Estimating the Distance to Lightning

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.

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/