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I was looking at lightning, and started to wonder if the speed of the thunder slowed down as it lost energy traveling far distances. I know the amplitude of sound decreases, perceived as volume. Im not certain, however, how to actually calculate the distance of a lightning strike based off of of the interval of time between observing the flash and hearing the thunder. Would this time be linear ( is the speed of sound constant?), or is it non-linear (Speed of sound loses velocity over time?)

If I were to determine this by comparing two audio recordings of the same lightning strikes' thunder, and seeing if the further one was lower in frequency, would that accurately indicate a deceleration of the sound?

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  • $\begingroup$ Regarding the 2nd paragraph: if the speed of sound slows down, does the frequency get lower or does the wavelength get shorter (or both or neither)? Hint: Snell's Law and wavefronts. $\endgroup$
    – JEB
    Feb 19 '18 at 0:56
  • $\begingroup$ The speed of sound should not vary with the "energy" left in the travelling wave. The energy only changes the frequency and wavelength. The speed completely depends on the medium in which the wave is travelling. $\endgroup$
    – fierydemon
    Feb 19 '18 at 1:17
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    $\begingroup$ The speed of sound in air is dependent on the temperature, pressure, and moisture content of the air. (And likely on the CO2 concentration as well.) $\endgroup$
    – Hot Licks
    Feb 19 '18 at 2:16
  • $\begingroup$ @probably_someone - I wonder where you found a dispersion relation of sound in air that gives you a speed of sound that depends on frequency. $\endgroup$
    – freecharly
    Feb 19 '18 at 2:34
  • $\begingroup$ @freecharly My mistake, comment is now rightfully deleted. $\endgroup$ Feb 19 '18 at 2:45
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Strictly speaking, the thunder propagation velocity does decrease with distance, as initially lightning generates a shock wave in air, whose propagation velocity is higher than the velocity of sound, however, such shock waves get weaker with distance and become ordinary sound waves at a distance of just about 10 m from the lightning (http://lightningsafety.com/nlsi_info/thunder2.html). For a nuclear blast, this effect of shock wave deceleration with distance is much more significant. See the relevant formulas at https://www.metabunk.org/attachments/blast-effect-calculation-1-pdf.2578/

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for lightning bolts in air, the speed of sound of the thunder will not change with distance. So to estimate the distance to the lightning, you start to count 0,1,2,3,4... at the instant you see the flash. If you hear the thunder at the count of 5 (5 seconds after you saw the flash) it means the lightning was about 5,000 feet away because the sound travels about 1,000 feet in one second and the relationship is linear.

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  • $\begingroup$ Yes, this is true, and it is a good approximation, especially since the time it takes decelerate is quite short and thus does not travel a big distance before acquiring the speed of sound in air. Nevertheless, at the first moments of the shockwave generation, the speed is indeed a lot higher than the speed of sound (in the linear regime). Some quite nice and condensed information can be found in Fundamentals of Acoustics by Kinsler et al., chapter 17. $\endgroup$
    – ZaellixA
    Feb 12 '20 at 12:34
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This is going to hurt, because so far I always got downvotes for this, but since it answers your question, I will give it to you anyway. You will not get a better answer from established science.

It is called the Waterham hypothesis. It suggests that the speed of sound is the internal speed at which the particles inside a medium move around. Air always moves at that 'speed of sound', regardless of the presence of sound. The density of the gas as well as its temperature only cause marginal differences. The differences caused by composition are larger, but still do not account for the existence of a 'speed of sound'.

The reason why sound never propagates faster than the speed of sound is because anything making air move faster than sound, compresses it into phase transition, forcing it into the liquid phase. That's the reason for the condensation shock wave in front of a jet flying at supersonic speed. That is what stops sound from traveling faster than that speed.

The decisively lower limiting factor to the speed of sound resides in the fact that phase transition from liquid back to gas is a tunnel effect result, meaning it only occurs at a very specific amount of energy release and therefore always results in the same particle velocity.

This is where it gets interesting, because this means the condensation energy may be more than the evaporation energy. That energy difference has to go somewhere and therefore results in radiation of energy or increase in thermal energy of the particles involved.

The reason why sound diminishes over distance, but not looses speed, is because that speed depends entirely on the characteristics of the medium. The source of sound, its amplitude or its frequency, bears no relevance to its speed whatsoever.

So yes, the speed of sound is constant and this is why.

Anyone can downvote this answer, but none of them will be able to give you a better one. All they got is a lot of in-the-box-science, explaining why they just don't know.

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  • $\begingroup$ This is very interesting indeed, because ideal gases also have a speed of sound, and, according to your arguments, this means that ideal gases can be liquefied. But even if one accepts ideal gases as an idealization, there are still surprising opportunities in the possible pressure liquefaction of hydrogen. Think only of efficient energy storage, which is one of the most seemingly trivial but then again annoyingly difficult problems of our time. But honestly, isn't this answer just a GPT-3 experiment on producing strikingly convincing scientific gibberish? $\endgroup$
    – oliver
    Apr 6 '21 at 20:53
  • $\begingroup$ You could call it that I guess, yes. Nevertheless, it does pose possibilities. The juicy part is in the fact that it explains things like the vortex tube and how bees fly and things like that.. It opens the possibility to use sound to concentrate gas into a liquid state and than subtract it from the process in that state. The only problem being , where do you leave the energy? Strictly speaking it should even be possible to push it into a plasma state, but that's a bit very far out. Main thing is, it answers a question where nothing else can. I'm still baffled by that. How can that be? $\endgroup$
    – Berend
    Apr 6 '21 at 22:17
  • $\begingroup$ To comment on the ideal gasses thing, yes off course ideal gasses can be liquefied. Any gas can be liquefied, unless it sublimates first. Stronger than that, any gas is in a continuous state of bouncing back and forth between liquefaction and evaporation. The speed of sound being the velocity at which it evaporates, which by its nature is fixed for that gas under that condition. $\endgroup$
    – Berend
    Apr 6 '21 at 22:38
  • $\begingroup$ Correction: An ideal gas is a model of a real gas and any real gas can be liquefied. The extend to which an ideal gas cannot be liquefied, is the extend to which it does not resemble a real gas. $\endgroup$
    – Berend
    Apr 6 '21 at 22:52
  • $\begingroup$ Amazing! -1 from me for this extraordinarily fantastic Mary-Poppinsesque piece of unicorn physics. $\endgroup$
    – oliver
    Apr 6 '21 at 23:18

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