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# How to Find the Distance to Thunderstorms and Fireworks

Learn some fun facts about fireworks and thunderstorms, and find out how you can use math to quickly and easily estimate how far away they are from you.

By
Jason Marshall, PhD,
July 3, 2015
Episode #111

Page 3 of 3

## How to Estimate Distance Using Sound

It’s now time to use the difference between the speeds of light and sound to our advantage. In particular, let’s use the fact that we see fireworks and lightning before we hear them to estimate the distance to the fireworks show or thunderstorm. Since light travels really fast, we can assume that we see fireworks and lightning as soon as they happen (while that’s not precisely true, it’s a really good approximation). With this assumption, all we have to do to estimate the distance to fireworks and thunderstorms is time the number of seconds between the flash and the bang. You can use a stopwatch if you’d like, but counting “one thousand one, one thousand two, …” should be accurate enough to get a decent estimate.

Since we know that sound travels about 770 miles per hour, we also know that it travels about 770 / 60 = 12.8 miles per minute, and thus about 12.8 / 60 = 0.2 miles per second. Which means that for every 5 second delay between a flash and a bang, the distance to the fireworks or thunderstorm must be about 5 x 0.2 = 1 mile. So if you counted 10 seconds, the distance must be about 10 x 0.2 = 2 miles. If you counted 15 seconds, the distance must be about 15 x 0.2 = 3 miles. Just remember that you can multiply the number of seconds delay by 0.2 to get the distance in miles.

## Use Math to Keep Safe!

If you live in a city where there are lots of big fireworks displays, you can use this technique to figure out how far away they all are from you. More importantly, if you live somewhere with lots of thunderstorms, you can use this technique to keep safe. The rule of thumb is that you should seek shelter whenever a thunderstorm is within 3 miles of you. Which, using our distance estimating technique, means that you should seek shelter whenever you hear a thunderclap within 3 x 5 = 15 seconds of seeing a lightning bolt flash. Thunderstorms move fast and can be unpredictable, so this technique won’t always be perfectly accurate—but it should at least give you a fair warning. So this 4th of July and summer thunderstorm season, remember to use math to keep safe!

## Wrap Up

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Fireworks image, bayasaa at Flickr, CC BY 2.0