That Day will come as a trap on all the world

[pocaracas]

Whenever it comes, the rapture will be a bang heard around the world.

Certainty gone, eh? That's economics for you. Prophet and loss.

Can anyone whose maths is not shit work out how long a bang would take to propagate around the world, and how loud it would have to be at source? I'm guessing quite a while, and a bit on the noisy side.

Sound travels at about 342 m/s.
Earth's diameter is about 12,742,000 m... this results in a circumference of (2.pi.r = ) about 40,030,173 m.
So, a bang would take some 40,030,173 m / 342 m/s = 117,047 seconds
Each hour has 3600 seconds, so that's about 32 hours.
If it travels in both directions (East and West), then we should halve this value. It takes 16 hours to reach the other side of the planet.

How loud must it be?...
Let's say, for simplicity's sake, that sound's power falls with the square of the distance traveled. P(r ) = P_0/r^2, like all homogeneous propagation.
The perceived sound intensity, measured in dB, is then given by D(r ) = 10 Log(P(r )/P_min), where P_min is the minimum power a sound wave must have for a human to hear it.
Half a world away, r = 20,015,086.5m.
I_0 is assumed to be 10^-12 w/m^2.
Also, the minimum sound a human can hear is graded at 0dB, so we expect 0dB at the other side of the globe.
So... let's put it all together, shall we?

P(r=20M) = P(r=0)/20M^2
10^-12 * 20M^2 = P(r=0)
P(r=0) = 10^-12 * 4 * 10^20 = 4*10^8 W/m^2

D(r=0) = 10 Log(P(r=0)/10^-12)
D(r=0) = 10 Log(4*10^8/10^-12)
D(r=0) = 10 Log(4*10^20) = 206dB

Doesn't look like much, does it? But has anyone ever been there for a 200dB blast?

What if I told you you feel pain at 130dB?
And what if I told you that immediate hearing damage occurs at 140dB?

How much must sound travel before it falls to 140dB?

D(r ) = 140dB = 10 Log (P(r )/10^-12)
e ^(14) = P(r )/10^-12
P(r ) = e^14 * 10^-12 = 1.2*10^-6 W/m^2

Which 'r' is required to get there?
P(r ) = P(r=0)/r^2
1.2*10^-6 = 4*10^8/r^2
r^2 = 4*10^8/(1.2*10^-6)
r = sqrt(4*10^8/(1.2*10^-6))
r = 18,257,418 m

All humans on 90% of the planet will go deaf.

That's what I call a Big Bang!