Why does moderately distant lightning sound the way it does: relatively quiet high pitched thunder first, and then much louder low pitched thunder? Why does thunder, that is heard about five or ten seconds after the lightning is seen, start as relatively quiet high pitched 'crackling' thunder which is, about five or ten seconds later than that, followed/replaced/drowned out by much louder lower pitched 'booming' thunder?
I am under the impression that loud low frequency sound travels much faster than quiet mid range frequency sounds (by a factor of approximately two in the case of the sound/blast of a large nuclear explosion, meaning that the blast wave of a large nuclear explosion travels at twice the 'speed of sound' i.e about 600 meters per second). So I would have expected the loud low frequency sound from the lightning to reach me earlier and not later. But the low frequency sound does seem to reach me later.
Edit: Another thing I find strange is that in many cases the later sounds (the loud booms of thunder) are remarkably distinct (or brief, being at most about 0.1 seconds in duration each, say), like a series of large bombs going off, as if coming from points or small volumes, rather than a continuous roar/rumble that gets louder and quieter at random. The latter might be what is expected if the loud later sound is coming from a randomly oriented line (with or without branches) with a length of five hundred meters to twenty kilometers.
 A: Air is not a dispersive medium for sound waves. At least, in normal condition.
When a lightning is produced, the air is heated up to a very high temperature, creating a shock wave like. The sound heard depends on the position of the observer, far way or near the thunder origin, and the shape and direction of the thunderbolt.
Lightning can be cloud to cloud or ground to cloud and they can have vertical or horizontal direction. They divided itself two or more times and then the sound produced from the forked thunderbolt depends also on this. After a first high frequency, the ramifications of the thunder produces the rumbles, due to the fact the waves bounce off the clouds and other obstacles.
Also, it is needed to consider the absorption of sound that is more important for high frequency than low frequency, in a manner that high frequency waves propagate less than low frequency.
Probably the most simple reason for hearing the rumbles after the high pitch is due to the fact that as i said the shape of the thunderbolt is complex and has horizontal and vertical directions. From vertical the sound from the channel comes at the same distance to the observer, while in horizontal channels sound comes from different positions and orientations creating rumbles because lightning segment propagates for long distance; considering also the selective absorbtion of high frequency this is why this produces low frequency tones that tends to propagate more distant and lasts long time.

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*Some interesting informations: Martin A. Uman, The lightning discharge.


*Most interesting (for me): Arthur A. Few. Thunder, Scientific American (1975).
Update:
Temperature in atmosphere also play a role. Sound waves goes faster in warm air than cold air. Also, cold air on the surface of earth and warm air above can create a cavity where sound waves can be reflected to the ground and refracted.
Other useful readings: A. A. Few, Power spectrum of thunder, Journal of geophysical research (1969).
A: Although I am not a thunderstorm expert either, my guess would be, that the reflections of the soundwaves between the atmosphere/clouds and/or ground are responsible for the delay of the low frequencies. If a planar waveguide is formed between either layers of clouds or clouds/atmosphere vs. ground, the waves would be forced to move in planar directions only.
For linear waveguides the dispersion relations are known, see this resource for acoustics, or this PSE question for electrodynamic waveguides (which are basically just another application of general wave mechanics as far as waveguides are concerned). Linear waveguide dispersion boils down to group velocity tending to zero for wavelengths approaching infinity (i.e. for low frequencies), while much smaller wavelengths approximately move as if there was no waveguide at all.
If one assumes that a planar waveguide is somewhere between a linear waveguide and free dispersionless wave propagation, it is clear that there will be some delay for lower frequency noise from a flash, while the higher frequencies will arrive according to the free speed of sound in air.
As to the possibility of a waveguide formed by the atmosphere, remember that the atmosphere is limited in height. And even if it is commonly considered thick of the order of several kilometers, air density is rapidly falling with height, and with air density changes speed of sound. This probably makes the atmosphere a waveguide for heights already much smaller than of order kilometers (even total reflections at density gradients can be observed for the optical phenomenon of Fata Morgana).
What this model also explains is that closeby lightning strikes always sound crisp, while only lightnings farther away show the frequency-dependent delay effect.
A: I'm not an expert, but I spent some time with references 1 and 2 several years ago. This answer is based on some notes I took.
Measurements using the radio waves produced by lightning indicate that lightning bolts inside thunderclouds (the ones that we can't see directly) are often mostly horizontal, and they can be anywhere from 1/2 km in length to 20 km in length, spanning a large portion of a large thundercloud. That says that the most distant part of the lightning bolt can be several kilometers farther away than the closest part. That is at least part of the reason why thunder lasts so much longer than the flash of lightning that produced it.
Also, lightning typically has a jagged, branching shape. Experiments with smaller sparks have shown that the sound from a given segment is typically directional (louder in some directions than in others), so different segments of a jagged lightning bolt will tend to contribute different amounts to the overall sound because they're oriented differently. This is at least part of the reason for the sound's rich texture.
Based on that information, here's a guess about why the sound from moderately distant lightning often starts with a quieter higher-pitched part. I'm picturing the shape of lightning as similar to the shape of a river with many smaller tributaries contributing to it. If we're closer to one of those small tributaries than to the main part of the river, then we'll hear the sound from that small tributary first (especially if its orientation is favorable, because the sound is directional), followed by the sounds from the more substantial parts that are farther away. This at least seems to explain the quiet-to-loud trend, and maybe it also helps explain the frequency trend: smaller sparks apparently don't produce as much lower-frequency sound as larger sparks, so most of the lower frequencies will come from the larger parts, which are farther away in this scenario.
Frequency-dependent attenuation in the atmosphere and in the ground might also play a role (reference 3).

References:

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*Rakov and Uman (2003), Lightning: Physics and Effects (Cambridge University Press)


*Holmes et al (1971), "On the power spectrum and mechanism of thunder" (https://doi.org/10.1029/JC076i009p02106)


*Lamancusa (2000), "Outdoor sound propagation" (https://www.mne.psu.edu/lamancusa/me458/10_osp.pdf)
A: I believe the initial "sound" of the lightning is likely to be close to an idealized impulse: an extremely large and sudden pressure differential.
Next, you have all of the things mentioned so far: the general properties of sound through air, the boundaries imposed by the ground and different layers of that air, etc. The sum of all these at that moment can be considered a transfer function.
Then what you hear is the impulse response of the atmosphere/ground system for a source at the lightning's location and a listener at your location at that exact time.
