I was out at 3am having been woken up by the wind to see the most fantastic light show (see video) it was continuous lightning, no rain yet but i could tell it was coming! The difference this time was there were no rumbles of thunder at all. It got me thinking why, what might be the cause and does it tell us anything about the storm?

I know, from my time in music college, that sound attenuates (dissipates) over distance and travels at approximately 343 meters per second (varies with environmental factors). With that knowledge one can safely assume that i’m not hearing the rumble of thunder because I am are simply too far from the source. However light travels at 299 792 458 m / s without the same levels of attenuation so we will always see it.
People often count 1, 2, 3, 4 and so on from the flash of lightning until they hear the thunder and assume that it is that many miles or kilometers away. i’ve see people do it many times and they are always half right half wrong. With the knowledge that sound travels at 343m/s (we will round it down to 333m/s for easiness) for every 3 seconds from seeing lightning to hearing it you can safely assume it is 1 kilometer per 3 seconds.
Combine that knowledge of the distance calculation with the direction of the storm winds you can work out if it is coming towards you or away from you. you can also do this by observing the change in time from the flash to the sound. If the counting decreases the storm is coming towards you if it increases it is moving away from you.
The sound itself is also an indicator of direction and distance. A high pitched crack is going to be closer than a distant low pitched rumble. Think Doppler effect; a vehicle far away sounds low, gets higher pitched the closer it comes to you and lower pitched again as it travels away from you.
Ok, i’m not quite finished with the maths… It still leaves the question of how far do I have to be away from the lightning to see it but not hear it?
Skip to end if you can’t be bothered with the maths to find out the answer!
What is Distance Attenuation?
Distance attenuation is defined as the way in which a sound level reduces as a listener moves away from a sound source.

As sound travels from the source, the area over which the sound is spread increases like ripples on a pond. This means that the same amount of acoustic energy is dispersed over a greater area, and as a result the sound level at any position on this surface reduces as the distance from the source is increased.
Stay with me…
If the source is suspended in the air, as in our case, for simplicity, it has spherical distribution. (I know it is actually slightly more cylindrical in nature as the sound emanates from the length of the lightning bolt)
The area of a sphere it is A = 4πr2

The area quadruples with every doubling of distance and increases by a factor of 100 if the distance is increased by a factor of 10.
Acoustically, the sound level under these conditions reduces at a rate of 6dB (the measurement of sound pressure) for every doubling of distance from a source. However, after the original distance has been doubled, this increased distance then has to be doubled again (i.e. the original distance from the source has to be quadrupled in order to achieve a further 6dB reduction and then increased to 8 times the original distance for a further 6dB reduction). This also gives a 20dB reduction if the original separation distance is increased by a factor of 10.
If that is a head spin, just know that the sound pressure (dB) reduces by 6dB every time you double the distance, compounded.
Answer:
It’s not completely straightforward because there are many variable factors, are you at sea or in a forest? this will impact the calculation so we will base it on having no variables you are standing on flat surface with nothing between you and the lightning.
A lightning strike measures roughly 120dB close to the source and at 100m it measures 100dB. That means you are up to 25km away from the source of lightning.
In reality thunder is seldom heard beyond 16 km under ideal conditions.
So there you have it… If you can see it but can’t hear it, but can see it, it is at least 16km away!