Why Does Sound Propagate?

[3v0]

Summary

At this point your self centered process corrupts everything. Reasoning in this kangaroo court is flawed because you are not willing to entertain any ideas but your own.

Your dislike of answering questions is wrong. When looking for truth you do not get to cherry pick questions regarding the data or the process.

You have screwed up and rather then admit it you say "Lets get back on topic".

In the final analysis the only point of this thread is its continuance.

3v0

 

[crashsite]

Come on in...the water's fine...

At this point your self centered process corrupts everything. Reasoning in this kangaroo court is flawed because you are not willing to entertain any ideas but your own.

Your dislike of answering questions is wrong. When looking for truth you do not get to cherry pick questions regarding the data or the process.

You have screwed up and rather then admit it you say "Lets get back on topic".

In the final analysis the only point of this thread is its continuance.

3v0

Actually, when I asked the initial question I had no knowledge of any of this stuff. I had duly learned about sound in science class but, when I went to apply it, suddenly realized that all I knew about it was pretty much useless.

So, virtually all I know about how (I now believe) it really works is as a result of what I've so selfishly learned in/from this thread. Even the posts that I haven't agreed with have often made me think of things in different ways and I hope that some of my ramblings have done the same for others.

So, let me personally invite you to leave the clean, well-lighted boulevards of, wave analysis and come join us in the narrow, crooked, tawdry backstreets of the molecular world...uneducated, stumbling urchins we may be in it. It really is kinda fun.

On topic: The whole "spring thing" seems to be one of the major keys to understanding sound propagation. I'm assembling a post but, it's kind of involved so, it will probably take me a few days to sort it out and compose it. Stay tuned.

BTW: I'm again assuming your post was aimed at me but, once again it's a guess because you don't provide the unambiguous clarification.

 

[3v0]

Crashsite, how in your wildest dreams could you imagine my posts are directed at anyone else? The only other member who has posted on this page is j.friend ?

You must have me confused with another poster. I openly stated molecular interaction results in wave motion. How can you accuse me on not wanting to look below the waves?

You are inviting me to leave the world of waves? In this post I suggested to you that YOU look deeper. But like much of what is posted her you blew it off.

In the final analysis the only point of this thread is its continuance.

3v0

 

[crashsite]

Down but, not out

You must have me confused with another poster. I openly stated molecular interaction results in wave motion. How can you accuse me on not wanting to look below the waves?

Okay, that was uncalled for....

In the final analysis the only point of this thread is its continuance.

That may well be true...for you (and for others). I can assure you that it's not true for me.

 

[crashsite]

Cherry Picking

...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?

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.

I've been accused of "cherry picking" answers and I surmise one or both of these posts of yours are the reason. Perhaps I didn't give them full, fair consideration. So, let me try again.

When a sound is generated, the disturbance heads out in all directions. The disturbande either adds some energy to the air or takes some away. Even in loud sounds, that energy is trivial compared to the energy inherent in the air. In either case (compression or rarefaction cycle), the "disturbance effect" propagates.

All the force that propagates the sound is already in the air but, exists as randomly moving molecules. The disturbance merely gives the molecules a push (for lack of a better word) in some direction. That gives the molecules a directional bias. So, the disturbing force doesn't actually spread over anything. It meerely couples to the first molecules it encounters and the air itself does the rest. As the energy in the air changes, the speed of propagation also changes and can both speed up and slow down enroute.

In your macro car and road surface model, you've set up a condition that's conceptually different than that encountered by the sound. You have the source (a car tire) continuing to add the force and controlling the action as the road surface changes. If I may borrow from the environmentalists...you added a completely new, non-native animal to the menagerie and that's why I didn't pursue it.

I apologize if this causes any inconvenience but, I want to try to cover all the bases on this topic. I feel that's the only way that I'm going to get to the root of it (at least in the way I need to in order to understand it).

 

[crashsite]

The Springs and Drift Times

I was looking back through some of the earlier posts in this thread, especially about user, notauser's SHM comments. I can better appreciate some of the things he was saying, in light of other stuff covered but, I still have some reservations. I also revisited some of the references made about it and continue to note the oscillatory nature of the the way SHM is described.

When thinking about the "spring stiffness" of materials, I can certainly see a natural tendency for some sort of period or frequency dependence during the time the spring is compressing (absorbing energy) and extending (releasing energy back to the system). But, that's only applicable part of the time. I'll get into this more in a little bit.

But, right now I want to think about the spring action itself.

Probably the easiest scenario to visualize is that of two identical, adjacent molecules heading straight for each other, head on. The two molecules will have virtually the same temperature so, there will be little or no tendency for them to exchange energy one way or the other. But, as they near each other they will feel their mutual repulsion.

Because the molecules have some thermal energy and mass, they have inertia and that inertia will drive them into the spring, compressing it. Now, I don't know what the spring is, and that question is beyond the scope of this thread. It may be the distortion of electron orbits or some quanutm effect or relating to the nucleas of the atoms, etc. But, the spring compresses and absorbs the energy of motion and eventually the molecules stop and the spring pushes the molecules apart again. When the molecules are apart they again have essentially all their thermal energy back (less what was lost to friction and radiation in the few picoseconds the interaction may have taken, which shouldn't be much).

If the spring is a "soft" one, the molecules will be able to drive closer together than if it's a "stiffer" one. But, that means it will take longer for the molecules to decelerate going in and longer to accelerate coming out. That time lapsed slows the overall rate that the molecular interactions can occur and thus slow the rate that sound can propagate through that environment.

That "spring stiffness effect" is a property of the material through which the sound is propagating. I don't know if that property itself is independent of temperature but, I'm guessing that it probably is. Others here may know.

I want to take this opportunity to make a couple of small side trips. The first is to note that if the two molecules in question are different temperatures (have different velocities) and/or have different masses, the way that heat will be exchanged should be pretty easy to visualize and from that, how heat flows through a material. Even if the two molecules are the same temperature (as defined by traveling at the same speed), if one is more massive than the other, there will still be an exchange of heat. So,l another question that's still unanswered for me is if a heavier molecule can be as hot as a lighter one even if it's traveling slower?

But, getting backt o the springs. A problem creeps in when the molecules are not colliding with each other; during the times that they are in the spaces between themselves. A molecule in that space will travel until it collides with a neighbor and that will happen in more or less time depending on how closely packed the molecues are. So, just as the softer spring slows the rate of sound propagation through a material, having the molecules further apart (such as when reducing gas pressure), should also slow the rate of propagation. The problem is that it doesn't. I'm not sure why.

I'm sure there are mathematical formulas that account for it but, is there a good conceptual explanation of why what must be a longer "drift time" for the molecules, in a less dense medium (at least not in less dense air), doesn't slow the overall rate of sound propatgation? I there some really basic principle I'm overlooking?

 

[3v0]

So, just as the softer spring slows the rate of sound propagation through a material, having the molecules further apart (such as when reducing gas pressure), should also slow the rate of propagation. The problem is that it doesn't. I'm not sure why.

Skyhawk answered that quite nicely.

3v0

 

[crashsite]

A wild stab

Skyhawk answered that quite nicely.

3v0

Once again, in the absence of specifics, I'm guessing and by-garshing what your reference is. Is this the one?

"The reason is easily understood by doing a control volume analysis, i.e. analyzing F = ma on the air in a fixed but otherwise arbitrary region of space. The resistance to compression, which is called the bulk modulus is given by κp where κ is the adiabatic coefficient (ratio of specific heats) and p is the ambient pressure. The density of the gas, ρ, is given by Mp/RT were M is the molecular weight of the gas, R is the universal gas constant and T is the absolute ambient temperature. The square of the speed of sound is given by the ratio of bulk modulus to density and the p's cancel. So 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. "

 

[3v0]

You found it.

3v0

 

[crashsite]

Yet another trip back to square one...(sigh)

You found it.

Okay, I'm going to quote the whole thing again so there will be no confusion.

Originally Posted by crashsite
So, just as the softer spring slows the rate of sound propagation through a material, having the molecules further apart (such as when reducing gas pressure), should also slow the rate of propagation. The problem is that it doesn't. I'm not sure why.

"The reason is easily understood by doing a control volume analysis, i.e. analyzing F = ma on the air in a fixed but otherwise arbitrary region of space. The resistance to compression, which is called the bulk modulus is given by κp where κ is the adiabatic coefficient (ratio of specific heats) and p is the ambient pressure. The density of the gas, ρ, is given by Mp/RT were M is the molecular weight of the gas, R is the universal gas constant and T is the absolute ambient temperature. The square of the speed of sound is given by the ratio of bulk modulus to density and the p's cancel. So 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. "

But, where does any of it address the quesion of the effect of the time it takes a molecule to transit the spaces within the mass of molecules between collisions as the molecules get closer or further apart?

I'm going to also reiterate the problem I had with his analysis when he first made it. He assigns variables to some mathematical terms and then by analyzing how they interrelate, mathematically, comes up with an answer to how it works. The problem is, it doesn't tell how it works. I don't know what methodology the person who came up with the math that, Skyhawk used, had employed to come up with the formula but, whatever it was, he, too did not bother to ensure that a description of how it works came along with the math.

Because of all this math bias, when you look the subject up in Wikipedia, what you get is one useless bit of fluff paragraph for a conceptual description followed by a spate of equations and formulas to "explain" how it works.

 

[crashsite]

Blind Canyon

In trying to account for the "spring effect" I think I may have added some stuff that just isn't germain to the speed of sound. While I still believe that what I said about what happens with a stiffer or softer spring effect is true, it's happening in a time frame that's completely removed from the speed of sound as we perceive it (picosecond interactions vs. 1100 mph molecular speed).

What is germain is the average speed of the molecules, regardless of what goes on to keep that average speed going (essentially the continual addition of heat to the system to replace the heat that is lost).

So, how the molecules interact, spring-wise or the time it takes for a molecule to transit the spaces is moot. Trying to fit the spring in was one of the blind canyons. I'm still glad I went through the exercise because it helped resolve some details and, I believe, adds some conceptual insight to other things (like heat flow and acoustical dampening).

 

[3v0]

Lets stick to one question for now.

Originally Posted by crashsite
So, just as the softer spring slows the rate of sound propagation through a material, having the molecules further apart (such as when reducing gas pressure), should also slow the rate of propagation. The problem is that it doesn't. I'm not sure why.

Allow me to expand on what skyhawk said, perhaps I can get you to see what I see in his explanation.

We can not count the number of air molecules in a mass of air. We do know that it remains constant. Thus as we increase the volume the molecules per unit volume (density) decreases.

1. As the pressure decreases so does the restorative force. I think you agree to this.

2. As the pressure (molecules per unit volume) decrease there is less mass (per unit volume) to be moved by the sound energy. Logic tells us that we must distribute the sound energy over fewer molecules. Each molecule gets more energy.

So when we decrease the pressure it decreases the restorative effect. This would slow sound but only if we impart the same energy to each molecule as we did at the original pressure. However each molecule will get a larger share of energy due to the lower density.

In short it takes more energy to move each molecule but there are fewer of them to move. It more or less balances out which is why the speed of sound does not change in proportion to pressure.

But, where does any of it address the quesion of the effect of the time it takes a molecule to transit the spaces within the mass of molecules between collisions as the molecules get closer or further apart?

This is a new but related question.
Lets save it till you are satisfied that the previous one has been answered.

3v0

My above text is based on this:

"So 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. "

 

[crashsite]

A Good Approach

Lets stick to one question for now.

Okay, first thing. I like this approach. To resolve each of the small details and concepts and then integrate them, methodically and logically, into the big picture.

Allow me to expand on what skyhawk said, perhaps I can get you to see what I see in his explanation.

We can not count the number of air molecules in a mass of air. We do know that it remains constant. Thus as we increase the volume the molecules per unit volume (density) decreases.

Agreed.

1. As the pressure decreases so does the restorative force. I think you agree to this.

I don't believe I do. I think that whether you are overwhelmed by the number of molecules or not, the molecules are still acting as individual molecules and you need to be careful about thinking of them as a "mass", acting in concert.

2. As the pressure (molecules per unit volume) decrease there is less mass (per unit volume) to be moved by the sound energy. Logic tells us that we must distribute the sound energy over fewer molecules. Each molecule gets more energy.

This assumes that the mass of air (let's stay with, air for consistancy, okay?) needs to be moved. This is one of the conceptual points that can best be explained with a model.

The model is the executive balls on strings desktop toy. One lifts the first ball in the series of balls and releases it. The ball strikes the next ball and the effect travels through the intervening balls and the ball on the end pops up as though it had been directly struck by the first ball.

Tthe intervening balls do not move at all. Still they manage to transfer the energy both through and between them. I believe that air operates in a similar manner when propagating sound. The disturber moves some air for sure but, the intervening air molecules don't need to move (as a mass) to transfer the sound. On the other end the sound is coupled to something (perhaps an eardrum) which then, like the last ball, does react in sympathy with the original disturbance.

So, if you are only propagating the "effect" through the air, you don't need to distribute the energy over more or less area/volume (whatever). You only need to think about the molecules that are being affected at any given instant as the effect passed through. User, J.Friend tried to put forth this same argument a while back.

Also, once you add the initial energy (or subtract it, depending on if you are doing a compression or rarefaction), the energy that does the propagation is contained in the air itself.

So when we decrease the pressure it decreases the restorative effect. This would slow sound but only if we impart the same energy to each molecule as we did at the original pressure. However each molecule will get a larger share of energy due to the lower density.

In short it takes more energy to move each molecule but there are fewer of them to move. It more or less balances out which is why the speed of sound does not change in proportion to pressure.

I have a problem with the whole "restorative effect" concept on the macro level of sound propagation. I do believe that it exists during the collisions of the molecules when there's the spring action taking place but, as I opined in my pool ball analogy, I don't think it comes into play in the overall picture.

Even though the pool balls are much bigger than molecules, I think the physics of how they act is the same. Just the scale is different. If a pool ball doesn't have a restorative inclination after it is struck (ie: doesn't tend to go back to some original position) then molecules probably don't either.

This a new but related question.
Lets save it till you are satisfied that the previous one has been answered.

Oops, sorry...I already opined on it. But, there is quite a bit more that needs to be said about it.

 

[3v0]

We are in agreement up to a point.

You did not buy into this.

Originally Posted by 3v0
1. As the pressure decreases so does the restorative force. I think you agree to this.

The restorative force is molecules repelling each other.

As the pressure decreases the molecules spread further apart. As the distance between molecules increases their interaction decreases. They repel each other with less force. Which is the same as saying there is less restoring force.

The disturber moves some air for sure but, the intervening air molecules don't need to move (as a mass) to transfer the sound. On the other end the sound is coupled to something (perhaps an eardrum) which then, like the last ball, does react in sympathy with the original disturbance.

Air beyond the source varies between compressed and rarefied for a distance at least equal to furthest distance at which we can detect the sound.

To create the compressed areas the molecules have to be moved significant distances. With that in mind
much of what follows in this section is unfounded.

So, if you are only propagating the "effect" through the air, you don't need to distribute the energy over more or less area/volume (whatever).

It ultimately the energy that travels at the speed of sound. The mechanism that conveys it is "traveling molecules" interacting with each other. Thus the force applied to each molecule is inversely proportional to the density of the air.

Do not beat me up with wave theory. I see the waves as a result of the molecular action. Not the cause.

Also, once you add the initial energy (or subtract it, depending on if you are doing a compression or rarefaction), the energy that does the propagation is contained in the air itself.

The restorative ability exists in undisturbed air and ensures it has a uniform density. It takes the energy from the item that produces sound to disturb that air and cause sound we hear.

Pool balls are a bad analogy for air molecules because they do not repel each other. Two magnets with like polarity would be more accurate.

If air molecules were uncharged like pool balls they would actually collide. But we know electrons exist on the outside of atoms and molecules which results in them having a negative charge. The charges interact prior to physical contact.

3v0

 

[crashsite]

Basic Premises

We are in agreement up to a point.

You did not buy into this.
The restorative force is molecules repelling each other.

I'm going to defer answering most of this right now but, let's both make a mental note of where you post is so we can get back to its points. There seems to be a lot that we need to be in agreement on (and, indeed, even if we agree that we also agree with the world).

First, the direct answer to your question/comment. Yes, I do agree that there is a "restorative force" that is related to the repelling action of molecules.

This is all pretty general but, see if any of these give you heartburn:

1. Are we in agreement that it's either known or is probable that the mutually repulsive effect of two molecules falls off as a square of the distance between them? Like magnets, that they have to be pretty close for the repulsion to be pretty strong.
   
   
2. That the absorbsion of heat (whether from conduction within the material or from radiation from outside the material) makes a molecule move? That it makes the molecule move at some speed, in a linear direction (as opposed to making it do some sort of vibration in place). And that the speed of that movement is determined by the characteristics of the molecule (probably nmostly its mass) and the amount of heat absorbed.
   
   
3. That the way a molecule (or molecules) move around within a material depends on how they are constrained in the material? For example, held tightest in a crystal lattice and possibly even forced to vibrate in place to being held most loosely in a gas (or plasma) where the molecules are not bound up at all and are free to move in any direction, only being constrained by collisions with their neighbors.
   
   
4. That molecules, in a gas, will naturally tend to move in random directions and within a relatively narrow range of speeds for a given temperature? That they will only move (or tend to move) a specific direction under the influence of some applied force.
   
   
5. That any disturbance in the air (the medum) will propagate through the air mass at Mach 1 (about 768 mph under 'standard conditions')?
   
   
6. That air is air and that sound propagates through it at the same speed for the same temperature regardless of the pressure? That air at 5 psi, at altitude, and air in a SCUBA tank, at 3000 psi, propagate sound at the same speed despite the large difference in the spacing between the molecules.
   
   
7. That the axiom that it's impossible to make an accurate measurement, due to the fact that the mere fact of measuring takes some energy from the system is true?
   
   
8. That sound propagation happens at speeds that suggest mechanical actions and thus can have any relativistic effects ignored? That Newtonian Physics prevails.

You may have some more thoughts on what I guess could be considered, "ground rules".

 

[3v0]

Near total agreement if we stay with gas.

5 I understand that the speed of sound is both temperature and pressure dependent. But if you change the temperature by changing the pressure (or the other way around) they two effects cancel each other out.

But if you change one without changing the other you will see a change in the speed of sound.

7 is not true in the Newtonian world. But is it true at the quantum level.

8 If we talk about electrons and below this may not be true. But I think we can ignore it for now.

3v0

 

[crashsite]

The Role of Pressure

5 I understand that the speed of sound is both temperature and pressure dependent. But if you change the temperature by changing the pressure (or the other way around) they two effects cancel each other out.

But if you change one without changing the other you will see a change in the speed of sound.

There are certain key points that are critical. This is one of them. This is what Wikipedia says about it (emphasis mine):

"Sound is a vibration that travels through an elastic medium as a wave. The speed of sound describes how far this wave travels in a given amount of time. In dry air at 20 °C (68 °F), the speed of sound is 343 meters per second (1,125 ft/s). This equates to 1,236 kilometers per hour (768 mph), or about one mile in five seconds. This figure for air (or any given gas) increases with gas temperature (equations are given below), but is nearly independent of pressure or density for a given gas. For different gases, the speed of sound is dependent on the mean molecular weight of the gas, and to a lesser extent upon the ways in which the molecules of the gas can store heat energy from compression (since sound in gases is a type of compression)."

One thing you'll notice about that description is that they refer to a "wave". Further, it is referred to as a "compression wave" (which can also be defined as a longitudinal wave). I think this is one of the reasons there is so much of a misconception about how sound propagates.

Did President Bill Clinton lie when he said that he didn't have sexual relations with that woman; Monica Lewinski? It depends on how finely you define, "sex". Likewise, you have to be careful how you define and think about, "waves". That's one of the key points that needs to be covered in detail and it will be.

For now, it's important that everyone accept that pressure is not a factor in determining the speed of sound through a specified gas. The formulas support this. The one given in Wiki, for air is, v = (331 + 0.6T) m/s. The only variable is, "temperature".

 

[3v0]

Good enough.

 

[skyhawk]

A number of misconceptions and little time to deal with them.

The forces between molecules are not inverse square forces. That only applies to charged particles. The forces are a short range attractive force and a very short range repulsive force. This force is often modeled by a leonard-Jones 6-12 potential.

Lennard?Jones potential - Wikipedia, the free encyclopedia

It's only an approximation, but certainly accurate enough for a conceptual discussion. Note that the force is given by the slope of the curve. A positive slope give an attractive force and a negative slope a repulsive force.

There is a wide distribution of molecular velocities for a given temperature. Take a look at the Maxwell-Boltzman distribution.

Maxwell?Boltzmann distribution - Wikipedia, the free encyclopedia

The speed of propagation is only independent of pressure for the range of pressures for which the ideal gas law is valid. I suspect (but haven't checked) that the ideal gas law is no longer valid for air at 3000 psi. At high densities a different equation of state is needed to describe a gas in order to include the effects of intermolecular forces and the size of the molecules, which become important at high densities. The first attempt at this was the Van der Vaals equation of state.

Van der Waals equation - Wikipedia, the free encyclopedia

Better equations of state have been developed, but the Van der Vaals equation demonstrates the concept.

 

[3v0]

I was uneasy with what I was saying regarding the molecular repulsion forces. If I had even know this I have long forgotten it.
Lennard?Jones potential - Wikipedia, the free encyclopedia

There is a wide distribution of molecular velocities for a given temperature. Take a look at the Maxwell-Boltman distribution.

I agree with this. I was thinking they averaged out and it would be easier to live with that then dispute it.

The speed of propagation is only independent of pressure for the range of pressures for which the ideal gas law is valid.

I understand. Again I opted to not push it. I am OK about limiting the pressure range to make it independent.

Given that we are not allowed to use math these simplifying assumptions should help the thread move in a realistic if not mathematically correct direction. Qual not Quan.