How may one calculate the loudness of an imploding vacuum?

[terrifel]

Is it even possible? I am assuming that it would be a fairly straightforward physics problem for someone who is friendly with equations, but maybe not.

[Ashman165]

Is it even possible? I am assuming that it would be a fairly straightforward physics problem for someone who is friendly with equations, but maybe not.

Well, I suppose that depends on whether you're on the outside or the inside of the vacuum. At any rate, it would seem to me that the crux lay in solving for the, wait for it, volume.

[Jaglavak]

I'm going to wuss out and just describe the general calculations.

Say you have an old fashioned light bulb. For tracking purposes, grid off the air around it into little airicules using spherical coordinates (radius, latitude angle, longitude angle).

Shatter the bulb and freeze frame. Suddenly you have a ball of more-or-less vacuum surrounded by atmospheric pressure. Slo-mo forward. The air accelerates inward, which is resisted by it's own inertia.

Starting from time zero when nothing is moving, allow one clock tick. Then sweep through and calculate the new position and velocity of each little airicule using Newton's laws of motion. P = Force/Area, Force = mass x acceleration. Calculate the new temperature and pressure for each airicule using thermodynamics equations (ideal gas law, combined gas law, etc). For calculation purposes assume the airicules can deform but stay in one peice. Step through time, sweep through space, repeat a whole lot.

Now consider the instant the leading airicules meet at the center. At this point you will know the temperature, pressure, and velocity of all the air in the region. It will look like a 3D version of a rock dropping into water. The air will smack into itself and compress until all of the kinetic energy from motion is converted to potential energy. Then it will rebound and ring. Peak pressure depends on how big of a bulb you break.

The loudness you hear will depend on where you are standing. Sound pressure level decreases by a factor of 1/(Radius Squared) as the sound wave sweeps outward.

Short answer: frikkin loud.

[Jaglavak]

BTW, if you want really loud it should be done under water. Water is about 800 times denser than air and 20,000 times less compressible. A precisely spherical bubble collapsing in water can momentarily generate enough heat to produce a flash of light. Perhaps even enough to initiate nuclear fusion.

Bubble Fusion

However small bubbles don't generate a lot of power, so the sound pressure diminishes rapidly with distance. I expect the collapse of a big bubble would be instantly fatal anywhere nearby.

I'm such a poster child.

[Cluricaun]

I'm such a poster child.

For being fricking awesome maybe. That was a cool thing to learn on a Wednesday afternoon.

[Jaglavak]

Fang Q!

[terrifel]

BTW, if you want really loud it should be done under water. Water is about 800 times denser than air and 20,000 times less compressible. A precisely spherical bubble collapsing in water can momentarily generate enough heat to produce a flash of light. Perhaps even enough to initiate nuclear fusion.

Bubble Fusion

However small bubbles don't generate a lot of power, so the sound pressure diminishes rapidly with distance. I expect the collapse of a big bubble would be instantly fatal anywhere nearby.

I'm such a poster child.

Hully gee! Then I want your poster, please. Will you sign it if I join your fan club?

Thanks muchly for the explanation! I am not actually planning to implode anything-- in fact, thanks to your link I am now deathly afraid of carbonated beverages and indeed all bubbling phenomena. Based on the linked article, bubble fusion looks like it is also effective at imploding academic reputations.

I was actually mulling over the notion of Fortean teleportation, wondering how indiscreet the effect would be if a person or object were to simply vanish without warning. Knowing that light bulb implosions are quite loud for their small volume, I was curious about how the effect would scale up to, say, a sphere with a one-meter diameter. Would bystanders be heard to remark, "Egad! What a colossal report! Thunder, from a clear sky? Zounds!" or would the phrase "YAAAUGH MY EARDRUMS BLOOD EVERWHERE" be a more likely response? From your analysis, I suspect the latter.

No doubt an object with an irregular volume such as a human body would complicate matters even further; but as the joke goes, "first assume that the chicken is a sphere." Based on your summary of the calculations involved, it appears that determining the sound energy of imploding even a spherical chicken would be a formidable task.

I worry about these things sometimes.

[Jaglavak]

Hully gee! Then I want your poster, please. Will you sign it if I join your fan club?

I have a fan club! Up 'til now I only had a fan and a club.

I was actually mulling over the notion of Fortean teleportation, wondering how indiscreet the effect would be if a person or object were to simply vanish without warning.

Oh! In that case a little imploding vacuum would be the least of your worries. At the other end, you need to arrive inside a people-size hole or else your atoms will try to shoehorn in to the same space as whatever is there. I would expect that would make a much bigger boom. Theoretically the simple way to solve both problems would be to swap matter from both departure and arrival ends.

Based on your summary of the calculations involved, it appears that determining the sound energy of imploding even a spherical chicken would be a formidable task.

I described the brute force method, aka computational fluid dynamics. In the case of a spherical implosion there may be simplifications you could make based on symmetry. But in the real world it's usually quicker to just heat up the old workstation.

I worry about these things sometimes.

Well sure. Doesn't everybody?