From the Book
Drake clutched his face, trying to ignore his growing headache. A bullet clanged off a nearby metal pole and restarted the ringing in his ears. A moment later he heard the much fainter crack of the shot.
He dropped his hands sharply. “That’s it,” he said. “Smith – how many rounds you got left?”
Smith checked. “Two.”
Drake nodded once. “Right. When I say, stick your head up and fire one round.”
Drake and his sergeant are pinned down inside a burning warehouse at the port. The bad guys have just driven off, but they’ve left two nasty surprises – a sniper in a crane, and a torrent of fuel gushing from a fuel tank into the warehouse.
To escape, Drake needs to fight back against the sniper, but he has no idea how far away the sniper is.
Determining the distance of the sniper
Drake notices the sounds around him – the clang as bullets hit the shipping container he’s sheltering behind, and the crack of the shot in the distance. He realizes he can use the sounds to work out the range.
Light travels so fast that it can be considered infinitely fast for many practical purposes. So when Drake sees the muzzle flash from the sniper, he knows that’s the exact moment when the sniper has fired.
When Drake hears the crack of the shot a moment later, he knows that’s the sound from the muzzle flash he just saw. He can time the difference and work out the range.
Drake times the interval a couple of times to get two readings, which he averages. To calculate the average of the readings, he needs to add the readings up and then divide by the total number of readings.
The reason Drake measures a few times is to make sure that the distance that he gets is accurate.
average shot time = (sum of shot durations) / number of readings
average shot time = (1.24 + 1.17) / 2
average shot time = (2.41) / 2
average shot time = 1.205 seconds
Drake knows that sound travels at about 340 metres per second, so he can multiply that speed by the time delay to get the range:
range = time * speed
range = 1.205 s * 340 m/s
range = 409.7 m
The sniper is about 410 metres away from Drake.
Real Life Example – Lightning
You may have already done this as a kid, but you can measure how far away a lightning bolt is, just by counting the number of seconds between when you see it and when you hear it.
When you see the lightning bolt, start counting. Then multiply that number by 340 and that’s the approximate distance that the lightning bolt was from you.
Let’s pretend that your little sister or brother is freaking out because there is a storm. You see a lightning bolt and count the number of seconds before you hear it. You count… 9 seconds.
range = time * speed
range = 9* 340 m/s
range = 3060 m
You can reassure your little brother or sister that it’s cool, there’s still 3 km before the lightning will be on top of you.
(NOTE: Storms can be spread over large areas and just because that lightning bolt wasn’t too near doesn’t mean none will be. Even math can’t save you once the lightning storm is closer to you and being shocked by lightning is not on the to-do list).