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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, 2018 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. $\endgroup$
    – Ryan Hendricks
    Feb 19, 2018 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, 2018 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, 2018 at 2:34
  • $\begingroup$ @freecharly My mistake, comment is now rightfully deleted. $\endgroup$
    – probably_someone
    Feb 19, 2018 at 2:45

2 Answers 2

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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, 2020 at 12:34

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