Please read the disclaimer - An Animator's Theory on Sound

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A Theory on Timing Action before Sound in Animation from an Amateur Animator
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When one searches for general advice on syncing sound to an action in animation, it usually goes like:
"Put the action two or three frames before the actual sound."

If looking for explanations, one would get something like this:
http://www.keithlango.com/tutorials/old/lipSync.htm wrote, "Humans see things faster than they hear them, so we pick up our cues from the shape before the sound."

I would like to add on to these explanations with some theory of my own. Sorry if what I state is obvious, but I can't seem to find any explanation other than something like the one above when looking on the web for sound syncing in animation. Remember that this is just an untested, unverified theory.

You can skip the Theory and read the Summary.
The Conclusion is most important though.
Please read the Disclaimer.

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Disclaimer
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I'm not a professional or expert so be cautious about everything below, I don't want to mislead anyone.
Especially for the fact that I do not have any formal art education whatsoever, I am an amateur.
Have no kinds of expectations for me or who I am because I don't want to betray them.
I think the amount I write is proportional to my ego at the time and I try to sound more "intelligent" than I really am.
I should get a free pass here though since this is my pastebin hmph.

Everything below is ignorable, biggest advice is "whatever personally works," and as Vilppu says, "No rules, only tools."
Different thought processes, tools, and opinions work for different people.

All/most of "one" or "you" below is directed at myself and can be wrong.
All/most of everything below is directed at myself to remember and can be wrong.
Hopefully it will be helpful to some to read what an amateur animator thinks.
Whether I follow the things I say and whether these things are true is something I have to work on, test, and refine.
But it can be wrong.

This is a pastebin that I can't edit so it may forever hold harmful bad information and can be wrong.

I sadly have much more theory than skill.
Thank you for your time if you read everything.

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Theory
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Light (~3.00x10^9 m/s) travels much quicker than sound (~340 m/s) so the light from an object that forms an image pretty much reaches our eyes in an instant compared to the time it takes sound to reach our ears. Hence why we see faster than we hear. That aside, let's take advantage of the knowledge about the speed of sound to estimate the timing of a sound for an object such as a lightning strike half a kilometer away.

Assuming that we are using the distance relative to the camera with a frame rate of 24 FPS, we divide our frame rate (24 FPS) by the speed of sound (~ 340 m/s) and get 6/85, or about 7.059x10^-2, which will stand for frames per meter. By taking the reciprocal, we get 85/6 or about 14.167, which stands for meters per frame.

    (6/85 or 7.059x10^-2) = (frames per meter)
    (85/6 or 14.167) = (meters per frame)


With this, we can conclude that about every 14.167 meters away from the camera the location of the object that creates a sound, we have to delay the timing by at least that many frames. When the object is close to the camera I believe there is a high amount of error when using this method, but the significance of the error should decrease as the distance grows. As for the reason why this error exists, I posit that the brain creates some "virtual distance" between our own eyes and the monitor/screen with which we use to view the animation. Example being how "smaller" things are interpreted as further away. Maybe there's also a delay when the brain processes the sound.

    So how many frames do we delay a lightning strike half a kilometer away from the camera?

    (frames per meter) x (distance from camera) = (frame delay)
    (6/85) x (500) = (~35 frames)


This can also be used for figuring out how far an object was when it produced the sound relative to the camera for timing between cuts. Example being one cut at the source of an explosion, which then transitions to a cut of two people talking to each other one kilometer away.

    When will the two people from the second cut hear the explosion from the first cut?

    (frames per meter) x (distance from camera) = (frame delay)
    (6/85) x (1000) = (~70 frames)


Note that the calculations above were done with approximate speed of sound in air at room temperature. If you want to get really technical, then you'll calculate the speed of sound while counting factors like temperature or the medium in which the sound travels in. You can time sound underwater if you want then.

    (speed of sound) / (camera frames per second) = metric unit per frame
    (camera frames per second) / (speed of sound) = frames per metric unit

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Summary
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When sound travels through air at room temperature you can figure out the frame delay with simple maths to time sound when objects are sufficiently far away.
When sound travels through water at room temperature you can figure out the frame delay with simple maths to time sound when objects are sufficiently far away.
If you are nit-picky, room temperature is 20 C.


    (frames per meter) x (distance from camera) = (frame delay)


Easy Sound Timing in Air
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(remember that objects should be sufficiently far away)

    14.167 meters = 1 frame
    28.333 meters = 2 frames
    44.5 meters = 3 frames
    85 meters = 6 frames
    170 meters = 12 frames
    340 meters = 24 frames
    510 meters = 36 frames
    680 meters = 48 frames
    850 meters = 60 frames
    1020 meters = 72 frames


Easy Sound Timing Underwater for Underwater Animals and Humans with Hearing Superpowers
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(not sure about error of close objects for underwater, but I assume it's the same)

    61.833 meters = 1 frame
    123.667 meters = 2 frames
    185.5 meters = 3 frames
    371 meters = 6 frames
    556.5 meters = 9 frames
    742 meters = 12 frames
    927.5 meters = 15 frames
    1113 meters = 18 frames
    1484 meters = 24 frames
    2226 meters = 36 frames

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   END and Conclusion
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This method is not an all-in-one solution to timing sound problems. More important things to consider is that if it looks right, sounds right, and conveys the scene properly rather than trying to emulate life exactly. Seems that the best usages is definitely for distant sounds that are far away and sound loud.

Values in the Easy Sound Timing in Air chart should be valid and to get other values is just adding them together. You can forget the chart and just memorize that 24 frames or 1 second means the sound was created 340 meters further away.

If choosing to apply this theory remember that this method is untested and unverified (at least by me). If you read this pastebin and by chance have posted in the original thread, I give thanks for your help and information.

Please read the disclaimer.

source: http://en.wikipedia.org/wiki/Speed_of_sound