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I am new to wave mechanics. It would be of real help if someone could elaborate, although not in too much detail(as I am still a beginner) regarding the conduction of heat during rarefractions and compressions. What I am looking for is not a mathematical explanation, but a visual one, with which I can visualize as to how the process happens. I am not able to understand and visualize how the temperature increases/decreases during a rarefreaction or compression, and how it is adiabatic. Thanks in advance

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As you might know, a sound wave is an example of a longitudinal wave. In brief, a longitudinal wave is a wave in which the particles of the medium vibrate( a more appropriate terminology would be 'perform a simple harmonic motion') in the same plane where the wave travels. This figure illustrates that:
enter image description here

Here, you see a tuning fork set into vibration which consequently sets the particles of the medium around it in vibrations as well and this finally results in a longitudinal wave being formed.


If we focus more on how this happens, we see that when the sound wave is initiated, (you can simply visualise this by thinking of talking to someone) When we speak, the air particles right in front of our mouth are set into vibrations.

These particles then set their neighbouring particles into vibrations, and so on. This gif illustrates this:

enter image description here

As you can see, in the region of compressions, the density is increased. And as you might know, any particle of any medium has the property that it has some amount of vibrational kinetic energy. In the compressions, particles are packed in a smaller region which means more pressure(as the density is increased here). Consequently, this increases the temperature in this region. which also results in more energy being trapped.

Also, this happens so fast that this thermal energy does not have any time to flow out from the compressed region. The same applies in the case of rarefied regions. Consequently, it is safe to assume this to be adiabatic which is what Laplace did to correct Newton's formula for speed of sound in medium.


Remember that these variations are quite small and negligible. Think! Have you ever felt the temperature suddenly increasing/decreasing while speaking to someone?

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  • $\begingroup$ That explains that temperature changes occur and when, but not how its generated and where it comes from. The variations may be negligible during speaking, but they are quite noticeable in a vortex tube. Can you elaborate? $\endgroup$
    – Berend
    Apr 1 at 15:23
  • $\begingroup$ I believe the part about the density getting increased which results in more collisions of the particles should explain that. I have tried to provide simple explanations as she mentioned in her post that she wanted to visualise how this works, I have also added the gif which shows how the compressions and rarefactions are getting formed and transmitted. You're right about the vortex tube but I preferred to give a rather simple case as an example. I would be more than happy if you could give more suggestions so that I can improve my answer :) $\endgroup$ Apr 1 at 16:08
  • $\begingroup$ I was hoping you had the answer to that. I have my own hypothesis on how thermal energy travels from one particle to another in a gas, why it tends to rise with rising pressure and why there is a speed to sound. But you know the reputation of such thoughts, so I am hoping for someone to correct me or come up with established relevant science known for ages. Conductive propagation of thermal energy in gases is observed and described, but not explained. More particular, the way thermal energy behaves in gas. It does weird things, like in the vortex tube. $\endgroup$
    – Berend
    Apr 1 at 16:56
  • $\begingroup$ Well I'm myself, dont have a lot of knowledge in this field and that's all I had. Maybe you can raise a bounty on this question to get it more attention and maybe then, you can get a more clear, descriptive answer which explains the more complex reasoning behind this! :) $\endgroup$ Apr 1 at 17:17
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    $\begingroup$ Are you kidding me? :) Raising a bonus on that might get me banned. I was just hoping this exact question would draw an answer from someone who can shed a light on what's behind where all common knowledge stops. Lots of people know what influences the speed of sound, but no one seems to know where it comes from and why it is so stable or even why it exists in the first place. Your explanation, which I find beautiful by the way., doesn't do that either. To me it feels like a 'the emperor's new clothes' kind of thing. Am I really the only one who is seeing this? $\endgroup$
    – Berend
    Apr 2 at 0:19
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OK, just so it is there, controversial as it is.

The way heat conduction takes place in sound wave propagation, is by a sequence of condensations and evaporations of particles as a consequence of local increase and decrease of pressure caused by the wave. As the energy provoking the condensation may vary, but the energy released in evaporation may not, the difference is shared by the particles involved as thermal energy. There is a radiating component involved too, but that is in comparison negligibly small. This concludes the full extend of heat conduction, caused by wave propagation.

All credits/discredits to the author. No references.

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