Why Does Sound Propagate?

[crashsite]

Deferral

(oh btw poor you, living in america....)

I'm going to defer answering the body of your post as it may end up being "off limits" to do so. We'll see how that shakes out.

I was in England, on a business trip several years ago, and I encountered an English gentleman on the street who picked up on my American accent and made a similar comment. He said, "Oh, you're an American (pause), I guess that's not your fault". My wits were a bit slow that day or I would have replied, "That's true but, I suppose it is my fault that I enjoy being an American so much".

I've never been to Aussieland...or Tasmania. I'm not sure what I'd even do there if I were to go. The thing is, that the mere thought of taking a cruise (to anywhere) or going on a "canned tour", just leaves me cold. I always enjoyed traveling on business and to visit people I personally know because you interact with "real" people instead of only those involved in the tourist trade. Plus, the notion bf being captive on a cruise ship, between ports, with...well...the kind of people who love being on a cruise ship...is not my cup of tea.

 

[j.friend]

I must concur, however there are a lot more opportunities than 'canned tours' when undertaking tourist activities. Say last year i traveled to New Zealand for a ski holiday, whilst we ahd the fair share of typical touristy activities (such as river cruises, etc) most of my time was taken up by the skiing firstly and secondly by exploring the areas where I was staying.

I travel for experiences, I rather enjoyed being the only aussie in the pub whilst watching a bledisloe game against the all blacks. there are plenty of opportunities for tourism around the world that do not include the typical tourist experience or your canned tours. it might take a wee bit more effort and preparation on your part, however it is certainly worth it.

Whilst maybe not Australia (although it is apparently held to be a top tourist destination in the world) you should perhaps try and see some of the world that you live on off your own back than just on business trips. Thats my view on it anyway

 

[crashsite]

Straying

I must concur, however...

I don't want to stray too far here. Hopefully, we can get some of this basic concept and terminology squared away and get back to how heat propels sound (or not, depending on one's view of it). And, how waves don't propel sound (or do, depending on one's view of it).

 

[j.friend]

so if you wouldn't mind could you again highlight just how you think heat propagates sound. For surely even if heat is the way in which it is propagated, it would still be in a form of wave

 

[crashsite]

Synopsis of how it works.

so if you wouldn't mind could you again highlight just how you think heat propagates sound. For surely even if heat is the way in which it is propagated, it would still be in a form of wave

If you look at the rather long post at the end of page 14 of this thread titled, "Got It", I explain my pool ball analogy and that ties in the "heat" component.

In synopsis, molecules are randomly bouncing around due to having thermal energy. That provides the power to propagate the sound. The sound energy just puts a directional bias on that random movement and that bias gets moved along as the propagation of sound.

It is imperative that you accept that the sound is being propagated on a molecule-by-molecule basis as the molecules collide with each other, carrying that bias along.

If you then want to integrate those molecular instances into what's happening over extended time periods, then you can see a wave structure develop. But, whatever wave you eventually come up with, it has nothing to do with the actual propagation of the sound. It's just a result...an artifact, if you will, of taking things to that next step of integration over time.

As to why the sound propagates at Mach 1 is directly related to the speed the molecules are traveling due to their temperature. You can see how that works on page 29 (fifth post down). It's all a vector summation thing relative to the speed of the molecules. I must warn you that not everyone agrees with it. For example user, Skyhawk branded it as being more like numerology than physics.

You also need to account for the fact that the speed of sound only changes with temperature...not with pressure. That means that the sound gets moved from molecule to molecule at the same linear rate even when the molecules are different distances apart (closer at higher pressure and further apart at low pressure). The only thing that can account for that is that the speed of sound is tied to the speed of the molecules themselves.

Of course, I'm open to alternate explanations of all these phenomena...but, they have to answer the questions at least as well as my hypotheses do if I'm going to accept them.

 

[3v0]

Two comments.

Compression waves are important because it the alternate high and low pressure that moves the ear drum.

The sound energy is not added to vibration or heat of a molecule. It displaces or moves the molecule. This is the cause of the compression waves.

3v0

 

[j.friend]

Ok so the basis of your theory is that rather the molecules gaining energy from collisions, their direction is altered and the speed of sound is propagate at a speed relative to the velocity of these particles (your heat energy).

Referring to your post on page 29 with the vector diagram, can I ask how you arrived at the value of 0.7 for the value of the average percentage of the actual velocity of the molecules?

 

[crashsite]

Damn it! You made me use math!

Referring to your post on page 29 with the vector diagram, can I ask how you arrived at the value of 0.7 for the value of the average percentage of the actual velocity of the molecules?

I'll answer your question first, since it can be done quickly and easily. User, 3v0's are goint to take a bit more...finesse.

Sin 45 degrees. The first thought might be that it should be 50% but, that number gets skewed by the fact that as the molecules tend to travel more toward the blue line than the red, not only is the angle directed more in that direction but the speed also increases in that direction.

You can alternately think about it as how much of the 1100 mph speed gets subtracted at each vector. I'm sure that when you consider this, you'll agree that sin 45 degrees (about 70%) is the right number.

 

[3v0]

This one I want to post just for fun. We can talk about it does or does not demonstrate at another time.

Make video about visible sound and vibration - Boing Boing

3v0

 

[skyhawk]

You can alternately think about it as how much of the 1100 mph speed gets subtracted at each vector. I'm sure that when you consider this, you'll agree that sin 45 degrees (about 70%) is the right number.

Unfortunately your average vector is incorrect. It does make an angle of 45 degrees but it doesn't have a length of 1100 mph. Its length should be reduced by a factor of approximately .900316. The exact value of the factor is 2√2/π. The result is obtained using integral calculus, but you can get a good approximation by summing a few uniformly spaced vectors. For instance vectors at 0, 30, 60, and 90 degrees or at 0, 15, 30, 45, 60, 75, and 90 etc.
I wrote a little program to average uniformly spaced vectors for different spacings. Here are the results:

     spacing      value
         30.00  .836516
         15.00  .868302
          9.00  .881068
          6.00  .887469
          3.00  .893885
          2.00  .896027
          1.00  .898170
          0.50  .899243
          0.25  .899780

As you can see the averages are converging nicely to the theoretical value.

Of course, there was no physical justification that the projection of the average velocity vector in the direction of sound propagation should be the speed of sound. I can see why you feel that answers obtained using math don't represent a physical concept because yours certainly doesn't.

 

[crashsite]

Math and More Math

Unfortunately your average vector is incorrect. It does make an angle of 45 degrees but it doesn't have a length of 1100 mph. Its length should be reduced by a factor of approximately .900316.

Well, I don't know about that. I got that nomial, 1100 mph number from the web page I've referenced a few times that gives a calculaltion for the speed of air molecules vs. temperature. If the chart changed the direction of propagation to the 45 degree line, then the red and blue lines would be the 45 degree lines but, they wouldn't change lengths (if I get it correctly that your problem is nhot with the 1100 mph speed but, just the 1100 mph speed for the 45 degree line).

What I was trying to show is not exact values but how, on a molecular collision by molecular collision basis, there's no way to definitively specify the speed of sound. It could be .02 mph or 492 mph or 1100+ mph (depending on how fast the speed distribution of the molecules may allow the fastest ones to go), in the direction of propagation and that it depends on the speed and direction that each molecule is carrying the bias that represents sound information. But, the average speed is that of the speed of sound for the medium and temperature.

There are probably some mathematical gyrations that show that there are variations to skew what seems like a pretty obvious answer. I recall reading something once that it's been proven (mathematically) that 2+2≠4.

To be quite honest, I'm not sure what your table of "vector spacings" is trying to show relative to how the summing of the vectors leads to an average speed of sound (or whatever the correct mathematical term is for how the overall efect transpires). How does it advance understanding the concept of how sound propagates?

I'm not going to be cowed by fancy math. My intent is to bring the discussion of sound propagation down to the level of the common man, not the common physics professor. I'm even willing to accept some inaccuracies and estimations in the values so long as the concept is intact and understandable.

 

[crashsite]

Patience

Two comments.

Compression waves are important because it the alternate high and low pressure that moves the ear drum.

The sound energy is not added to vibration or heat of a molecule. It displaces or moves the molecule. This is the cause of the compression waves.

3v0

I haven't forgotten this but, I'm figuring out how to best reforumlate what I've said before on these. Give me a few days.

 

[Mikebits]

I must say, this has turned into quite an interesting post, somewhat beyond anything I could comment on but interesting to say the least. Just 90 or so more post and this thread will make the headlines and bump the useless SSB thread. Keep it going guys

 

[j.friend]

I'll answer your question first, since it can be done quickly and easily. User, 3v0's are goint to take a bit more...finesse.

Sin 45 degrees. The first thought might be that it should be 50% but, that number gets skewed by the fact that as the molecules tend to travel more toward the blue line than the red, not only is the angle directed more in that direction but the speed also increases in that direction.

You can alternately think about it as how much of the 1100 mph speed gets subtracted at each vector. I'm sure that when you consider this, you'll agree that sin 45 degrees (about 70%) is the right number.

Im sorry but this seems a little unclear.... Just probably my thick head. Why would the molecules travel more towards the blue line rather than the red line if it is truly random, I mean if it were truly random they would have equal probability of going everywhere.

When you say sin 45 degrees is that because that is the supposed average speed of the molecules?

 

[Mikebits]

I was wondering the same thing. Something about that heisenberg fella came to mind.

 

[j.friend]

Unfortunately your average vector is incorrect. It does make an angle of 45 degrees but it doesn't have a length of 1100 mph. Its length should be reduced by a factor of approximately .900316. The exact value of the factor is 2√2/π. The result is obtained using integral calculus, but you can get a good approximation by summing a few uniformly spaced vectors. For instance vectors at 0, 30, 60, and 90 degrees or at 0, 15, 30, 45, 60, 75, and 90 etc.
I wrote a little program to average uniformly spaced vectors for different spacings. Here are the results:

     spacing      value
         30.00  .836516
         15.00  .868302
          9.00  .881068
          6.00  .887469
          3.00  .893885
          2.00  .896027
          1.00  .898170
          0.50  .899243
          0.25  .899780

As you can see the averages are converging nicely to the theoretical value.

Of course, there was no physical justification that the projection of the average velocity vector in the direction of sound propagation should be the speed of sound. I can see why you feel that answers obtained using math don't represent a physical concept because yours certainly doesn't.

Well the length of the line would be 1100mph as the diagram effectively depicts a circle, with the radius being the velocity of a molucule. Therefore at any angle the speed will be the same, however the proportion of the speed in the 'direction of the propagation of sound' will differ.

I understand how he gets the value 0.7, as sin 45 degrees = 1/√2 ≈ 0.7
The only thing that i have a little doubt about is what angle you should take the average speed to be. it seems logical that it would be 45 degrees, however i'm not 100%

 

[skyhawk]

Well, I don't know about that. I got that nomial, 1100 mph number from the web page I've referenced a few times that gives a calculaltion for the speed of air molecules vs. temperature. If the chart changed the direction of propagation to the 45 degree line, then the red and blue lines would be the 45 degree lines but, they wouldn't change lengths (if I get it correctly that your problem is nhot with the 1100 mph speed but, just the 1100 mph speed for the 45 degree line).

The point is that if you average vectors with lengths 1100 mph but with directions uniformly distributed over 90 degrees you do not get a vector with length of 1100 mph. I don't ask you to believe it because I say it. You can check for yourself. I know doing it analytically is beyond your math abilities, but you can write a program like I did. It took me about ten minutes. You can even do it graphically. Let 1 inch equal 1000 mph, so each vector is 1.1 inches long. Drawn vectors at various angles, 0, 15, 30, 45, 60, 75, and 90 degrees. Add them by putting the tail of one to the head of the other. Measure the resulting vector and divide by the number of vectors that you summed. Its so simple that I could have done it in the 8th grade with my mechanical drawing set. I've made a testable statement that anybody can check using at least three different methods.

For anyone who would like to do the sum graphically here is a link to explain:

https://www.electro-tech-online.com/custompdfs/2009/08/Vector_addition_05.pdf

Please note what you said:

The question is, what is the average speed, in the direction of the blue line, based on the vector summation of all the directions the sound can radiate from the point of distrubance. It's impractical to show them all so just a couple of representative lines are shown.

It would appear that you didn't do a vector sum and based on your inability to understand the results I presented in the table you don't even understand how to do a vector sum.

To be quite honest, I'm not sure what your table of "vector spacings" is trying to show relative to how the summing of the vectors leads to an average speed of sound (or whatever the correct mathematical term is for how the overall efect transpires). How does it advance understanding the concept of how sound propagates?

Not sure your hand waving advances the concept of how sound propagates. What principles of physics did you employ? It is well known by physicists that the average speed of the molecules and the speed of sound are in the same ball park. It's no coincidence. The factor connecting the rms speed of the molecules and the speed of sound is in fact √(gamma/3), where gamma is the adiabatic index. For diatomic molecules such as oxygen and nitrogen gamma = 1.4 therefore the factor is .683 not .707. On the other hand for noble gases such as helium and neon gamma = 1.67 with the result that the factor is .745. Polyatomic gases have a gamma around 1.33 thus the factor is .665. The speed of sound not only depends on the temperature but also the material propeties. The differences are measureable and verifiable.

There are probably some mathematical gyrations that show that there are variations to skew what seems like a pretty obvious answer. I recall reading something once that it's been proven (mathematically) that 2+2≠4.

No gyrations on my part. I've told you what I did. I added N equal length vectors and divided by N to get an avaerage. No tricks! The problem is that what you think is the obvious answer is the wrong answer.

I'm not going to be cowed by fancy math. My intent is to bring the discussion of sound propagation down to the level of the common man, not the common physics professor. I'm even willing to accept some inaccuracies and estimations in the values so long as the concept is intact and understandable.

LOL It's hardly fancy math. As I said it just takes a simple computer (or calculator) program. Anybody who truly wants to know the answer can find it.

 

[skyhawk]

Well the length of the line would be 1100mph as the diagram effectively depicts a circle, with the radius being the velocity of a molucule. Therefore at any angle the speed will be the same, however the proportion of the speed in the 'direction of the propagation of sound' will differ.

But he claims the vector is the result of averaging. The length of such an average vector is not the same as the radius.

 

[3v0]

Prior to working on the vector thing one needs to know if the sound energy is added to the heat/vibrational energy.

 

[skyhawk]

Prior to working on the vector thing one needs to know if the sound energy is added to the heat/vibrational energy.

It does and to show that you need to do the averaging process. When there is no sound present, if you average the velocities of the molecules you get zero. As sound passes when you average the velocities you get a small number and that number oscillates at the frequency of the sound. This small average velocity serves to change the number of molecules in a unit volume resulting in the compressions and rarefactions.