Calculating the distance between a nuclear bomb and an object hit by the shockwave, all the while taking the video frame rate into account? Imagine you are watching a YouTube video where a nuclear bomb goes off. Exactly six seconds later, the shockwave arrives and hits an object that is some distance away. How would you go about calculating the distance between the bomb and the object? Now, naturally, you would be tempted to take the six seconds and multiply that by the speed of the shockwave. I'm curious though; doesn't the video frame rate matter? Why aren't we considering it? If we did, how would we go about taking it into account? It gets even more problematic when the video camera (that was used to take the video) was recording at a different frame rate than YouTube's playback frame rate of 30 or 60 frames per second. That is exactly what happened in this video. Trying to calculate the distance, one commenter posits:

...you can measure the time between the flash and the shockwave to get a rough estimate. The shockwave travels about about 1km in 3 seconds or 1 mile in 5 seconds, so e.g. the tent was about 2 km away, since the gap was 6 seconds. This assumes the footage is in real time, of course.

However, the video's uploader offers the following rebuttal:

the footage ran at 64 frames per second, about 2.7 times faster than standard 24 frames per second.  Since I can cheat and know the actual information, the distance to ground zero was 2938 ft (0.9 km).

Hmmm. 0.9 km. That's a long way off from the conventional calculation that gave 2 km. I am of the opinion that the two video frame frates (YouTube's playback frame rate and/or the video camera's frame rate) are responsible for the huge discrepancy in distance. How should we account for them? Am I missing something?
 A: You can trivially change the playback frame rate on YouTube. On my device, I click a gear-shaped icon and I can tell the video to play at half or double speed.  Does that halve or double the time between the blast and the shockwave?  It does not.  That was a real thing that happened in the real past, and you can't change it by looking at its record differently.
If you have information that each original frame of film represented 1/64th of a second and that the distance was 0.9km, you can count video frames and learn something about YouTube's compression/interpolation algorithm.  But I can save you some headache by telling you that video uploading processes, like all data-copying processes, run the risk of destroying some information in the copy. It sounds like, in this case, changes in video standards over the past half-century have made the timing information unreliable.  If you had a physics question you might have to look for a more reliable copy, or even for the original film, which probably lives at a library somewhere with lots of useful metadata attached to it.
A: Assume for simplictiy the footage was captured with 60 FPS and Youtube allows 20 FPS. Well two things can happen:

*

*Two thirds of all frames are dropped: 1 second in the video is equal to 1 second in real life.


*No frames are dropped, but instead the 60 frames captured in one second are spread out across 3 seconds of 20 FPS video: 3 seconds in the video is equal to 1 second in real life.
I can not tell you which option the editor chose.
A: The important thing about frame rate in this case is that it limits the precision of measurement.  If a particular frame  shows arrival of the shock wave, and you base your calculation purely on that, then you only really know that the shock wave arrived sometime between that frame and the previous one.
The speed of a shock wave depends on several factors, and unless you know the factors and their values, you can only roughly estimate distance from the bomb to the object, even if you know the exact time of arrival at the object.  At relatively large distances, the speed of a shock wave is simply the speed of sound, which depends on temperature, humidity, and pressure. See here.
