I ran across this video of the destruction of munitions, 100 tons' worth. Check it out.
You see a cool explosion, but I see a question. How far was the camera (and maybe the people) from the explosion? Oh, this might be in the comments for the video – but I don't want to see that. Instead, let me look at the time in the video that you can first see the explosion and then when you can hear the explosion. If I assume the time it takes the light to get to the camera is insignificant and I know the speed of sound, I can get an estimate for the distance.
If I call the time for the sound to get to the camera ts and the speed of sound vs, then the distance can be written as:
I can get a very good estimate for the time from the video. A quick note about that. Most video players only show the time in the video down to the one-second change. This won't be good enough. There are two options to get a better estimate for the time. First, you could move one frame at a time and count the frames. From this and the frame rate, you could get the time. The other option is to use something like Tracker Video analysis tool. Even though you aren't tracking the position of an object, you can still use it to get changes in times.
Finding a value for the speed of sound is a little trickier. The speed of sound in air depends mainly on the temperature of the air. Here is an expression showing the relationship between speed and temperature.
But what is the temperature? The guy is wearing a jacket, so I am just going to guess about 10°C. This would put the speed of sound at 338 m/s. Now, what about the time? Here is the frame that I think you can first hear the explosion.
This is about 0.835 seconds after you can see the first explosion. I could probably be off by a frame for this time (about 0.033 seconds per frame). With these value for the speed of sound and the time, I get a distance of 282 meters (about 925 feet). That seems pretty close. But maybe that is just the location of the camera and the people were much further away. What do I know about explosives though? Clearly, not much.
But wait, what about another approach? I noticed one piece of debris seems to be moving straight up after the explosion. What if I track that? Here is the vertical motion of the piece of explosives:
This looks rather parabolic (but not perfectly). It is good enough to get a reasonable fit. From this, I can see the vertical acceleration is -33.4 units/s2. Here, the "units" are some arbitrary distance units. If I assume this explosion is on Earth and effects of air resistances are too big of a problem, I can find out the distance in meters by setting the acceleration also to be -9.8 m/s2. This would give make 1 video unit = 0.29 meters.
Big deal, right? Wrong. First, I can use this to get the height of the explosive cloud of dust - about 80 meters high. Other than that, I really can't do much with this scale? Or can I? If I knew the angular size of the camera, I could use the height of the cloud and the angular size of the cloud to find the distance. But alas, I don't know the angular field of view of the camera. However, I can make a pretty good guess. Look at this frame.
What if I guess that the guy is 1.8 meters tall and standing 3 meters from the camera? Actually, I guess I should say that the part of the guy in the frame is 1.2 meters. If I pick out a feature of the explosion with the same angular size, I can figure out how far away the explosion is from the camera. Here is two shots showing the two objects.
Since the angular size is the same, I can say:
The "C" is just some constant. It doesn't matter. What matters is that this result looks silly. Clearly, the camera was more than 30 meters away from the explosion. So, what happened? Well, I guessed. I could easily guess values that give a camera distance that agrees with the sound estimation. I am going to go with the sound estimation instead. You should give me partial credit for trying, though.
Oh, I was also going to estimate the speed of the debris using that sound of something whizzing by the camera. However, I am not sure when that object started its motion. It could have been from a secondary explosion or something. It still sounded cool.
