You maybe surprised to learn that thunder is, or at least was, less understood than lightning and tornadoes put together. We know the end product is a very loud sound wave emerging from the lightning channel (or any electrical arc), however the intricate process of its development is somewhat uncertain, and many environmental conditions need to be considered when listening to the tone and texture of the thunder.

THEORIES                   
There have been a few theories that have arisen through history:

Clouds colliding One of the first theories by Aristotle in the 3rd century BC was that thunder was the sound of clouds colliding with each other.

Thermal expansion of rain droplets or moisture An old theory from the 19th century was when a lightning channel cut through rain or cloud droplets, they exploded into steam creating sound waves. This has been dismissed after the observation of sound from electrical arcs in dry air.

Explosion of gaseous chemicals created by the lightning channel It was also thought also that explosive gaseous chemicals produced by the arc of lightning were being ignited in turn by the arc and exploding.

Thermal expansion of surrounding air By the mid 19th century it was thought that the superheating of the air immediately around the lightning channel caused the air to expand leaving a vacuum, and then collapse immediately with such force that a sound wave radiates from around the channel.

Thermal expansion of plasma
The more widely accepted theory nowadays, similar to the above theory, is that the expansion of the plasma (ionised gas) within the lightning channel itself is the cause of the sound wave. However this theory has not yet been fully proven.


SPEED DIFFERENCE                  
Although the shockwave of thunder occurs at the same time as the lightning, unless the lightning strikes within 100 metres of where you are, you will always hear the thunder after the lightning because light travels through the free atmosphere faster than sound. Typically, light travels at approximately 186,282 miles (299,791 kilometres) per second in a vacuum (a fraction slower in air) whereas sound travels at a mere 343 metres per second (in dry air at 20C) which differs depending on pressure, temperature and humidity. In this case light works out to be somewhat 866,428 times faster than sound.


JUDGING DISTANCE                   
The distance the lightning has occurred can be judged by roughly counting 5 seconds for every mile after the discharge. This is a good generalisation. It is worked out from knowing that sound travels at approximately 0.215 miles per second at surface pressure, so after 5 seconds it has travelled 1.075 miles (approximately 1 whole mile). This is the general rule for cloud-base and cloud-ground lightning (within the atmospheric boundary layer). But the speed of sound is dependant on air pressure, humidity and temperature. For example with upper-level lightning, air pressure is much lower which reduces speed, the air is dryer which reduces speed, but it is colder which increases speed, so overall the sound wave could travel at a much slower speed than normal. This has been linked to anvil lightning, which can be seen clearly but is so far away and high up its usually silent.

On average thunder is usually inaudible after 10-12 miles of travel distance, although this depends on the magnitude of the discharge. Distant rumbles and sub-bass booms may be heard from high-amp lightning more than 15-20 miles away, such as positive flashes (P-Fs).


AMPLITUDE AND TEXTURES OF THUNDER                   
The sound of thunder can depend on a number of conditions, such as the air pressure in which it occurs in, temperature inversions within the atmosphere and orography where mountains and valleys can cause echoing and modulation of sound. Aside from these influences, in my personal experience as an thunderstorm observer, it appears that thunder from different types and intensities of lightning have their own different textures and intensities despite the distance at which the lightning has occurred. It is the general notion that the closer the lightning is, the louder the thunder. This is true as sound waves reduce in intensity with distance from the origin (obeying an inverse-square relationship), but it also depends on how energetic the lightning channel was. For example the thunder from a high-energy Cloud-to-Ground (C-G) lightning from a 1-mile distance can be much louder than a low-energy C-G from half a miles distance.

Lightning varies electrically in amplitude. Most discharges are on average 5,000-30,000 Amperes, but it has been reported to reach in excess of 200,000 Amperes. In one such case the famous strike just before the Apollo 15 launch in 1971 was measured around the 100,000 Amps mark. The higher the current the brighter and more energetic the lightning channel, and this generally follows suit to the amplitude of thunder produced based on the thunderstorms I have observed.

"High-Amp" lightning, e.g. C-Gs, P-Fs and organised (channelled) C-Cs / I-Cs can produce loud thunders featuring bangs, crashes and sonic booms. C-Gs especially tend to be louder due to the fact they occur close to the ground in higher pressure environments allowing for a sharper sound propagation.
"Low-Amp" lightning, e.g. disorganised (broken) C-Cs, I-Cs, C-As and A-Cs (Anvil Crawlers) can produce softer thunders featuring crackles and rumbles. Also contributing to the softer thunder is the occurrence of lightning in lower pressure environments aloft where sound propagation isn't as efficient as at the surface.

Using this fairly crude trend you can judge what type of lightning may have occurred from the thunder. However there are other reasons why thunder sounds vary in texture. It can also depend on the shape of the lightning channel. A fragmented channel with many branches can produce crackly low-amp thunders whilst a single high-energy channel may produce bangs and crashes. Sonic booms can also occur freely as sound waves from different areas of the storm build on top of each other as they overlap causing increased amplitude, rather in the same way a super-sonic jet produces a boom as it touches or breaks the speed of sound. Wind-shear and temperature differences at higher levels could also distort a thunder, similarly to how the jet sound from a high-altitude plane is distorted by the time it reaches the ground. 

Cloud-Ground (C-G) "Fork" Thunders
Cloud to Ground (or C-G) lightning, also known as "fork" lightning, is likely to be the closest anyone will get to a lightning channel at ground level, and in turn will usually produce the loudest thunder you will hear during a thunderstorm, (unless you have witnessed an exceptional distant lightning discharge e.g. as seen in T0011). In the low-level atmosphere where the pressure is around 1012mb on average the sound wave travels very well, and can be very stunning and pronounced, usually without a "build-up". To double-up a C-G's thunder-strength, the electrical discharge often occurs as a high precision channel with minimal branches, concentrating the current flow down one channel.
High-Amp C-G Example (T0022 mp3)
High-Amp C-G Example (T0036 mp3) - Very close double-strike
Mid-Amp C-G Example (T0067 mp3)

Cloud-Cloud (C-C) & Intra-Cloud (I-C) "Sheet" Thunders
C-C lightning occurs along the cloud base or between two cells and is the most common type of lightning. It tends to create a softer thunder of a more crackly nature with strong rumbles. I-C is similar to C-C but occurs within the cloud and lights it up like a bulb (the type of lightning often called "sheet"). Some C-Cs and I-Cs may possess upper-level origins and can be unusually high-amp as observed in storms such as T0011 and T0049, especially during "initiation discharges" as I like to call them. These are the first discharges of a thunderstorm's life and have been observed to be fairly very powerful in nature.
Ultra High Amp C-C / I-C Example (T0011 mp3) - Initiation discharge 8 seconds away (1.6 miles)!! Impressive.
High Amp C-C Example (T0049 mp3)
Low Amp C-C Example (T0019 mp3) - Very close, 1 second away
Very Low-Amp C-C + High-Amp I-C Example (T0020 mp3)

Positive Flash (P-F) "Anvil Lightning" Thunders
This is the king of all tropospheric lightning and will produce the biggest thunder sound possible. However it is quite rare to see at just <5% of all lightning, but some storms produce more than others given the right conditions. These are on average 5 times the length of a normal C-G and extending up to the upper-level regions of the cloud from the ground. During PS0001 a positive flash struck around 20 miles away, (it took an entire minute and a half for the thunder to reach me), but the thunder still had a bassy-kick to it and sounded like a distant fireworks crescendo.
Possible P-F Example (T0021 mp3) - This singular storm was several miles to the north yet this discharge occurred 2.5 seconds to the east out of view (0.5 miles away). Due to the nature, position and duration of the thunder and the immense flash off the roof-tops, it was most likely a 6 mile-long P-F extending southwards out of the top of the cumulonimbus.

Anvil Crawlers (A-C) & Cloud-Air (C-A) Thunders
These tend to occur within and around the upper-level anvil (or towers) of a well-developed strong thunderstorm cell. A-Cs are huge, but possess thousands of small branches that distribute the energy spatially as they "crawl" across the sky. Combined with the nature of how far up in the atmosphere they occur, along with C-As, you tend to hear a soft rumble or distant crackles as the thunder from these discharges, sometimes no thunder at all is observed.
Low Amp C-C + A-C Example (T0024 mp3) - Mid-level C-C mixed with Anvil Crawlers


MY CLOUD DAMPING THEORY                   
Sound is modulated easily by barriers and mediums (like how sound-proofing works in studio rooms). Have you ever noticed during a thunderstorm that most thunders, typically close C-Gs and C-Cs, tend to be loud and sharp for about 3-4 seconds and then quickly become muffled/quiet and distant in nature? I have seen evidence of C-Gs falling outside rain curtains appearing to produce sharper thunders than those falling within. Positive anvil strikes are louder in treble for longer than negative strikes from the base.

Whilst the treble (high-frequency) parts of sound waves have been shown in experiments to be modulated, and attenuated by increased humidity, consider also that the damping of these sounds in studios, or in ear mufflers, is achieved by adding insulation such as foam, cork or wool. My theory is cloud-droplets and rain curtains should act as insulation to sound in a similar way to sound-proofing foam. Therefore the treble should usually be heard from the exposed part of the bolt only, and not from parts within the cloud or within/behind a dense rain curtain. Usually only the low-frequencies can penetrate, such as bass booms and low-rumbles.