss that I am, the temptation is there but, this really is straying pretty far from the centerline of the thread so, I'll show some rare prudence here in the hopes that it can still self-correct.

 

[crashsite]

Balloons

In the absence of feedback, I’ll just forge ahead.

The thing I’m finding most frustrating about this sound propagation issue is that nobody (with a very few notable exceptions) seems to even want to think about or address the “heat” issue of it. That’s in spite of the fact that, once the medium has been established, heat variations seem to be pretty much the only variable (under “normal” conditions, anyway) that affects the speed of sound.

Even the Wikipedia explanation goes back to that same old mantra of wave analysis to explain sound propagation…and…virtually nobody challenges it. That leads me to believe that either I’m completely wrong and everybody else is right or that the 8th grade science class explanation is so strong and pervasive that it can’t be overcome.

If the wave theory would just explain the thermal aspect, I’d have no problem with it. But, it doesn’t. So, rather than even attempt to gin up a thermal explanation, the usual approach is to move right into the formulas and equations (which do nothing to explain the effects…merely to quantify them).

But, in addition to affecting the speed of Mach 1, heat has other properties and I’m not convinced that, in the final analysis, they are not very directly related.

I posed some thoughts about how heat may be related to how an airplane flies which apparently is so boring as to not even be worthy of ridicule. So, taking that as my cue to proceed, here’s another (yawn) one…

A hot air balloon rises serenely into the early morning sky. The usual explanation for why this happens is explained by, “buoyancy”; that the sum of the weight of the balloon and its payload and the air inside it are lighter than the air it displaces. In fact, it’s called a, “lighter than air” craft.

It’s also the reason a helium balloon rises into the air and why a block of wood or even an iron ship floats on the water.

But, like trying to explain sound propagation with wave theory, merely invoking the word, "buoyancy" does not really explain how balloons fly and stuff floats.

Anyone who has ever held onto the string of a helium balloon knows that there’s a force there that makes the balloon want to “defy” gravity and float up into the air. That force comes from somewhere. But, from where? Ultimately, I suspect that it’s, heat.

In the hot air balloon it’s pretty easy to develop some sort of simple-minded rationale where the hottest air rises to the top of the balloon and so the most thermal activity of the air molecules push hardest on the inside surface there, pushing the balloon up. That essentially makes the balloon work a lot like a rocket except that the pressure differential created is more subtle. But, that turns out to be a very poor explanation because the buoyancy effect must also account for the buoyancy of the helium balloon.

There is no appreciable thermal gradation inside the helium balloon and, in fact, the pressure inside all parts of the balloon are about the same.

One thing we know is that gravity is involved. Think about a helium balloon floating around in the zero-G environment of the ISS (International Space Station). It’s certainly lighter than the air in the ISS modules that the crew is breathing and floating around in. But, what direction does the balloon float within the cabin?

In fact, there’s only two things that ever make things move or tend to move a certain direction (at least in the Newtonian world). One is some sort of pressure differential across them. That is, something is pushing on one side harder than on the other. The other is, gravity. For, ”inertia fans”, we can discount that because it doesn’t make things move or change direction.

So, we know that the volume of helium in the balloon (plus the mass of the balloon itself) has less mass than the air that surrounds it. We know that it only works in a gravity field (and, thus we can think of the mass as, “weight”). We know that there is a force that is trying to pull the balloon upward (against the gravity) and that the force is there even when there’s no movement involved. That means that there are no aerodynamic forces involved.

But, we also know that the only way for the balloon to move is if there’s a greater pressure on one side of it than on the other. In this case, the greater force is on the bottom, pushing upwards harder than the force on top of the balloon pushing it downwards.

A logical conclusion might be that the air pressure of a planet, such as the Earth, has a gradient. The air at sea level has more pressure than air at higher elevations. But, for this logic to work, the pressure gradient across the balloon would have to be great enough to give a sufficient pressure difference to push the balloon up. That air-filled balloons don’t tend to rise, in the same environment and that Zeppelins don‘t fly oriented vertically (in order to give the maximum pressure differential between the “top“ and “bottom“), suggests that this is not the answer.

This is where it sort of stalls for me. I strongly suspect that heat is the force but, like the thermal aspects of sound propagation, I can’t quite reconcile it. An admonition that, well, that’s just the way nature works so there’s not much sense of even thinking about it, as has been suggested regarding the sound propagation issue, is not a satisfactory answer. In fact, it’s not an answer at all.

 

[skyhawk]

But, we also know that the only way for the balloon to move is if there’s a greater pressure on one side of it than on the other. In this case, the greater force is on the bottom, pushing upwards harder than the force on top of the balloon pushing it downwards.

A logical conclusion might be that the air pressure of a planet, such as the Earth, has a gradient. The air at sea level has more pressure than air at higher elevations. But, for this logic to work, the pressure gradient across the balloon would have to be great enough to give a sufficient pressure difference to push the balloon up. That air-filled balloons don’t tend to rise, in the same environment and that Zeppelins don‘t fly oriented vertically (in order to give the maximum pressure differential between the “top“ and “bottom“), suggests that this is not the answer.

This is where it sort of stalls for me. I strongly suspect that heat is the force but, like the thermal aspects of sound propagation, I can’t quite reconcile it. An admonition that, well, that’s just the way nature works so there’s not much sense of even thinking about it, as has been suggested regarding the sound propagation issue, is not a satisfactory answer. In fact, it’s not an answer at all.

This thread has been going a while, but I would like to jump it here to address some basic concepts.

Buoyancy does in fact arise from a pressure gradient. The mathematical demonstration is taught in the fluid statics part of a fluids course taught in just about any engineering school or physics department.

Remember that pressure is a force per area, thus the net pressure force on a object is the normal force arising from pressure integrated over the entire surface of the object. Thus

F = -∫pndA, where n is the outward pointing normal to the surface of the object.

Using the divergence theorem this can be written as:

F = -∫grad p dV,

but for a static fluid grad p = -ρgk, where g is the acceleration of gravity and k is the upward pointing unit vector. Therefore

F = [g∫ρdV]k = Mgk.

Therefore, there is an upward force on the object equal to the weight of the fluid displaced by the object. When the object is in equilibrium this upward force is exactly equal to the downward force of gravity on the object.

Notice the resulting force is independent of the orientation of the object.

 

[crashsite]

Math is good for producing numbers...

This thread has been going a while, but I would like to jump it here to address some basic concepts.

Buoyancy does in fact arise from a pressure gradient. The mathematical demonstration is taught in the fluid statics part of a fluids course taught in just about any engineering school or physics department.

I know this is not the way to "win friends and influence people" as Dale Carnegie would say and I agree that this thread has been going on way too long. I profusely apologize for the length but, not for continuing it because the question still hasn't been answered. Perhaps, from a mathematical formulation, engineering viewpoint maybe it has but, the underlying physics of it surely haven't been.

You give a formula and some, "therefores" and I have no doubt that if one is careful to ensure that the right numerical units are adhered to and the signs duly noted, you can come up with the correct vector value and it's direction.

Likewise, I can apply Ohm's Law to a series resistor problem and, by adhering to the correct numerical units, come up with the "correct" answer that will allow me to successfully select a current limiting resistor for my LED. I can "therefore" that, because of the way the formula is written, there are either direct or inverse relationships between E, I and R. But, it doesn't tell me diddly about what E, I or R are or how the circuit works.

When you start getting into semiconductor theory, you almost start getting into the "right" vein of thinking. You learn about the crystaline nature of the basic material and how the doping creates N and P materials with mobile electrons and holes. Then you put the N and P materials together to form a diode and create the depletion region and how that forms the potential hill for forward current flow and inhibits reverse current flow. Then you put the N and P and more N material together to form a transistor with the BE junction forward biased and the BC junction reverse biased and....then it all stops.

Beyond saying that the base is very thin and that you inject "current carriers" into the base, unless you are in a pretty advanced class (ie: lots of math), pretty much the next step is the invoking of, magic. Current gain happens by, "transistor action".

Like the question of sound propagation and buoyancy, I'm not entirely convinced that there isn't a fairly simple answer that can be understood (at least on a fairly mechanical level) by us math morons.

Back to the balloon

There are heavier molecules outside the balloon and lighter ones inside it. Under the influence of gravity, somehow those lighter molecules tend to float upward (against the gravity), taking the balloon with them. The molecules inside and outside the balloon are somehow producing the pressure gradient that's making that happen.

I can think of possible reasons why that happens, each crazier than the last (and, have expressed a couple earlier) but, they don't seem to answer the question satisfactorily. Why are those forces being generated and how are they being developed?

Just from empirical thinking that, in an air system, it's pressure rather than vacuum that's actually doing the work, so it would make sense if it's the heavier air molecules that are doing the lifting and the lighter molecules, inside the balloon, are just along for the ride. But, I don't know...maybe not...

I might also be bold enough to conjecture that, for a given heat, heavier molecules will have more momentum and that may what gives them the ability to exert more pressure...again...maybe not...

 

[skyhawk]

I know this is not the way to "win friends and influence people" as Dale Carnegie would say and I agree that this thread has been going on way too long. I profusely apologize for the length but, not for continuing it because the question still hasn't been answered. Perhaps, from a mathematical formulation, engineering viewpoint maybe it has but, the underlying physics of it surely haven't been.

I never said that the thread was too long, I only commented that I was jumping into a discussion that I had not been following in order to address a point about bouyancy.

From an underlying physics point of view the question of bouyancy has been addressed and is well understood. The upward force is the result of the fact that pressure varies with position. Pressure increases as one moves down in a static column of fluid. BTW the term gradient is a mathematical term, if explanations using math are unacceptable then you should stay away from using math terms.

The rigorous math was used to demonstate that the result is valid regardless of the shape of the object. However, in order to eliminate the math beyond algebra to which you object, let's consider the a rectangular prism with sides a, b, and c.

rectangular prism - Google Search

Let the dimension a be in the vertical direction, so that the top and bottom surfaces both have an area of bc. Suppose the pressure at the top surface is P then the force on the top surface pushing down is bcP. The pressure at the bottom surface is P + ρga with the result that the upward force on the object is bcP + abcρg. Thus the net upward force is abcρg. Since abc is just the volume of the prism and ρ is the mass density, then abcρ is the mass of the object, which when multiplied by g gives its weight.

The four vertical surfaces also experience forces, but the forces are horizontal and the forces on opposite sides are equal and opposite so that they contribute no net force.

I don't believe that the math can be made any simpler and still get a quantitative result. If you need to know why the pressure at the bottom surface is P + ρga, consider a static column of fluid with cross section A and length L. Let the pressure at the top be P and the pressure at the bottom be P + ΔP, then a force balance on the column of fluid gives:

A(ΔP + P) - AP - ρgAL = 0, where ρgAL is the downward force on the column due to gravity.

Simplifying gives ΔP = ρgL.

A "proper" derivation would have used δz instead of L and taken the limit as δz goes to 0, but you object to any math beyond algebra so this is what we are stuck with.

Editted to correct mixed up symbols

 

[crashsite]

Okay...give me the dunce cap and let me know which corner...

let's consider the a rectangular prism with sides a, b, and c.

Let the dimension a be in the vertical direction, so that the top and bottom surfaces both have an area of bc. Suppose the pressure at the top surface is P then the force on the top surface pushing down is abP.

bcP?

The pressure at the bottom surface is P + ρgc with the result that the upward force on the object is abP + abcρg. Thus the net upward force is abcρg.

Trying to figure out why, "a" is included there if the pressures in the a direction don't contribute to the lift.

I'm getting (from the description further down about the static column of air) that P + pg ends up being the pressure at the bottom of the figure pushing up (presumably pushing against the same area as P is pushing down on the object). And, that pg is greater than P because thee's more air above the bottom of the object than there is at the top.

That was the analysis I had sort of rejected earlier (and the question of why don't Zeppelins fly oriented vertically to maximize the pressure differential).

Since abc is just the volume of the prism and ρ is the mass density,

Not sure how or when p became the "mass density"...

then abcρ is the mass of the object, which when multiplied by g gives its weight.

The four vertical surfaces also experience forces, but the forces are horizontal and the forces on opposite sides are equal and opposite so that they contribute no net force.

I don't believe that the math can be made any simpler and still get a quantitative result.

I'm not really looking for a quatitative result at this point. Still trying to get a sense of how it works.

If you need to know why the pressure at the bottom surface is P + ρgc,

Not sure what c is there.

consider a static column of fluid with cross section A and length L. Let the pressure at the top be P and the pressure at the bottom be P + ΔP, then a force balance on the column of fluid gives:

A(ΔP + P) - AP - ρgAL = 0, where ρgAL is the downward force on the column due to gravity.

Simplifying gives ΔP = ρgL.

A "proper" derivation would have used δz instead of L and taken the limit as δz goes to 0, but you object to any math beyond algebra so this is what we are stuck with.

BTW: This is exactly how I was always in trouble in math classes. I'm not dyslexic or anything but, when I see formulas, where math types see clarity, I see a jumble of letters and symbols that need to painstakingly be sorted out. By the time I've sorted trhough some of it, what I'm supposed to be seeing has been pushed to the back burner of my mind and, I've not likely sorted the stuff out in a way that would do me any good in that regard, anyway.

That's why I need to drive these concepts down to the very lowest, most mechanical level to feel like I understand them. When I look at the sound propagation wave analysis answers, I think that maybe others could also sometimes benefit from this apprroach.

 

[skyhawk]

I apologize for getting my symbols jumbled and ruining what I thought was a clear explanation and instead creating more confusion. It goes to show that it is hard to proof read ones own work, since you know what you mean to say.

I've editted the previous post, and I hope that I fixed all the errors. (If I haven't, I'll try again.)

Let the dimension a be in the vertical direction, so that the top and bottom surfaces both have an area of bc. Suppose the pressure at the top surface is P then the force on the top surface pushing down is bcP. The pressure at the bottom surface is P + ρga with the result that the upward force on the object is bcP + abcρg. Thus the net upward force is abcρg. Since abc is just the volume of the prism and ρ is the mass density, then abcρ is the mass of the object, which when multiplied by g gives its weight.

The four vertical surfaces also experience forces, but the forces are horizontal and the forces on opposite sides are equal and opposite so that they contribute no net force.

I don't believe that the math can be made any simpler and still get a quantitative result. If you need to know why the pressure at the bottom surface is P + ρga, consider a static column of fluid with cross section A and length L. Let the pressure at the top be P and the pressure at the bottom be P + ΔP, then a force balance on the column of fluid gives:

A(ΔP + P) - AP - ρgAL = 0, where ρgAL is the downward force on the column due to gravity.

Simplifying gives ΔP = ρgL.

Not sure how or when p became the "mass density"...

Not p but ρ, the Greek letter "rho". Rho is a standard symbol that is used in physics for a density, in this case mass density, mass/volume.

I'm getting (from the description further down about the static column of air) that P + pg ends up being the pressure at the bottom of the figure pushing up (presumably pushing against the same area as P is pushing down on the object). And, that pg is greater than P because thee's more air above the bottom of the object than there is at the top.

P + ρga is the pressure at the bottom. Yes, it is greater than the pressure at the top because there is more air above.

I'm not really looking for a quatitative result at this point. Still trying to get a sense of how it works.

I'm not sure how you can test a hypothesis unless you can get a quantitative answer. The idea that it is the pressure gradient that gives rise to a bouyant force is a hypothesis. In order to test that hypothesis you need to compute numbers to see if the hypothesis agrees with experiment. If you computed the volume of a Zeppelin and multiplied by a value for the density of air would the force be sufficient to lift to lift it? The answer turns out to be yes.

Simple answer for the reason that it works is that the pressure is greater at the bottom than at the top. The "amazing" result is that the force is independent of the shape or orientation of the body, but only depends on the weight of the fluid displaced by the body.

BTW: This is exactly how I was always in trouble in math classes. I'm not dyslexic or anything but, when I see formulas, where math types see clarity, I see a jumble of letters and symbols that need to painstakingly be sorted out. By the time I've sorted trhough some of it, what I'm supposed to be seeing has been pushed to the back burner of my mind and, I've not likely sorted the stuff out in a way that would do me any good in that regard, anyway.

And I apologize again for adding to the confusion. However, I'm not sure how one reasons through a physical problem of any complexity without at least some math. Usually results having the most generality require the most sophisticated math. That just seems to be the way it is.

 

[skyhawk]

Thought I would add this quote:

To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

Richard Feynman. 1918-1988.
American physicist.
The Character of Physical Law

Richard Feynman was "The Teacher" for my generation of physics students.

 

[crashsite]

That helps!

Not p but ρ, the Greek letter "rho". Rho is a standard symbol that is used in physics for a density, in this case mass density, mass/volume.

Ah, okay. Bad eyes.

P + ρga is the pressure at the bottom. Yes, it is greater than the pressure at the top because there is more air above.

So, essentially my original analysis about the air pressure that I had rejected because it didn't seem to be significant enough to make a large enough differential was right after all?

I'm not sure how you can test a hypothesis unless you can get a quantitative answer. The idea that it is the pressure gradient that gives rise to a bouyant force is a hypothesis. In order to test that hypothesis you need to compute numbers to see if the hypothesis agrees with experiment.

There's no denying that someone needs to work out and test the numbers but, once that's been done, then descriptions, pictures, tables, graphs, animations and greatly simplified math should be able to give the "common man" the how and why.

The "amazing" result is that the force is independent of the orientation of the body.

I am assuming that the reason the "amazing" part works is because of the reciprocity between having a smaller pressure differential across the height of a horizontal Zeppelin, acting on the large area along its length and the larger differential acting on the smaller area across its girth of the vertically oriented Zeppelin. And, that for any orientation of any geometric volume, that same effect would hold true.

And I apologize again for adding to the confusion. However, I'm not sure how one reasons through a physical problem of any complexity without at least some math. Usually results having the most generality require the most sophisticated math. That just seems to be the way it is.

I see it just the opposite. Big ideas need a lot of conceptualization and the ennui details need the precision of math. But, of course, even the big concepts need to be tested by experimentation or math or both...by somebody...with more aptitude for it than myself...

I was kind of hoping that the, heat issue would have come into play more. Perhaps, as how the adibiatic heating and cooling relate to the pressure fifferential and how that might be related to molecular thermal activity of the air. Again, trying to get back to the temperature effects on Mach number. But, it's not something that I desire to try to force...I just thought it might have been a natural extension of the buoyancy thing. That air pressure is a force suggests that there is a dynamic component to it

BTW: I did look up, "gradient" at https://dictionary.reference.com/browse/gradient and the mathermatical definition was #4.

Anyway, thanks for your time and efforts. It's been very helpful even if I don't get it in the "proper", engineering sort of way.

As a side note, I need to think about other things differently than I have in the past.

I'd always thought of the way air-filled balloons "float" through the air as an air resistance issue with their slow rate of descent being because that large area of the balloon needs to push air molecules aside as it falls. But, it would appear that buoyancy is the primary determining factor.

Or that an airplane with a thicker wing cross section will have more lift than a thin one because of the pressure gradient across the thickness due to gravity in addition to the aerodynamic forces generated in flight. In wings with larger wing area, it could be an appreciable effect.

 

[crashsite]

Smugness

Thought I would add this quote:

To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

I've seen that quote and that sentiment. While I can't disagree with it, I would caution against giving in to the smugness it can engender. I know very well how "having the answer" can make a person quite smug.

A couple of years ago, I made a visit to South Africa. Even with these eyes and can't see a rho from a row, I could see the direction the country is going with their new government. And, it's not good. What's more, I know the solution for it. Of course, I seem to be a minority of one on that. But, that doesn't keep me from being at least a little smug about having the answer.

I can also be a little smug for having the solution to the problem of racism. Again, others just can't or...wont see it.

Trying to put the universe into order through mathematics may seem like a noble endeavor but, not all of even the human population have that aptitude or a sense of need of it. There's a very real question if, for example, an elephant or a polar bear or a house cat or even a head of lettuce might not have a sense of being that transcends the artificial nature of mathem-a-tizing everything.

After all, isn't mathematics a lot like examining and analyzing the pixels of a digital photo of a mountain lake scene as opposed to simply going to the lake and just taking a deep breath of the cool, crisp mountain air? One is analytical and the other is purely tactile.

 

[tcmtech]

I actually found this an interesting read. A few big problems you are having is actually a simple lack of or incomplete knowledge of how things in general work.
The lighter than air objects you mentioned are simply pinched up ward by the denser surrounding media trying to fill in below it. This is a well known physical fact present in gas, liquid and solid matter. Check out salt domes in geology. Its denser solids pinching less dense solids out of the way. These pinching effects are purely gravitationally driven.
Blow an air bubble under water and it rises because gravity is pulling the denser surrounding media in underneath it. Do that in a zero gravity environment and the air bubble will stay in the place its was put inside the denser media. No gravity no power to displace it. In zero gravity a typical plane actually flies less efficiently because of the lack of gravity.

Your sound Dilemma is actually known and not new. Trade mark not applicable perhaps.
One of the problems you are facing from being an audiophile is your trying to produce and artificially made reproduction of a sound using devices that are not found in nature.

Speakers dont work like the voice of a song bird. Or anything that is real true natural sound. Why does no man made light source exactly equal the sun? Simple. Its not the sun itself! Why does your million dollar sound system not sound like a simple song bird? Because its not a song bird!

The true nature of reality is its uncopyable! It can be replicated but will always end up with flaws simply because it wasn't built by nature!
Its one of life's most enduring slaps in the face. No matter what you do to replicate something its not the original and you cant copy anything and have the one original back!
Reality is time stamped and locked away forever in that moment. It happened once and thats it, its done. Everything attempted to replicate it is never never going to be the original.
You can clone your favorite pet but despite being identical down to the molecular level its still not the original pet you had. Natural influence will always put some tiny variation into the end result and thus make it a new and different object that is still time stamped and locked away in that new moment.

Your perfectionists quest is ultimately futile simply because once it happened it cant happen exactly the same again. New variables will change the results no matter how tightly you control the replication of it.
What you and every other obsessive compulsive person is having a hang up with is time it self and it unyielding nature.
Time allows for all of realities infinite variables to change and rearrange everything down to the sub atomic level of matter and never be exactly recreated or reproduced again. Every instant in time is unrecoverable. Your wasting your instances trying to reproduce a lost one.

If you want to hear real life sound go for a walk! Your better off for it! I promise! Soak in the fact that you and only you are the only one in the history of the universe that will hear what you hear exactly as you heard it and where you heard it at.

Thats life.

 

[crashsite]

Zeroing in

I actually found this an interesting read. A few big problems you are having is actually a simple lack of or incomplete knowledge of how things in general work.

The lighter than air objects you mentioned are simply pinched up ward by the denser surrounding media trying to fill in below it.

Actually, I had thought of that but, my analogy was like sqeezing a watermelon seed to shoot it across the room. I didn't try to advance it because I was trying not to continue the mechanical analogy in the hopes of getting back to the thermal issue.

One of the problems you are facing from being an audiophile is your trying to produce and artificially made reproduction of a sound using devices that are not found in nature.

The adibiatic heating and cooling of the sonic wavefront was actually kind of a farce. Even in a grosser manner than the objections you raise, it's essentially impossible to correct using analog or digital techniques. To do so forces one to resolve the audio equivalent of the Heisenberg Principle; you have to know both the distance and amplitude of the source sound at the same time and do so from a location that tells you neither one.

But, whether the topic is, buoyancy, sound propagation, adibiatic heating and cooling, aerodynamics or the variations thereof, there's still a need to define just what "pressure" is and, it appears to be thermal activity.

Speaking of gross, it may be a gross simplification but, it's looking more and more to me like heat is pretty much the answer to just about everything that does anything. But, for this particular instance, I would be happy just to get the thermal issue related to Mach number conclusively squared away. I still feel like there's a piece missing.

 

[tcmtech]

Read up on temperature Vs pressure effects of gasses. There is already a well studied and well defined correlation between the two. Its basic college level physics. It even covered in basic chemistry.
Sorry but what I understand you to be questioning is already well known if you know where to look and who to ask!
TO me most of your questions come across as simple lack of proper knowledge and or correct sources of information.

If the source has 'Ophile' associated with its name thats the worst place to get information from!
Pedophiles are not experts on children! Just as audiophiles are not experts on sound!
Both are misguided and messed up in the head. They molest what they are so fixated on and do not keep it pure or make it better.
They also will argue their reasons for doing it but its just a unhealthy fixations being backed by twisted logic and poor moral and ethical character.

Read up on obsessive compulsive disorder if you want to know more about what putting ophile behind something means.

 

[crashsite]

Mortarboards are also good hods for bricklayers...

Read up on temperature Vs pressure effects of gasses. There is already a well studied and well defined correlation between the two. Its basic college level physics. It even covered in basic chemistry.

Ah, where to start, where to start?

Yes, these things are covered in college level physics and chemistry classes. Which has some implications. The main one being that the prerequisites for these classes are some level of math proficiency. We have to go waaaaaay back in my initial posts but, my comment was basically that there are a lot more of us in this world than there are of you. "Us" being defined as people who are interested in how things work but we just don't "see" the mechanism of it in formulas and equations. In other words, we need to have it explained differently than a math wiza does.

Typically, "we" can see things pretty well when they are described pretty well with textual descriptions and visual aids, such as charts and graphs and pictures and animations, and with examples. In asking the question in the form I did and with the "text oriented" descriptions I put forth, I was hoping to get that. But, I have no starry-eyed misconceptions that there aren't some hurdles that need to be crossed...

First, I know that the mindset is very strong among those who do tend to do well in college level physics and chemistry classes that, there is a "proper" way to learn these things. Second, that simply asking for the answer in the form I (and my ilk) need it, would not only utterly fail to get the answer but, would most surely get the response you gave. Third, that there would also be a very strong bias that, if one does not...shall we say..."pay one's dues" by attending the "proper" classes and grinding through the homework assignments, they don't deserve to be given the answer. Fourth, that it's a waste of precious time to try to go back and explain it to some ignorant dolt.

But, hope springs eternal and I hoped (still hope) that some (or, at least, someone) may be both smart enough to understand it on the college physics and chemistry or even professional level and, in fact be smart enough to understand it well enough to be able to explain it to an ignorant dolt. To be able to work with a math moron to keep "dumbing it down" until it truly does make sense in a non-mathematical way. That takes a special talent and also a completely different mindset. Rather than being seen as a burden, it could be seen as a worthy challenge. From your response, I'm guessing those rare people probably do not include you. That's okay, it doesn't include me, either.

If the source has 'Ophile' associated with its name thats the worst place to get information from!

That's kind of a generalization but, I don't know that I can completely disagree with it. But, if the definition of an audiophile is that of being a true affectionado of the quest for perfection of audio reproduction (the operative word being, "quest"), then the audiophile is rather noble. However, if the audiophile is seen as the stereotypical pompous gadget geek then perhaps it's not unreasonable to lump them (at least OCD-wise) in with the pedophile community. (yeah, yeah, yeah...I know, that's an unfair gneralization, too but, I couched it that way in keeping with tcmtech's response.)

I, myself, am always just a little bit nervous when I go out for a walk since I can never be absolutely certain that some local crusader may not know the difference in the definitions of pederast and pedestrian...

 

[crashsite]

The Wiki Connection

Maybe it can help if I can zero in on this “sound propagation” problem using the Wikipedia. It’s mostly taken from the article on, “Speed of Sound”:

Speed of sound - Wikipedia, the free encyclopedia

The very first sentence gets into, “waves”:

“Sound is a vibration that travels through an elastic medium as a wave“.

This is augmented when the author says:

"The transmission of sound can be illustrated by using a toy model consisting of an array of balls interconnected by springs. For real material the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to their springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly).”

If we look at the Wikipedia article on, “Sound”, we get a slightly different description on the same theme:

“The speed of sound depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium to its density. Those physical properties and the speed of sound change with ambient conditions.”

There’s a couple of things we know about the ambient conditions and the speed of sound. One is that the speed of sound is pretty much unrelated to the pressure. The other is that the speed of sound is directly and dramatically affected by the temperature.

Looking out to other places on the internet, we find that the actual speed at which air molecules (sticking with air for consistency and simplicity) are moving is very close to the speed at which a sonic wave front (sound) propagates through through the air.

If we put this into a situational case study, we can take a volume of air at a specific temperature and measure the speed of sound through it. We can then pressurize the air and then, making sure it’s the same temperature as before, recheck the speed of sound through it and find that it’s at least essentially the same.

We are being asked to believe that the elastic interaction between air molecules is completely unaffected by their being in closer proximity to each other…or worse, that the “square rot of the ratio of the elastic modulus (stiffness) of the medium to its density” remains exactly the same regardless of the pressure change (within nominal values...gotta add that for the nit-pickers!).

If we hold the air at a given pressure and change the temperature just a little, we are then asked to believe that, even though changing the pressure had no effect on the speed of sound, changing the speed at which the air molecules move, due to a change in heat will have a dramatic effect on the elastic modulus of air. Worse, we are asked to believe this while ignoring how the change in the speed of the molecules might affect anything.

We are asked to concentrate only on the “ball and spring” analogy of how sound propagates as a “wave” using the time-honored concept of the exchange between potential and kinetic energy.

No matter how I roll it up in my mind and then unroll it, I keep coming back to the same result. That the speed of the molecules, due to thermal activity, is what drives the sonic wave front and that the sonic wave front must be thought of on an instant-by-instant basis rather than as a wave and that the sound propagates through the air due to a vector bias of the molecular collisions. To me, that and that alone, ties the speed of sound to temperature and makes it independent of pressure.

Now, I’m in no way saying that answers all the questions and, in fact, it raises some new ones. But, I can say the same for the Wikipedia explanation. Either way, there’s a big hole in the “simplified” explanation of sound propagation and, I’m not so sure that the math hasn’t been “adjusted” to make the numerical results come out right.

We must remember that Isaac Newton was a very smart man and, his laws were taught in physics classes for a couple hundred years. But, it wasn’t quite right. I’m certain that there were plenty of deriders and nay-sayers, among the academia, to pooh-pooh those who would dare to dip their filthy toe into the hallowed chalice of, Sir Isaac Newton’s physics but, in time, Einstein (and others) did. And, the challenge even to Einstein continues.

I’m most certainly not equating myself to the likes of Newton or Einstein. I'm not even saying that Wikipedia is wrong. But, when something just doesn’t make sense, I feel like it needs to be at least explained so it does. I'm pragmatic enough to realize that, being the ignorant peon that I am, the usual attitude I get is that I’m just not smart enough to “get it” so why bother…

 

[tcmtech]

When you compress a gas it heats up. simple law of physics. Sound is also a series of waves that travel by a compressive action of sorts.
So yes in a way you are right about the thermal interaction of sound with air. Still a known principal though.

For a real life demonstration of thermal acoustic effects go to a car audio crank it up contest.
Do a temperature measurement of the air in one of the highest powered vehicles you can find. Then do another test just at the end of a run. You will find a several degree temperature rise just from the intense compressing and vibrating or the air in the vehicle. More so than what thermal radiation from the speakers and amplifiers would account for in that time period.

Just an observation to help you out. I dont think your wrong on your question at all. I do however think you may just be looking at the wrong places for your information. Perhaps using 'Thermal acoustic effects' as a way to narrow your search will help.

For a possibly better or more application specific device that uses thermal acoustic effects to do work read up on hot air engines. There are thermal acoustic resonance engines that use nothing but heat and a tuned chamber to drive a piston and produce mechanical motion. They are a cousin to the sterling engine. They are very simple and easy to build too!
And being a centurys old design there is a good deal of documentation and written work on how they do what they do with heat and sound.