Why Does Sound Propagate?

[j.friend]

That's just it. Even with large pressure changes, the speed of sound is virtually unchanged. At about 18000 feet, there is about half the atmospheric pressure. But, whether an airplane is flying at sea level or 18000 feet or 50000 feet, Mach 1 is still the same for the same temperature.

So, the distance between molecules doesn't seem to be a factor. That's one of the paradoxes of it and, one of the things that seems so intrisically sensible that it's widely accepted that air pressure simply must an effect on the speed of sound propagation.

Your musings about it have been very helpful in sorting out some of the things that seem to be happening. Even when I may not agree with it, disagreeing makes me have to think about it in new ways.

Firstly I'm glad to have helped. I woke up this morning and had a bit of a think over why the pressure may not be a factor. If sound is created by a force, this this force has to be spread over a greater number of particles meaning a lower average force felt by each particle. (i.e. air of greater density). Alternatively in airs of lower pressure the force is shared by fewer particles which means each particle would experiences a greater force.

If you think in terms of doubling the pressure. The particles have to travel half the distance before transmitting the energy, however the force has to be spread out over double the amount of particles. This would effectively cancel, as the lower speed is accounted for by shorter distances and vice versa, hows that tickle your fancy?

 

[crashsite]

I see problems there

...had a bit of a think over why the pressure may not be a factor. If sound is created by a force, this this force has to be spread over a greater number of particles meaning a lower average force felt by each particle. (i.e. air of greater density). Alternatively in airs of lower pressure the force is shared by fewer particles which means each particle would experiences a greater force.

If you think in terms of doubling the pressure. The particles have to travel half the distance before transmitting the energy, however the force has to be spread out over double the amount of particles. This would effectively cancel, as the lower speed is accounted for by shorter distances and vice versa, hows that tickle your fancy?

I don't think I buy into that.

Sound is defintiely "created by a force". Something disturbes the air (staying with air). But, I think the forces that propagate the disturbance are already in place.

Awhile back you mentioned the similarity to light:

I see you have sort of borrowed the concept of speed of light through mediums.

Like light, sound can slow down and speed up, enroute. Let's say a sonic wavefront travels through a thermal of warm air with fairly sharply defined sides. It's kind of akin to light traveling from air, through glass and back to air. In this case the sound will speed up and then slow down again.

Only if the energy is already "there" can that happen.

I suppose a rather convoluted model of how the sonic energy can spread and re-group could be developed but, it doesn't seem to square with other aspects of the sound thing.

 

[j.friend]

Like light, sound can slow down and speed up, enroute. Let's say a sonic wavefront travels through a thermal of warm air with fairly sharply defined sides. It's kind of akin to light traveling from air, through glass and back to air. In this case the sound will speed up and then slow down again.

Only if the energy is already "there" can that happen.

See that is just the things, if the energy transferral is the same in essence the velocity depends on effectively the medium which it is passing through. To put it into a macro context, you are driving your car with a constant force being applied, as in travelling at a constant speed. This is true for the surface that you are on. If you start off on a pool of oil and use the same amount of throttle (i.e. same force) you will not go nearly as fast due to the nature of the road surface. Once you hit the tarmac, assuming the oil doesn't stay on the tires, you will start to go a heck of a lot faster. In this way it is the medium that defines the speed of the car at a constant force.

If you apply this to the model of air, a parcel of moving air (lets say the wave of energy for convenience sake) exerts a force on the next parcel of air. in truth this works on a much smaller scale, from particle to particle. If the energy in the cooler air is transferred to the particles in the warmer air then the overall force per particle in the warmer air is greater. This means that the energy tranferral will happen faster in the hotter air.


EDIT: whoops lets play spot the error in logic here. Will think about it and try again later :s

 

[3v0]

Speed of sound vrs Pressure

It seems you rejected skyhawk's logic because it was proceeded by math. In this case the order could have been reversed and it would still make sense, because it makes sense without the math.

The logic part was:

Originally Posted by skyhawk

... as the pressure increases the air acts like a stiffer spring creating more restoring force, but the mass to be accelerated also increases in exactly the same way resulting in no pressure effect.

He is saying as pressure increases the restoring force increases. If that was the only thing happening the speed of sound would increase. However we are also packing in more particles which increases the mass that has to be moved by the restoring force. The two cancel each other out.

No math required.

 

[j.friend]

I have no objection to skyhawks explanation, in fact it seems most logical. I was merely continuing on from my last post in which I was attempting to explain things in terms of my explanation.

sorry

 

[crashsite]

Ditto

It seems you rejected skyhawk's logic because it was proceeded by math. In this case the order could have been reversed and it would still make sense, because it makes sense without the math.

The logic part was:

Originally Posted by skyhawk
He is saying as pressure increases the restoring force increases. If that was the only thing happening the speed of sound would increase. However we are also packing in more particles which increases the mass that has to be moved by the restoring force. The two cancel each other out.

No math required.

No, I didn't "reject" what he said. In fact, I came up with the exact same thing a couple of pages ago (which, since he derived his conclusion from math and I from a conceptual viewpoint, were certainly independently derived). In fact, it was my own analysis that I questioned the validity of. However, having the independent corrolary makes me more confident with it.

For your reference, this is what I had said:

"If one envisions air molecules to be vibrating with some level of vigor (due to their temperature), in a closed tank, they will be interacting with their neighbors to some degree. If the air is heated, their activity level increases and they will be interacting on their neighbors more vigorously. One of the results of that will be that they will tend to push harder and that will continue from molecule to molecule until the walls of the tank limit the travel. But, by pushing harder, the air pressure in the tank will increase.

"But, a molecule pushing harder has its neighbor pushing harder back (action and reaction). That has the effect of being like a stiffer spring. Aha, you say. Exactly what you'd expect and the stiffer spring makes the interactions faster. Ergo, the sound will travel faster.

"But, now let's take the same tank of air but, instead of raising the temperature, you add more air to increase the pressure. The air molecules are pushed closer together and, even though their thermal activity is lower, there will be a greater interaction (more stiffness) between the molecules because they are simply in closer proximity.

"There must be some level of equivalence of "force" or "stiffness" for the molecular interactions for the two cases. The upshot of all this is the question of, "Can you generalize that intermolecular stiffness is the key to the speed of interactions?". My first thought is that you can't since you can have similar stiffnesses at different temperatures and the speed of sound propagation only depends on the temperature.

"In the second case I came up with, there is a "same stiffness" between the molecules but, it takes more molecules to acheive it. For a disturbance to pass through the molecules is still dependent on the intermolecular stiffness and that determines the rate of propagation from molecule to molecule. But, since the disturbance must interact with more molecules to get from point A to point B, it takes longer. Ergo, slower rate of propagation."

Now, you can say, "But, he said the same thing in a lot less words", and that's true. But he didn't say how or why that extra mass might actaully do it.

I'm trying to figure out how it works. Like I've said, I believe I am slowly getting closer and closer to that elusive answer that I want and will accept.

What's more, none of this line of reasoning, in any way, negates any of my "vectored, pool ball analogy" of how a disturbance may pass through a randomly moving mass of particles.

 

[3v0]

I still don't know. My problem with Skyhawk's answer is that he posed a formula and then, based on how the formula acted, derived an answer.

and

I have no objection to skyhawks explanation, in fact it seems most logical. I was merely continuing on from my last post in which I was attempting to explain things in terms of my explanation.

Thus answers other then yours are automatically problematic.

You are doomed if you fail to listen to anyone but yourself.

3v0

 

[3v0]

I would like to touch on this again.

Totally modeling the weather requires that all possible data which may effect the weather be collected. We do not have the resources to do so.

This is NOT a failure of math.


An it is not in the same class of problems as understand the propagation of sound.

3v0

 

[j.friend]

I have no objection to skyhawks explanation, in fact it seems most logical. I was merely continuing on from my last post in which I was attempting to explain things in terms of my explanation.

You are doomed if you fail to listen to anyone but yourself.

3v0

Hey man it was me who said that, you can't get on his back about it

 

[3v0]

Hey man it was me who said that, you can't get on his back about it

Sorry I did not realize you had already cracked that whip. My bad.

3v0

 

[crashsite]

Sound Judgment

Sorry I did not realize you had already cracked that whip. My bad.

3v0

My question is: Why are you carrying on about who said what to who when the topic is sound propagation? There must be a Dr. Phol forum somewhere on the internet where people would just love to get into the psychology and trauma and disfunctioanality of people who have the audacity to question how the school system teaches sound propagation...

I suspect that you're still not convinced that the action is occuring at the molecular level rather than at the "longitudinal sound wave" level. But, it should be getting apparent, by this time, that I was right all along and the classical, "undulating Slinky model" of sound propagation, as taught in science classes, is just wrong.

All this stuff about the validity/usefulness/limitations/wonderfulness of math is really just a nagging side bar.

 

[crashsite]

See that is just the things, if the energy transferral is the same in essence the velocity depends on effectively the medium which it is passing through. To put it into a macro context, you are driving your car with a constant force being applied, as in travelling at a constant speed. This is true for the surface that you are on. If you start off on a pool of oil and use the same amount of throttle (i.e. same force) you will not go nearly as fast due to the nature of the road surface. Once you hit the tarmac, assuming the oil doesn't stay on the tires, you will start to go a heck of a lot faster. In this way it is the medium that defines the speed of the car at a constant force.

If you apply this to the model of air, a parcel of moving air (lets say the wave of energy for convenience sake) exerts a force on the next parcel of air. in truth this works on a much smaller scale, from particle to particle. If the energy in the cooler air is transferred to the particles in the warmer air then the overall force per particle in the warmer air is greater. This means that the energy tranferral will happen faster in the hotter air.


EDIT: whoops lets play spot the error in logic here. Will think about it and try again later :s

I thought about this and have decided not to pursue it becasue it really does just restate the same principle as we've been discussing but, with a different slant. The notion that the speed is related to the energy of the medium.

 

[3v0]

Carrying On ??

Between j.friend and myself we used exactly 2 lines of text.

Math is important. You can come up with as many bogus reasons for reject it as you like. It does not change the validity of it.

I suspect that you're still not convinced that the action is occuring at the molecular level rather than at the "longitudinal sound wave" leve

I am not sure why you would say that.

When you look at enough molecules you see compression waves. You can choose to say "The Action" is at the molecular level because you can see the interaction at that level, it causes the waves.

Why stop at the molecular level, keep peeling the the onion. What happens at the atomic, sub atomic, string theory, etc ? Does it make sense to talk about sound at these levels? It must if each level drives the action in the level above it.

3v0

 

[crashsite]

Applying Some Numbers

I'm copying a post I made (the only post I made) over in the Physics Forum. Unfortunately, those guys are completely wrapped up in their math and formulas and equations and little else, so it's not a good match for me. Anyway, the post conceptualizes a corrolation between the molecular speed of air and the speed that sound propagates through it. The referenced web page was from this forum.

Now, is where the math and forumlas come into play. When you need to start actually putting in some numeric values the math is proper and needed. When trying to conceptualize the concept, the math is just not a good fit. That's been my point all along.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

If the question is how fast the molecules of air are moving, here's a web page that may be of interest.

**broken link removed**

But, let me quote a passage of interest here:

"There's a really neat mathematical equation based on a theorem called
the "equipartition theorem" which states that the energy of a gas system
(equal to 1/2*mv^2) is equal to the temperature of the gas (equal to 3/2*kT).
If we rewrite this equation to solve for velocity we get:

sqrt(3*T*k/m) = v

where T is the temperature in Kelvin, k is the Boltzman constant = 1.3805*10^-
23 J/K and m is the mass of the gas particle.

If we assume that the average mass of air (since it is a mixture of different
gases) is 28.9 g/mol (or each gas particle is around 4.799*10^-26), and room-
temperature is 27C or 300K, we find that the average velocity of a single air
particle is around 500 m/s or 1100 miles per hour!"

The reaon I find this particularly interesting as it relates to the speed of sound is by thinking of what the average speed might be in a linear direction.

If an air disturbance is propelled by the collisions of the molecules and the molecules are moving at a nominal 1100 mph, some of the time the sound will be propagted at that speed. But, related to that selected direction, some will be at right angles to that direction and will propagate along that axis at zero mph. Other rates will depend on other angles and should average out to about the speed of propagation at 45 degrees.

That puts the average at about 770 mph along any given axis. To me that seems just a little too close to the nominal Mach 1, under standard conditions, of 761 mph to be a simple coincidence. What accounts for the difference? I can't really answer that. For example, I don't know how their base values equate to "standard conditions". I don't know how precise their, "around 500 m/s" (1100 mph) is, etc.

At a vector of 45 degrees a speed of sound of 761 mph works out to about 1076 mph for the molecular speed...assuming my logic works out to be correct, that is.

 

[crashsite]

Applying Some Numbers

Oops...I thought this had only previewed. Didn't realize it had already posted. Sorry for the dupe.

 

[crashsite]

Carrying On ??

Between j.friend and myself we used exactly 2 lines of text.

That one post.

Math is important. You can come up with as many bogus reasons for reject it as you like. It does not change the validity of it.

Math is important...in its place. But, like the honey bee, it's just a dangerous nuisance when it's in the wrong place. For the bee, that's down your shirt. For math it's when you are trying to come up with a concept.

Quote:
Originally Posted by Crashsite
I suspect that you're still not convinced that the action is occuring at the molecular level rather than at the "longitudinal sound wave" leve


I am not sure why you would say that.

Well....it could be becasue you've been one of the chanpions of wave analysis throughout this thread? In fact, your very next sentence tries to steer back to wave analysis.

When you look at enough molecules you see compression waves. You can choose to say "The Action" is at the molecular level because you can see the interaction at that level, it causes the waves.

That's just it. When you're analyzing what's happening acorss a lot of molecules you're no longer dealing with sound propagation. Now, you're dealing with wave analysis. If the topic is the wave analysis of sound, then that would be proper. When the topic is, sound propagation, it's just not germain. I now post that as a fact because every time I've asked a wave analyst to show the corrolation between analyzing sound waves and sound propagation, the answer has been a deafening silence. But, I'm still open for it.

It's very difficult to keep a thread on topic under the most ideal of circumstances. But, if ya let wave analysis creep in as the arguing points, you may as well just throw up your hands and give it up. That's why I've been so adamant about trying to vector away from it so vigorously.

I've let a lot of unrelated stuff slide by in this thread exactly because it is so far removed from the topic that it doesn't threaten to derail the discussion. But, I can't let wave analysis get a foothold.

Why stop at the molecular level, keep peeling the the onion. What happens at the atomic, sub atomic, string theory, etc ? Does it make sense to talk about sound at these levels? It must if each level drives the action in the level above it.

That's easy to answer. Because at some level, it stops being "sound" and "sound propagation". So far, at the level this thread has progressed, we have stayed solidly on "sonic" ground.

Can we get back to, "Why does sound propagate"?

 

[3v0]

Well....it could be becasue you've been one of the chanpions of wave analysis throughout this thread? In fact, your very next sentence tries to steer back to wave analysis.

Originally Posted by 3v0

When you look at enough molecules you see compression waves. You can choose to say "The Action" is at the molecular level because you can see the interaction at that level, it causes the waves.

Once again if you did not write it, it has to be wrong! The quoted text does not steer the investigation in the direction of waves. It points out that molecular interaction is what sets up the waves. That favors molecular interaction.

Further it was part of a paragraph which talks about the the interaction at lower levels.

Originally Posted by 3v0

Why stop at the molecular level, keep peeling the the onion. What happens at the atomic, sub atomic, string theory, etc ? Does it make sense to talk about sound at these levels? It must if each level drives the action in the level above it.

That's easy to answer. Because at some level, it stops being "sound" and "sound propagation". So far, at the level this thread has progressed, we have stayed solidly on "sonic" ground.

At what level does it stop becoming sound and why is that relevant ?

By your thinking I can easily argue (wrongly) that at the level of forces that govern molecular interaction (not waves) it stops being sound. Therefor waves are the only possible answer !

If I understand it correctly you are looking for what causes sound to propagate. Can you stop at a given level because it does not meet some canned definition of sound. You can stop because you choose to, but that does not change the physics.

In short it is OK to say you do not care what happens below a given level. But you can not say it does not contribute or is unimportant.

 

[crashsite]

Back to Topic?

Once again if you did not write it, it has to be wrong!

There's a lot to be said and argued and defended but, I think this line of bickering wearies people who come to discuss, sound propagation. This is a technical forum, not the Dr. Phil hour.

I have found that merely asking a question virtually never garners an answer. The best approach seems to be to state an opinion and then, as people see the problems with it, try to defend it. If they turn out to be right, then you change your position.

You have to remember that just because I've written something it doesn't make it correct. But, since it's my best effort based on what I know when I write it, I welcome challenges and the opportunity to at least try to defend it.

Now, can we quit sparring and get back to sound propagation. There's plenty that needs to be covered.

 

[j.friend]

so just to clear it up you dont believe that sound propogation is due tot he kinetic interactions of air particles?

 

[crashsite]

Is the basic question covered?

so just to clear it up you dont believe that sound propogation is due tot he kinetic interactions of air particles?

No, I do believe that sound propagation is due to the "kinetic interactions of air particles" (so long as we can agree on that terminology). I'm not sure it needs to be reiterated in another format.

I'm thinking that it may be time to summarize all that this thread has culminated in and see if the question has been adequately answered. By, "answered", I mean if the basic principle of it is adequately clarified. I'll be posting that summary in the next few days (I want to try to keep it concise and cogent).

But, I would welcome anyone else taking a stab at it, too.

EDIT: I lied. There's another facet to this that needs to be addressed before it can be put to bed. The "spring function".