Thunder and lightning - part II

Glance back to yesterday's post to get the scenario.

So Mr Smokie had counted 7 seconds from seeing the lightning to hearing the thunder, and said it was 7 miles away.

Something told me this was wrong, a gut feeling if you like, and then I remembered somewhere I know well. It has an echo! The only place the echo could come from is a row of terraced houses a couple of hundred yards away (there is nothing else, just open fields), but the echo is loud and distinct. Clap hands and about a second later it's repeated back to you. Remembering that the sound has to travel maybe two hundred yards, bounce, and return back; then a crude estimate of the speed of sound might be 400 yards in a second. This slowly percolated into my brain.

But then, due to alcohol induced delirium joining in with the general early-evening banter around the bar, it took ages for these thoughts and numbers to congeal...

1760 yards to the mile (call it 1800), divide by 400 yards per second gives about 4½ seconds per mile. Mr Smokie was way wrong - 400 yards per second times 7 seconds is 2800 yards. Just over a mile and a half. That was eventually my guesstimate. Of course by this time Mr Smokie had buggered off and my taxi was due. So I went home and then just had to look it up.

The speed of sound in air? Can vary from about 330 to 340 meters per second and, as RBH pointed out, it depends on pressure, temperature and (I'd never have thought this) humidity; which I guess changes the overall density of the air by adding water vapour.

For simplicity lets say air pressure is normal, it's a bit above 0°C and not damp. The speed of sound works out to be 333.33 meters per second. You may guess where I'm going, that's 3 seconds per 1000 meters. Or 3 seconds per kilometer.

Mr Smokie counted 7 seconds, multiply by 333.33 meters per second gives you 2333.33 meters or 2.3 kilometers, give or take a few yards.

That's 1.45 miles.

Wahhh! Across the valley that's about where I liv.. Oh, other direction.
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And RBH was right:
5s x 333m/s = 1666m = 1.035mi