A rule for lightning that’s like the inverse square

[thenewmans]

A point source of energy often follows the inverse square rule. So if I move my projector back twice as far, the image is 1/4 as bright. If I move half the distance closer to the TV, I can hear it 4 times louder. I’m guessing this rule doesn’t work so well for thunder and lightning since it’s more like a line source than a point source. So if lightning strikes a mile from Alice and 2 miles from Bob, is it half as loud and half as bright for Bob?

 

[Born2bwire]

An infinite line source will fall off as 1/s in power because it is only spreading out in two dimensions, not three, due to its invariance in the third dimension. However, lightning is not an infinite line source, so it will still follow the inverse square law rule in the far field. The inverse square law is not applicable to only point sources. If I have a large antenna array, I will still experience the same space loss factor as I would for a Herztian antenna in the far field. The largest difference is where that far fiel starts since it is dependent not only on the wavelength but the characteristic size of the radiator.

 

[dE_logics]

I think we'll need mathematical analysis to figure this out.

 

[flatmaster]

You could treat this line source as an infinite number as point sources each acting as an inverse square. It would be a integral over all of the individual point sources.

 

[thenewmans]

Here's the reason I thought it might just be the inverse of the distance. You can relate inverse square with the area of a sphere, 4pi*r^2. The volume (loudness) at 1 mile from an explosion is spread out over a greater surface at 2 miles. If you compare the surface areas, the 4pi parts cancel out and you're left with the r^2 part. So sound energy gets spread out over an area 4 times larger. So it's 1/4 as loud. That's inverse square.

For a line source, I'm thinking of a cylinder with the surface area of 2pi*r*h. If you use that to compare 1 and 2 miles from lighting, the 2pi*h parts cancel out and you're left with r. So it's half as loud and half as bright at 2 miles.

Another way I thought about this is if Alice and Bob both got photos of the middle section of the lighting. The bright part in Bob's shot would be half as wide as it is in Alice's. Yet they'd both go from top to bottom in the shot sh they'd have the same height. So Bob's bright part would cover half as much of the photo. Does that make sense?

 

[flatmaster]

Well, if you're far enough away, it does turn into a point source. To us, the sun is a point source in some cases.