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### Estimating the Distance to Lightning

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Date: 08/16/99 at 23:43:15
From: nick
Subject: Calculating the distance of lightning from the thunder

Hello Dr. Math:

I have been having discussions with friends about how far away
lightning is, based on when we hear the thunder. I've explained that
since sound travels about 1122 feet per second through air, and there
are 5280 feet per mile, for every 4.7 seconds between the lightning
and the thunder the lightning is one mile away. Can you explain it any
better?

Thanks.
```

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Date: 08/17/99 at 13:11:46
From: Doctor Peterson
Subject: Re: Calculating the distance of lightning from the thunder

Hi, Nick.

You've got it right. Let's see if I can give a fuller explanation.

When lightning strikes, it produces light and sound. The light travels
fast enough that we can think of it as instantaneous over distances of
a few miles. So when we see the lightning, we are seeing it at the
time it actually struck.

The sound travels at about 1/5 mile per second (to keep the numbers
simple). So for every mile the sound has to travel, it will take about
5 seconds to reach us. If we divide the time between the light (the
time of the flash) and the sound (the time when we hear the thunder)
by 5, we get the distance in miles. Or you can say we're multiplying
the number of seconds by 1/5 to get the number of miles the sound
traveled in that time:

mile
distance = 1/5 ---- * time
sec

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Division

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