Scientific Misunderstandings #1: How Far Away was that Lightning Strike?

Picture this:

[There's heavy rain outside, with periodic flashes of lightning followed in a few seconds by the low rumble of distant thunder. One particular flash occurs five seconds later there's another rumble of thunder]
Person #1: It's getting closer. That was five miles away.
Person #2: I know it's getting closer, but why do you think it was five miles away?
Person #1: [Smiles at Person #2 like they are passing on some important knowledge] The thunder came five seconds after the lightning.

I've read a few things similar, and even been present a couple of times when it was actually said. The thing is, it's wrong.

As with anything like this, the truth is much more complicated than it appears. You can guess at how far away the lightning was by how long it took the thunder to reach your ears, but Person #1 in this story doesn't know what they're talking about. Either they don't know the distance of a mile, the speed of sound, or either.

In the case of a mile I've already covered that, so I'll make it simple. It's 5,280 feet. I won't hold that against them, since most people don't know it anyway.

The speed of sound is more complicated. It's used as a measurement of speed, called Mach, but in reality that speed actually varies. If you just want to know the answer don't expand the post, but this is where it gets interesting.

Sound is vibration. Something starts the molecules vibrating in a localized area, and those vibrations spread out from that localized area. If there's someone around, those vibrations reach our ears and our brains translate the vibrations into something we can comprehend. (Scientific philosophical note: when a tree falls and no one is around to hear it, it does make a sound. There's just no brains around to translate the vibrations.)

To produce vibrations into the air something has to interact with the air molecules. In some cases, the object itself vibrates. Like a guitar string, or even your layrnx. However, in the case of lightning and explosions it's the rapid change in localized pressure that create the vibrations.

For details you can go here, but essentially the air around a bolt of lightning is really hot. So hot that we use the term super-heated. The approximate temperature is around fifty-four thousand degrees fahrenheit. Yes, you read that right. That fifty-four has three zeros that follow it. To give you a comparison, that's about six times hotter than the surface of the sun.

When you heat air up it expands. In this case, it expands really fast. That expansion of super-heated air transfers to the surrounding cooler air producing a shockwave that creates the vibrations your ears translate into sound.

Calculating the speed of sound is complicated... really complicated. Fortunately, all we're concerned with is the speed of sound through air, so it's much simpler. The equation basically breaks down to:

v = 331m/s + 0.6m/s/C * T
v = speed of sound
T = temperature in celsius
(Don't like metric? This website will show you USsom units.

So the only variable you have to know is temperature, but why does temperature affect the speed of sound?

The answer is that sound and temperature are related. Vibrations and heat are both forms of kinetic energy. Since the higher temperature means the molecules contain more heat they are able to vibrate faster, so they can transfer the sound vibrations more efficiently. As an example, from 0 degrees F to 70 degrees F the speed of sound increases by about 78 feet per second (53 mph). That may be nearly highway speeds, but when you take into account that the actual speed of sound at 70 degrees F is 1,129.5 feet per second (771 mph), that's slightly less than a 6% change. Not negligable, but not drastic either.

All right, if you're an aerodynamicist having an accurate speed of sound, which they refer to as Mach, can be very important. However, we're only trying to figure out how far away that lightning actually was.

So, we'll divide the speed of sound (1,129.5 fps @ 70 deg. F) by the number of feet in a mile (5,280), and we get a result of about 4.7. That's how many seconds it takes sound to travel a mile under these circumstances. You can round it to five which makes it easier to calculate, because then each second is two tenths (0.2) of a mile.

So, using our opening example, Person #1 thought the lightning was 5 miles away, but now you'll know it's less than a mile away. Not only are you now better educated than they are, but you also know to get somewhere safe. There's a storm almost on top of you, for crying out loud!