Over at the Library I got a question from Herr Wozzeck about this passage. Specifically, how utterly impossible it is.
The people in the chambers clapped so much that the noise echoed so much that the sound was still heard after a minute or so.
Yo, Taco! Would you be so kind as to give a scientific deconstruction of this claim?
*Rubs hands together*
Oh, this is gonna be fun.
The phenomena on the table in question is an echo that rebounds around a room for 60+ seconds. Now, to give Thomas every possible benefit of the doubt, I’m going to assume they are in a perfectly acoustic room for creating echoes. By that I mean the walls are built out of the best possible material, the room is spherical, and that the audience is sitting in the dead center of the room. I’ll also not be addressing the cancellation effect of sound waves hitting each other, because there’s only so many variables I want to juggle at once.
There are two ways this could go down. First, the least physically likely, is that the sound just bounces around the room for 60+ seconds while everyone listens to it echoing, or, more likely, the clapping itself lasted for 60+ seconds and that the walls are far enough away that the echo doesn’t start until they’re done.
Now, the best material for reflecting sound that we have today has an absorption coefficient of around 0.01 at 125hz. The problem here is that sound absorption varies rather drastically based on what frequency the sound is at. Clapping covers a huge spectrum of frequencies, so it’s really hard to justify the 0.01 number. However, the average frequency of clapping is about 2khz, so if we say we’ve got one of the best acoustic materials, then we can assume that our absorption coefficient will be no greater than about 0.05, and that’s if we make the sphere almost completely out of acoustic wood paneling backed by solid brick.
Sound, as it travels through the air, loses energy (gets quieter) based on the frequency and relative humidity of the air. The lower the sound, the less attenuation it receives, and the higher the humidity (to a point) the slower it attenuates. For our 2khz clap-wave, our sweet spot is actually a room with a relative humidity of 80%. At this humidity, we’re only going to see an attenuation of 9 db/km. Also important is the speed at which the sound is moving. Assuming we’re keeping the room on the warm side of the average room temperature (25ºC) sound will be chugging along at 347.6 m/s.
Finally, the human ear can detect sound in a range of about 0 to 120 dB, depending on acuity. Since the passage didn’t really seem like the echo was whispering back past the people, we’ll just arbitrarily pick 40dB as our target for when the sound is still faintly audible.
So, now let’s tackle the second, easier case. We’re looking at a 60 second round trip for the sound to reach the edge of our sphere so that the clapping sound will keep going for a full 60 seconds after the crowd stops. At our speed of 347.6 m/s, that means our sphere is roughly 20 kilometers in radius (about 25 mile total round trip). Pretty damn big.
At 20 kilometers each way, the sound will lose approximately 360 dB as it travels this distance, and another 5% when it hits the wall. Doing all the math back to the start, the initial sound the audience makes by clapping would be roughly 401 dB. For comparison, the human eardrum ruptures at about 150 dB, so not only would no-one in the audience actually be able to hear the echo once it got back to them, most of them probably wouldn’t be conscious due to the pain of having 401 db smash through their eardrums. There’s some more interesting stuff that’ll go on here, but let’s go to the harder case, where things are going to get a bit more extreme.
If you bring the spherical room in to a more realistic size, say the size of the main performance hall in a popular opera house in Sydney; roughly 100 meters in diameter. This means it takes sound less than 1/3 of a second to reflect back at the origin, so we can pretty much discount the fact that people will be able to clap for that long. In order for a sound to continue to reverberate around the room for a full 60 seconds, it’ll have to bounce 208 times; remember each time it bounces it loses 5% of its energy. And we’re still ignoring the fact that the sound waves would run into each other and make the system way less efficient.
I hope you see where this is going. The sound will still need to cover the same distance as it did in the huge room scenario, but now, rather than bouncing once and losing 5% of its energy, it’s going to bounce 208 times and lose approximately 99.99998% of its energy. Thus, the initial applause will need to be around 446 dB, that’s several orders of magnitude louder than the 400 DB we had earlier.
This is where things get really, really strange. At that kind of energy, expressing it at sound really doesn’t make sense anymore. So let’s just convert it to a pure wave of pressure. 446dB is roughly equivalent to 4.1×10^12 atmospheres. Forgiving the fact that there’s just no way to produce that kind of pressure with clapping… at all, we’ll move on with it.
So, what just happened? Well, it’s really hard to predict, but I’m gonna try anyway. You see, as best we can calculate, the pressure in the center of our sun is approximately 1×10^14 or so atmospheres, so that’s about 25x the pressure we’re talking about here. Neutonian physics don’t really work anymore at that kind of energy, so things will get kinda strange.
In any event, we’ve gotta think bigger.
Here’s what’s probably going to happen. If we start just a micro-fraction of a second after the sound starts, we basically see a vast pressure wave originate in the center of our audience. As this pressure wave moves outward, it carries the audience members and everything else with it, but it’s also accelerating very quickly because of the immense amount of energy that is now trying to spread out, kind of an energy run-away. This is going to cause the audience, who are now being torn apart down to the sub-molecular level by this pressure wave, to undergo fusion with the air, which itself is undergoing radical fusion as it’s pushed forward. Now, normally this much fusion all happening at once would lead to an out-of-control plasma explosion, which would likely level an area a few hundred miles in radius but otherwise peter out. However, it’s all happening on the outside of an immense pressure wave that also now has a pure vacuum inside it, which actually stabilizes the whole thing… sorta. Things get really goofy because we’ve now got quantum physics and astral physics colliding in one spot, the fusion edge of an expanding wave of pressure.
As the pressure wave expands, it gobbles up more and more matter into this sphere of fusion… and then it runs out of stuff as it finishes devouring the Earth. As this happens, the vacuum that was inside the pressure wave normalizes with space and the pressure wave vanishes. What’s left is an expanding sphere of fusion that’s traveling in every direction. As this sphere impacts some of the other planets in our solar system, it causes massive explosions, ripping some of them apart, and severely damaging others. Basically, an energy bomb about 1/25th the size of the sun just went off where Earth used to be and hot, fusioning shrapnel just got spewed all over the solar system.
The sun would probably survive this ordeal since it’s already hot, undergoing fusion, and is still a lot larger than the explosion.
Way to go, Jerry.
EDIT: Updated with better, unfortunately less crazy, numbers.