Why Does Sound Propagate?

[crashsite]

Right Thinking

Math in not coarse. Think about calculating pi. 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 ...

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

The last I heard, pi had been worked out to a couuple billion places...and, still math can't accurately predict the magnitude or time of the next earthquake on the San Andreas fault. Even though it may well occur tomorrow.

Ane, for all the math that's tossed around so casually in these types of forums, the "wave nature" of sound propagation still manages to persist. Not a very good showing for "math".

QUOTE=3v0;766695] I agree that human conceptualization is required but it works in conjunction with math.[/quote]

You do a pretty good job of arguing my point.


QUOTE=3v0;766695] Why did the rock move? Some would tell you it moves because the the laws of motion. You would correctly argue that the laws are based on observation and show how but not why. For years we have lived without knowing why. Some of that is now being determined. I have not seen much of it but expect it is mostly over my head due to the math.[/QUOTE]

"Why" did the rock move? Who knows. Some believe it's because the rock wanted to move. Some, because of some higher power. Some, because of the laws of physics. Some don't believe that the rock moved at all but, rather the universe moved around it. Some, that the rock didn't move except in our imaginations. The way an elephant perceives a moving rock is no less valid but, is almost certainly different than how you or I see it. And, on it goes.

When conceptualizing these things it's important to keep an open mind and to realize that it may not be possible, within the confines of our universe (whatever that might mean) to be able to resolve why a rock moves.

What we can do is make our best observations and draw our best conclusions and sometimes that does involve the inclusion of some absolutely alien, contrived and convoluted fabrications such as mathematics. But, while math can be a helpful tool, it must be the slave, not the master.

When I see or hear someone touting the demigod, Feynman and professing that mathematics is the "language of the universe", I just wince.

 

[j.friend]

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

This is indeed true, i'm sorry for putting it this way. let me put it in a way that makes some semblance of sense. When I said density, it is a combination of the velocity of the particles in the medium (directly affected by by temperature) and for want of of a better word the compressibility of the medium. By compressibility I mean the relative distance that the particles can get to one another. This variable would be directly related to the intermolecular forces present in the medium

With lower compressibility (particles cannot get as close to each other) the sound would propagate faster. I think somewhere I saw the analogy used that a lower compressibilty is akin to having stiffer springs. Whilst the energy transferred is the same, the rate of transferral is much quicker when the compressibility is lower (stiffer spring).

This would indicate, assuming sound is dependent on the kinetic interactions between the molecules, that sound would indeed travel slower in a cooler air than hotter air. In regards to why pressure doesn't affect the speed of sound i'm going to have to use an equation to help illustrate the point.

The equation used to describe the interaction of Ideal gases is PV = nRT.
In this P is pressure, V volume, n the amount of gas in mols, R is a constant and T is temperature in degrees kelvin.

What I want to pull out of this equation is that provided temperature remains constant, pressure and volume are inversely proportionate. This would mean if you increase the pressure and the volume would decrease. This would result in the molecules being closer together, however the velocity of the molecules would not change, nor would the compressibility of the air. This would indicate that the pressure is not a huge factor on the speed of sound as the variables on which the speed of sound remains constant.

In practical applications I believe that the velocity (temperature) of the molecules within the medium would also change in such a way that the speed of sound remains very similar. In this way an increase in pressure would probably result in a reduction of temperature. This makes sense to me within reasonable parameters. Of course if you are changing the pressure be large proportions there would be some affect. As to what extent this would be I could not say as I don't know what happens.

I would also like to point out that there are people much much smarter than I that have thought about this. Everything that I say is how I see it, I haven't learned about this so am presenting what I see to be happening.

Finally, after you think about it, go back to the wave analysis model and tell me how "longitudinal waves", generated by some subsonic disturber (such as vocal cords, a speaker or a steamship whistle) virtually instantly accelerate to Mach 1 and propagate at that speed.

In regards to why sound propagates at Mach 1 in air is due to the energy transferral of energy between molecules. I have never been very good at explaining things however i will attempt to.

Say that at a given temperature the particles within a medium have a certain velocity oh their movement. In this I'm saying that the particles in hotter air move faster than the particles in cooler air. You apply a force to these particles by any form of sonic disturber, be it your vocal cords, a speaker or steamship whistle, and the changes in pressure is propagated at a velocity proportional to the velocity of the particles within the medium.

I can expand on this if you want

 

[crashsite]

A Brand New Theory is Brewing

This is indeed true, i'm sorry for putting it this way. let me put it in a way that makes some semblance of sense. When I said density, it is a combination of the velocity of the particles in the medium (directly affected by by temperature) and for want of of a better word the compressibility of the medium.

Why would you include the temperature (velocity) of the molecules as part of the definition of, "density"? I looked up, "density" and there's nothing in any of the definitions that even suggests a dynamic aspect:

Density Definition | Definition of Density at Dictionary.com

By compressibility I mean the relative distance that the particles can get to one another. This variable would be directly related to the intermolecular forces present in the medium

With lower compressibility (particles cannot get as close to each other) the sound would propagate faster.

I think somewhere I saw the analogy used that a lower compressibilty is akin to having stiffer springs. Whilst the energy transferred is the same, the rate of transferral is much quicker when the compressibility is lower (stiffer spring).

There's usually a key point to a discussion like this and I believe that this is it. Just exactly how the molecules behave at this level.

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.

This would indicate, assuming sound is dependent on the kinetic interactions between the molecules, that sound would indeed travel slower in a cooler air than hotter air.

I don't see why that would follow at all. But....there is a possible answer. This is a new thought so it's still a bit embryonic.

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.

To be quite honest, I'm not sure if I like that explanation but, it's something to consider.

 

[3v0]

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.

It is an indication of the limits of humans and their technology.

When I see or hear someone touting the demigod, Feynman and professing that mathematics is the "language of the universe", I just wince.

Your mode of operation is to write off anything that is above your level of comprehension. I will go with Feynman!

3v0

 

[j.friend]

Why would you include the temperature (velocity) of the molecules as part of the definition of, "density"? I looked up, "density" and there's nothing in any of the definitions that even suggests a dynamic aspect:

Ok I'm sorry for being vague, I sorta went off and went on to the factors that affect the speed of sound. When i refer to density I mean the compressibilty of the molecules. The temperature is another aspect that affects the speed of sound.

Also temperature is the same as energy of the molecules. I hope that this is evident. So what I am trying tho say is that the speed of sound is proportional to the energy of the particles of the medium and inversely proportional to the compressibility of the medium.

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.

The key to this is the relative distance between the particles. If you increase the pressure by large amounts, i.e doubling, I would presume that there would be a difference. All my reasoning comes not from experimental data but from the perspective of a 17 year old. I have seen somewhere that the speed of sound is only minimally affected by the pressure, but I don't know to what extent. Even the minimal effect that is seen would indicate that there is some sort of interaction which affects the speed of sound due to the proximity of the molecules.

What I would hazard an educated guess at is that the relative distance between the average air molecule is so large, that even with an severe decrease, the effect that this has on the interactions between the molecules will not be so great. I know that in Air the molecules are extremely 'spaced' out in comparison to the atomic radius. (you can see this from the refraction index of air in correspondence to light waves seeing as light travels nearly at the speed of light through air there is relatively very few molecules).

To put this in perspective apparently the average air molecule can travel 500-1000 times its own size in distance before hitting another air molecule. So even if you double the amount of molecules they still have a heck of a lot of empty space around them. What I propose is that the relative decrease in space between the molecules is insignificant in proportion to the force exerted inbetween them. I know its a little preposterous, however If the compressibilty starts affecting a molecule only when the molecules come within a certain distance say 10 * the size of the molecules, then that is insignificant to the relative pressure.

It makes sense in my head... i'll sleep on it and try to come up with a better way to explain it

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.

I see you have sort of borrowed the concept of speed of light through mediums. Nice. I will try to look at it more when i'm not so tired

 

[Hero999]

Here's an interesting thread.
**broken link removed**

The highest (effective) frequency that can exist is linked to the
mean free path. This at sea level is about 10^-7m. Hence the highest
frequency (even loosly defined as sound) is 340e7 Hz. Even that is
stretching a point.

So the highest frequency sound in air is 3.4GHz

The speed and attenuation of sound 2.4.1

gives a general account of attenuation. At 100kHz we have about
1800dB/km in fairly dry air. Attenuation on a simple model goes up as
f^2. Range of 1000kHz therefore bein of the order of 10m (1.8dB/m). At
1MHz we have 10cm. At 10MHz 100 microns. In my book 100MHz+ can't
really exist in air.

I take from this that in the real world >1MHz isn't of much use.

 

[ericgibbs]

hi hero
Interesting data.

gives a general account of attenuation. At 100kHz we have about
1800dB/km in fairly dry air. Attenuation on a simple model goes up as
f^2. Range of 1000kHz therefore bein of the order of 10m (1.8dB/m). At
1MHz we have 10cm. At 10MHz 100 microns. In my book 100MHz+ can't
really exist in air.

Puzzled at the BOLD text, 1000KHz is 1MHz, must be a typo, as at 1MHz it states 10cm.??

If it is a typo ie: 100KHz and wouldnt agree with a range of only 10mtr.???

From experience I have used 200KHz in air at 15mtr.??

 

[crashsite]

I take from this that in the real world >1MHz isn't of much use.

To be quite honest, I haven't researched this much but, I can say, with certainty that useful acoustical applications well above 1 MHz are common.

I used to work for a company that built and maintained satellite gound station equipment (and satellites, although I didn't work for that division). A device calles a SAW filter was commonly used in the downlink converters for the 70 MHz baseband.

Here's some background and general info in the SAW filter:

**broken link removed**

I don't know what the upper frequency limits of acoustics is or the practical limits. But, 3.4 GHz doesn't sound unreasonable.

BTW: Did you intend to write, 3.40e7 rather than 340e7?

 

[Hero999]

I was talking about the maximum frequency of sound through air at standard conditions, through other substances it will be different.

EDIT:
I read somewhere that the maximum possible frequency of sound in any medium is 12.5THz

I posted this in another thread.
https://www.electro-tech-online.com/threads/ultrasonic-fogger.26813/#post190056

Unfortunately it looks like the journal where I got the information from has started charging people to read it.
https://www.research.ibm.com/journal/sj/393/part1/gerasimov.html

I don't know if it's true or how the figure of 12.5THz was calculated.

 

[crashsite]

The Pressure is On

The key to this is the relative distance between the particles. If you increase the pressure by large amounts, i.e doubling, I would presume that there would be a difference. All my reasoning comes not from experimental data but from the perspective of a 17 year old. I have seen somewhere that the speed of sound is only minimally affected by the pressure, but I don't know to what extent. Even the minimal effect that is seen would indicate that there is some sort of interaction which affects the speed of sound due to the proximity of the molecules.

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.

 

[skyhawk]

Explains why sound is faster in desnser air. Denser air allows the molecules to collide faster thus increasing the speed of sound.

Not necessarily. If you change the density by varying the (ambient) pressure holding (ambient) temperature constant) the speed doesn't change. On the other hand if you change the density by varying the temperature and holding pressure constant it does.

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's post disappeared while I was composing mine!

duh, I was looking at the first page of this thread!

 

[crashsite]

Master and Slave

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.

First, where does any of that relate to analyzing it in a fixed but, otherwise arbitrary region of space?

So, you gather up some values, assign them to variables, throw in the "cheat" (universal gas constant) that makes the numbers come out "right" and make a formula. With that formula, you determine what must be happening by how the relationships between the different values act and interact, mathematically. At the end, you pronounce that you've "easily" explained what happens to make the speed of sound change.

I can take some voltage, current and resistance and assign them to the variables E, I and R, respectively. Then I can show that, if I use the formula E=IR that the voltage is proportional to the product of current times resistance. Unfortunately, what I haven't done is explain anything about E, I or R or what they are or consist of or how to concptualize them except as they numerically relate to each other. For someone who wants to know how electricity works but, isn't particularly interested in actually designing a circuit, the info I've given is useless.

Math needs to be the slave that supports the concept. Not the master that dictates how it must be viewed.

I would be a lot more impressed with a nice, concise, understandable, conceptual description of what's happening to the air that makes the sound propagate through it at differing speeds for differing conditions. Later, if I need to get the actual values, then, I'll need the formula. What's more, the formula will then be a lot more useful because I'll already know the nitty gritty of how it works, conceptually.

Yes, I can hear the heavy sighs...

 

[3v0]

Once again you have overlooked useful information.

A few posts ago you asked why pressure/altitude did not make much of a difference.

That's just it. Even with large pressure changes, the speed of sound is virtually unchanged.

Skyhawk provided that information and you ignored it.

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.

Either you are not reading or not understanding.

3v0

 

[crashsite]

Verifying

Once again you have overlooked useful information.

A few posts ago you asked why pressure/altitude did not make much of a difference.
Skyhawk provided that information and you ignored it.



Either you are not reading or not understanding.

3v0

It's unclear from the quotes/references but, this sort of seems to be aimed at me. That right?

Just want to clarify.

 

[3v0]

Yes, and I clarified it for you.

 

[3iMaJ]

I can take some voltage, current and resistance and assign them to the variables E, I and R, respectively. Then I can show that, if I use the formula E=IR that the voltage is proportional to the product of current times resistance. Unfortunately, what I haven't done is explain anything about E, I or R or what they are or consist of or how to concptualize them except as they numerically relate to each other. For someone who wants to know how electricity works but, isn't particularly interested in actually designing a circuit, the info I've given is useless.

Math needs to be the slave that supports the concept. Not the master that dictates how it must be viewed.



Yes, I can hear the heavy sighs...

What you've stated is a huge simplification of Ohm's law, I'm not surprised that it's not enlightening. If you want to understand the concepts described by Ohm's law then use Maxwell's equations and derive Ohm's law and I guarantee you that you'll understand exactly how Ohm's law works and what it is conceptually. Mathematics generally explain what you claim they so severly lack but are generally at a much higher level than most people are used to seeing/using them at.

Unfortunately 'nature' is rarely described by some simple linear equation and are certainly approximations used for quick calculations, so you shouldn't be surprised when you don't find the mathematical approximations enlightening. If you take a look at history some of the mathematics we have come to accept actually determined experimentally, from people just like yourself seeking to understand what exactly was going on, but chose to express that understanding in a form of a mathematical equation. Ampere's law (one of Maxwell's equations) was determined just in this fashion.

 

[crashsite]

Once again you have overlooked useful information.

A few posts ago you asked why pressure/altitude did not make much of a difference.

Quote:
Originally Posted by crashsite
That's just it. Even with large pressure changes, the speed of sound is virtually unchanged.

Skyhawk provided that information and you ignored it.

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.

Either you are not reading or not understanding.

I'm certainly not understanding the concept of sound propagation from the "ifs" and "thens" of mathematical formulas. I've made no secret of the fact (sad as it may be) that I just don't see the workings of science in mathematical formulas and equations.

But, even with that limitation (possibly because of it) I do feel like I'm getting closer and closer to getting an understanding of sound propagation. It's sad to say that not too much of it has come from the classically trained engineers who just don't seem to think about it much beyond the numbers (or, if they do, just don't have the verbal skills to impart it). I pick up a bit here and a piece there and plea for the answer. But, I'm not complaining. It's good for me to do it this way.

 

[crashsite]

We do what we can with what we got

What you've stated is a huge simplification of Ohm's law, I'm not surprised that it's not enlightening. If you want to understand the concepts described by Ohm's law then use Maxwell's equations and derive Ohm's law and I guarantee you that you'll understand exactly how Ohm's law works and what it is conceptually.

That's not quite true. You will understand the concepts behind Ohm's Law from using Maxwell's equations. And, i'm happy for you. You may also be able to do David Blain tricks...if you have a magician's dexterity and can hold your breath for several minutes at a time (I can't). You may be able to displace Dr. Phil...if you can become a prominent psychologist and develop an even catchier way to garner a daytime TV audience (I can't do that one, either).

Sonmetimes you just have to work within your limitations. I've never had too much trouble conceptualizing things but, I've always had trouble "seeing" the aswers in equations. That's not to say that I don't use math or that understand none of it. I do question how it's taught. I didn't learn the sin function in trig class. But, with the aid of a circle and a scientific calculator I was able to get the gist of it. There are other examples as well.

Regarding this thread, one of two things will happen. I'll either work my way through the mechanics of it or eventually realize that it's all math and futile for me to even try.

 

[3iMaJ]

My point is that most of the mathematics that are used to describe nature started out as experiments similar to this thread. Once the mechanics were thoroughly understood they were simply translated to mathematics. There are dozens of examples of these, quite rarely did mathematicians have anything to do with it. Most times it was practitioners that were interested in finding out more. Faraday and Ampere are two such examples. Using mathematics is a convenient way to express the results of the experment.

Try describing A = k*∫∫∫J*exp(-jkR)/R dv' in less than a paragraph, but after quick inspection some might recognize it as an electric vector potential that describes EM radiation. Mathematics is just a concise langauge used to describe nature in a lot of cases. I would agree some treat mathematics as simple formulae without giving any though to what a particular expression means, but we're not all that way. I'm happy that you have the intellectual curiosity to pursue this type of academic endeavor, but mathematics generally do describe the things you're talking about, perhaps just not in a way that most would prefer to understand.

P.S. You've spent more time thinking about sound propagation than most "classically trained engineers." Simply being an engineer does not make one well versed in every aspect of physics, just the particular area that we're interested in. My area is radar, and I'm well aware I'm out of my element which is why I've taken to talking about the mathematical side of this discussion. I make a point to understanding what mathematics "mean" not just what the mechanics of a particular formula are. I find number grinding not very enlightening.

 

[crashsite]

I try...in fact, people often tell me that I'm very trying.

My point is that most of the mathematics that are used to describe nature started out as experiments similar to this thread. Once the mechanics were thoroughly understood they were simply translated to mathematics. There are dozens of examples of these, quite rarely did mathematicians have anything to do with it. Most times it was practitioners that were interested in finding out more. Faraday and Ampere are two such examples. Using mathematics is a convenient way to express the results of the experment.

On that note, I must say that I have a lot of respect for, Eintstein. He's generally thought of as being a great mathematician and physicist but, that's not the part I like. He used to do, "thought experiments". As I understand it, he would just think about how something worked (especially if it didn't seem to work quite right). Of course, being Einstein (perhaps the only egghead in history that didn't take offense when somebody would say, "Hey, way to go, Einstein!"), he was then able to actually do something with it.

I fear that no matter how much I may learn about this subject, it probably wont go any further in the service to mankind.

Radar. Hmmmm. I've had some back of the mind thoughts about the state of sonar, radar and prehaps lidar for applications like collision avoidance and precision positioning. I've heard rumors that some Mercedes models may be using the 'radar-on-a-chip' devices for the sollision thing.