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The speed of sound is 768 miles per hour. Of course, that is the speed of sound through air at about 68 degrees Fahrenheit. If the air temperature is warmer sound moves a little faster. Although it varies with temperature, it does not change with altitude even though the air pressure may be different. Knowing that the speed of sound is constant under these conditions and the fact that light travels so fast as to be nearly instantaneous for all practical purposes, we can tell how far away an event is from us by the difference in time between when we see it and when we hear it.

The classic example is lightning and thunder. Thunder is the sound of the air being superheated by the incredible energy of a lightning bolt. The sound is created simultaneously with the flash of lightning. However, since light travels so much faster than sound we see it well before the sound reaches us. Most people have a little formula they use to tell how far away lightning is. They count seconds between the visible lightning flash and the thunderclap. Some say every second it takes means the lightning was one mile away. Others use different figures.

If we know the true speed of sound, then we can calculate the correct distance. 768 miles per hour is 12.8 miles per minute or 0.213 miles per second. So every second that passes between the lightning flash and the time when we hear the thunder means the lightning was 0.213 miles away. Rounding for convenience, then we can say that the lightning is a little more than one mile away for every five seconds that we count between the flash and the sound.

If you can’t get to one second before hearing the thunder, then the lightning was closer than 1100 feet. Sometimes, though, the sound and the flash seem to happen at the same instant. When this happens, the lightning is very close indeed!

The same calculation can be used for any event that we see happen at a great distance. This same effect is often why the sounds we hear at a concert may seem to be a little out of phase with the performers on the stage (if we have seats that are relatively far away from the stage that is).

Another fun example of this phenomenon happens every Fourth of July. We can actually tell approximately how high up the fireworks are when they explode by using an accurate digital stop watch which measures in increments of a tenth of a second or less. A full second equates to about 1100 feet so every tenth of second is about 110 feet. Remember that with fireworks, you are getting not just the height above the ground, but the distance between your ears and the firework explosion. If it isn’t exactly overhead then you are including some sideways distance as well.

It can also be fun to try to figure out how far away a distant canyon wall is by the time it takes an echo to return to us. Remember when using echoes the sound is going there and back again so we need to divide the time by two to get the right result. A little applied science can be fun and give us a reason to keep our math skills sharp.