# Without seeing the lightning, can you tell how far away it struck by how the thunder sounds?

Is there any way to tell how far away a lightning strike is by how its thunder sounds? I thought one way might be by using the fact that higher frequencies travel faster than lower frequencies. Would you have to correct for the fact that thunder may not take a straight path? (If so, this would affect the distance calculation based on the time between lightning and thunder as well.)

• @jinawee: the last sentence of the question shows the questioner knows how to estimate distance from the time delay. The question is about estimating the distance from sound alone, and I think that's an interesting problem. – John Rennie Mar 19 '14 at 20:05
• Sometimes. Thunder that seems to roll on and on and on, is coming from a long way away, and rolls on like this because the sound is reaching you through more than one path. – RBarryYoung Mar 19 '14 at 22:57
• So, wouldn't the thunderclap's decay be (inversely) proportional to the distance? I thought temperature has an affect on how sound travels too. – Lee Kowalkowski Mar 20 '14 at 17:03
• @RBarryYoung I have experienced thunder that rolled on and on continuously for 10-15 minutes as a storm passed overhead, simply because there was so much constant activity of lightning. Looking at the sky directly overhead reminded me of a flickering fluorescent light. – Michael Mar 20 '14 at 18:50
• You can't get a number, but you can get an approximation. If there's an incredibly loud KA-BOOM! and the building shakes - that was way too close. If the thunder is a low-pitched rumble - that was several miles away. More boom, less rumble - closer. More rumble, less boom - farther away. My rough estimation is that if the lightning is more than two or three miles away (10 - 15 second gap between lightning and thunder) you won't hear it much, although farm animals and pets may get nervous. – Bob Jarvis - Reinstate Monica Mar 22 '14 at 11:54

This is an interesting question. Unfortunately, the answer is probably no for two reasons. There is a nice way of telling how far away a lightning strike was by counting the seconds before the thunder reaches you though. First let me tell you why your method probably won't work, then I'll tell you how to calculate the distance based on the time of arrival (a method which you might already know).

## Why your method won't work without sensitive equipment.

• The phenomenon you are trying to use to calculate the distance to the source is called dispersion. This is the general term used when waves of different frequencies propagate at different speeds in a medium. Unfortunately, the dispersion of air, particularly at the low frequencies associated with thunder, is very low. The sound speed in air is a relatively constant $$343\tfrac{m}{s}=0.21\tfrac{mi}{s}$$.
• Even if the dispersion were relatively high, you would need to know something about the way the thunder sounded when it started. This isn't a strong limitation as you would probably be able to pick up on it by listening for closer and farther thunder claps.

## What relatively simple method will work?

A trick I learned as a child (perhaps you did too) is to count down the seconds between the lightning flash and the thunder clap. From this you can calculate roughly how far away the lightning was. Since the speed of light is so fast as to be considered instantaneous in this situation, the time it took the sound to get to you tells you how far away the lightning struck. If the time for the sound to reach you is $$\Delta t$$, then the lightning was a distance $$d=\Delta t*v$$ away, where $$v=0.21\tfrac{mi}{s}$$ is the speed of sound in air. As an example, if you count $$5\ \text{seconds}$$ for the sound to reach you, then the lightning would be roughly $$1\ \text{mile}$$ away. You can remember to simply divide by $$5$$ as a rule of thumb. This calculation gives the distance to the source of the thunder which may be a couple of miles above the ground.

• Maybe one could record a lot of thunder sounds and calculate the distance via the lightning. Then create spectra and do some regression between frequency distribution and distance. Sounds like a nice research project. – Martin Ueding Mar 19 '14 at 20:18
• If you happen to live outside the US, divide the second count by 3 and you get it in kilometers. – Martin Ueding Mar 19 '14 at 20:18
• @Chris: you might want to mention that your computation gives the distance to the source of the thunder, not its projection on the ground. As the thunder might easily occur at 1 or two miles altitude, it is a factor to take into account for low counts. – Martin Argerami Mar 19 '14 at 21:55
• @queueoverflow The km trick also works inside the US :D – Kyle Strand Mar 19 '14 at 23:44
• And if you hear the lightning and see it at the same time (i.e. delta = 0 seconds), I reckon you've got problems... – McGafter Mar 21 '14 at 9:16

I think yes, you can get some distance information from analyzing the thunder sound. I am basing this mostly on having personally heard many thunderclaps, both far and near, of reasonably known distance to the lightning.

Anyone that has ever experienced a near (100 m or less) thunderclap can tell you it sounds a lot more "sharp" than a distant one, not to mention louder of course. Let's ignore volume, because lots of things can interfere with received volume. It will give you some broad measure of distance, but won't be all that accurate.

I think the key is the strength of the high frequencies relative to the low ones. Air will attenuate the high frequencies relatively more, so more distant thunder will have less high frquency content. This also makes intuitive sense in that near thunder sounds sharp and sudden whereas distant thunder is a low rumbling sound.

So, do some spectral analisys on thunder of various known distances, and I expect you can find frequency ranges such that the amplitude ratios of these ranges make a reasonably predictable monotonic function of distance.

I think that looking at just duration will not work. This is because lightning is actually made up of (or can be approximated as) many short segments of the "zap" end to end. Each segment produces its own thunder, which is why thunder often appears to "crackle". When you are really close, the sound from the bottom of the lightning is so overwhelming that you tend to not notice the following crackle of the segments higher up (and therefore further away from you). Also, you don't get as much sound when you are end-on to a segment. Loosely think of a dipole radition pattern.

I'd be interested to hear what you find if you persue this. Please keep us posted.

• I'd be a little hesitant to assume that all thunderclaps sound the same to start with. There are certainly many very different types of lightening; intracloud, cloud to cloud, cloud to ground. Perhaps each different class has a distinct sound though. – Chris Mueller Mar 19 '14 at 21:51
• @Chris: I agree there is likely some variation in frequency content. This is why you need a bunch of test cases to find the few key frequency ranges that are best for predicting distance. However, all thunder is ultimately caused by the same thing, which is air whacking itself as it rushes back into the near vacuum caused by the short-lived super-heated plasma cooling and very quickly dropping in pressure. Pressure, temperature, and moisture content all probably have some bearing. Still, I bet you can make reasonable distance predictions, for reasonable values of "reasonable"... – Olin Lathrop Mar 19 '14 at 21:55
• In addition to the air attenuating the high frequencies, there may be another effect -- the angle. As the lightning gets farther away, the angle to the normal to the earth increases. Low frequencies may bounce off the earth or propogate through things like trees and buildings, but high frequencies will die as soon as they hit something. – Patrick Mar 20 '14 at 18:29

I presume you did not see the flash, so cannot use that as a timing mark. From Wikipedia "The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about 0.1 m/s as the frequency rises from 10 Hz to 100 Hz. For audible frequencies above 100 Hz it is relatively constant. " You might try to use the fact that high frequencies are attenuated more than low frequencies, but that seems very dependent on the terrain.

If you just want a "rough" idea of how far away the lightning struck, then the answer is yes. You can use the loudness of the thunder as an indicator of the relative distance (a loud strike will be closer than a faint strike). More accuracy could be be gained with a loudness measuring device calibrated with known average strength of strikes and how far they struck.

There is no way unless you see the Lightning. You need a frame of reference.

Even radar detectors have a frame of reference.

You need a visual approach. Or einstein to work out some new formula

In anycase, Without seeing the lightning how do you know the sound came from one.

It could be a Scud missile up above breaking the sound barrier.

When lightning strikes close by it does indeed sound with a loud crack like a gunshot rather than the customary rumbling sound we hear when it is further away.

• Welcome to phys.SE! The 'frame of reference' in this case would be knowing what the nature of the sound when it was emitted. As I've said elsewhere on this question, it isn't clear how well that can be known. – Chris Mueller Mar 20 '14 at 21:15
• My guess is that your answer isn't accurate. For example, if all lightening created sound with the same peak intensity then you could measure distance by measuring how much it has been attenuated. There are probably tricks involving the echo of lightening bolts too so that you could triangulate its location. – Brandon Enright Mar 21 '14 at 5:54
• I don't think so, with your method you are not taking into account the factors that prohibit your technique from being an exact science, including: wind speed and direction, terrain, temperature, and ambient noise. Humidity has a small but measurable effect on sound speed (causing it to increase by about 0.1%-0.6% – Tasos Mar 22 '14 at 9:50