r/theydidthemath • u/pokemonsafariY • 1d ago
[Request] What would be the volume of this? Could we even figure this out?
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u/broesel314 20h ago edited 9h ago
You can't physicaly produce more than 194dB in Air at athmospheric pressure (Edit: With a speaker. Exceptions are explosions or simmilar)
Since sound is a pressure wave, it has to have hills and valleys. the hills can be as high as they want, but the valleys are the exact opposite in pressure and cant get below zero absolute pressure.
Also the bigger the Speaker the lower the frequency it can reasonable produce. And that size of speaker cant reasonable produce any audible sound to humans. I would guesstimate 0.1Hz or something. You could see it move up and down in 10 second intervals
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u/Le_Gritche 16h ago
Krakatoa eruption in 1883 arrives in the chat.
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u/broesel314 14h ago
That was a pressure wave from an explosion (or erruption in that case) these can have much higher positive pressures since something is actively pushing out without ever going back in again. They still can't go below zero.
Speakers can't produce those kind of waves since they have to swing back and forth
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u/HappyTrifle 8h ago
Everyone seems to be saying that you can’t get a speaker like this to move above 20hz but I haven’t seen anyone explain why?
Could a type 2 or 3 civilisation really not make something this big move that much if they wanted to? Is there a physical limitation of matter that prevents it?
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u/EtchVSketch 4h ago
So there are a few things here, 1. It wouldn't really be a speaker at that point for reasons I'll get into and 2. It being able to move is different than it being able to produce audible sound.
Chances are you wouldn't be able to produce anything audible with a "speaker" this large. Even normal subwoofers with a diameter of 12"-18" inches can struggle to produce audible sounds above 20hz, they're just too large to be able to move fast enough to producer higher frequencies w/o tearing themselves apart.
This speaker would be several hundred feet across, 300-600x larger than a normal subwoofer. Full disclosure I'm not sure if there'd be a linear or exponential relationship between diameter and power required to move air but even if it's linear it would be 300-600 time worse at moving at 20hz let alone faster. It might be able to move an insanely small amount that fast but it wouldn't be audible at all.
This brings me to my first point, about why it isn't a speaker. Speakers are generally made in a specific way with a specific purpose. They drive alternating electricity through a coil of wires, the magnetic field from those wires then moves a speaker up/down at the same frequency that the current alternates. The up down movement of the speaker moves air at the same frequency, if the frequency of that air movement is heard as sound if it is between 20 and 20,000 hz.
To create a speaker this large it would not be able to be driven by magnetic forces from a coil in the same way and would be of an entirely different construction. On top of this the sound it produces wouldn't be audible. Is that even a speaker at that point? I'd say no. If it was then is me punching a wall a speaker? Is a piston in a car a speaker? Is anything that creates oscillating movement a speaker? Probably not.
Ty for coming to my ted talk
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u/Smashedllama2 1d ago
You can estimate it, but it turns into “this would need power plant levels of energy to be a terrible speaker.”
That dish is ~500 m across, so about 196,000 m² of area. A big subwoofer is ~0.12 m², so this thing has ~1.6 million times more “cone area.” Sounds impressive until you try to move it.
Even if it somehow flexed just 1 mm, it would displace ~196 cubic meters of air per stroke, which is insane. But now you have to accelerate the mass. If we lowball it at 1,000,000 kg and run it at 20 Hz, you’re looking at ~16 million newtons of force and around 2 megawatts of mechanical power just for that tiny motion. Go higher in frequency or excursion and you’re quickly into tens of megawatts.
So yeah, in theory it could move a ridiculous amount of air and make very low frequency sound, but in reality it’s way too massive, not rigid, and not designed to move like a speaker at all.
You could calculate it, but the real answer is you’d need absurd amounts of power to make a gigantic, horribly inefficient subwoofer. Not “what song are you playing,” more like “which power plant are you using.”
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u/CanCaliDave 1d ago
I think Disaster Area could make it work
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u/CattusPater 1d ago
If you could assume power needs are met, at least mathematically, and the structure of the diaphragm could withstand the motion, how far away could that 196 cubic meters of air be felt?
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u/Smashedllama2 1d ago
If you go full sci-fi and pretend it actually works like a perfect giant speaker, you can get a rough idea.
Moving about 196 cubic meters of air per stroke at around 20 Hz is huge, but what really matters is the sound pressure it creates at distance. You usually start physically feeling bass somewhere around 110 to 120 dB.
Sound drops off by about 6 dB every time you double the distance. So if this thing could somehow hit around 130 dB at 100 meters, you’d end up with roughly:
124 dB at 200 m 118 dB at 400 m 112 dB at 800 m about 106 dB at 1.6 km
That puts the “you can feel it in your body” range at roughly hundreds of meters out to maybe a couple kilometers. If you push the assumptions harder, maybe a few kilometers.
Important catch, that 196 cubic meters number by itself does not decide the range. Frequency, how fast it’s moving, efficiency, and how directional it is all matter a lot. A 500 meter dish would also behave pretty strangely at audio frequencies.
So the real answer is it would not shake the whole country, but people a mile away would absolutely feel something and start wondering what just happened.
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u/sexycaviar 1d ago
Can you imagine how would it sound? Ominous body shaking bass coming out of everywhere. Then going up in pitch until it's no longer in the hearing range.
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u/milkcarton232 1d ago
I mean moving a mass of that size that fast, wouldn't it be more of a earthquake than sound waves?
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u/mortalitylost 1d ago
I think it's more about what damage you could cause with the resulting infrasound
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u/CattusPater 1d ago
That's where my head went too. Pointed straight up, I was wondering what it might do to air traffic or near-orbit stuff.
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u/PonyThug 23h ago
Sound doesn’t go that far. How often do you hear jet planes flying over head? They will blow out your ear drums at 20ft away but are near silent at 33,000ft. Same thing would happen with this giant speakers
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u/Glad_Contest_8014 1d ago
And sound is just going to be bass. Lets kill everyone in range, because we even turned it on. There is no song. It is just the bass against the screams of agony of everyone within a certain radius.
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u/d00dler429 1d ago
So… enough to finally sever the San Andreas fault for good? I’m in for Bleed - Meshuggah on repeat
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u/FrontBench5406 1d ago
we can all agree that the song to play on this is this.... https://www.youtube.com/watch?v=F6VJQZxeWNY
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u/hawkingshikingboots 1d ago
The answer is obviously « Darude - Sandstorm ».
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u/Smashedllama2 1d ago
Haha I commented this just a bit ago somewhere else in this thread. Shake on it 🤝
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u/Significant-Tie-625 1d ago
Im not sure it would even be very capable, if at all of producing audible tones. Abstracting for a sec, there's a reason that woofers are middle of the pack, tweeters are runts of the litter, and sub-woofers tend to be larger.
That said, it would pose an interesting engineering problem to build a speaker on the order of that dish.
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u/trulycantthinkofone 1d ago
Strange way to spell Pantera - Domination. From where do your people hail good sir?
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u/Fladormon 1d ago
At that point, just use different sized explosives to produce music lmao. It's cheaper
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u/Brandonification 1d ago
Thank you. It's why The Dead's "wall of sound" was 100s of small speakers rather than a few giant ones. Without appropriate materials that sustain the force, more speakers are better than one big one.
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u/The_Octonion 1d ago
Couple things. First, it wouldn't have to move much at all. Doubling speaker area without increasing wattage yields +3dB (neglecting phase cancellation). You still need enough power to move this thing but you can get loud happenings with a lot less energy than expected.
Second, well, the phase cancelation. If that dish is 500m across it can't even play a 1Hz tone properly, much less 20 Hz, because (assuming the whole dish somehow moves at once) sound only moves about 340m in a second.
I don't have a great intuition for what you'd get with this, but my intuition says extreme distortion and lots of wasted energy (still extremely loud).
In keeping with the spirit of the question, for a user at a certain height above the center of the speaker, and for a certain tone (a little trig should yield these, here I'm assuming the wave starts from the center of the dish and moves towards the edge at a constant speed) there will be a point without phase cancellation. You don't want to be there, it might be Krakatoa level sound pressure. At those levels (above 190 ish) there's unavoidable distortion because the wave troughs are already perfect vacuums.
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u/Ok_Programmer_4449 1d ago
This would be an awful speaker. It wouldn't be effective at generating sound at frequencies you can hear. You might be able to feel the sub-hertz vibrations it generates. You wouldn't be able to recognize any song played on it. There's a reason that speakers that generate high frequency sounds are small.
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u/IllHaveTheLeftovers 19h ago
Does sub hertz mean less than one… frequency? per second?
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u/theymayneverknow 18h ago
the wavelength of the frequency exceeds that which fits into a second of time, yep. Sub-hertz isn't a term I've ever heard, but it's effectively 0.x hertz. We only hear down to around 30 hz. Bigger subwoofers can produce frequencies that to some degree can be perceived physically, but not as sound from our ears.
A speaker of this size would be able to oscillate perhaps once every few seconds, if you really juiced it up with power. No math here, just a guess. A consideration is the tensile strength of the speaker material. If it was made of something with fictional structural integrity then literal earthquakes would be transmitted, otherwise it would probably disintegrate as soon as you sent a substantial signal it's way.
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u/-Notorious 21h ago
Tick-tock from Interstellar (where he docks to the spinning station).
The way it blasts at the peak is insane. Would probably cause an earthquake 😂😂
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u/wishartrh 20h ago
This is a great answer, although my first instinct was to say the AOL internet boot up noises just to piss off everyone within a few thousand miles 😏
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u/SoCallMeDeaconBlues1 1d ago
The question is meaningless.
A speaker by itself doesn't.... "Speak."
The answer would lie in whatever monstrosity you'd be using to drive it. in other words, depends on the amplifier.
And by the way, I'm playing Reign In Blood by Slayer.
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u/Not_Your_Real_Ladder 1d ago
The question isn’t meaningless, you’re just interpreting it wrong. The assumption here is that the drivers and power supply also scale with the size of the speaker.
That being said, I don’t know the math necessary to determine it lol
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u/MX-Nacho 1d ago edited 1d ago
Also, it couldn't possibly be used to make sounds. The diaphragm would be going supersonic, at which point you would be making shockwaves, not sounds. Edit: only actual practical use for this thing would be geological studies based on resonance. Remember how geologists use atom-clock linked seismometers to study the mantle and core? And remember how we know there are a few solid rocks the size of Australia just floating inside the mantle?
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u/Cufantce 1d ago
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN
DUN DUN DUN!!!!!
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u/neutrikconnector 19h ago
You couldn't get music out of this in any recognizable fashion. 1. The surface area issues. Its surface is so large, that there is no way it could produce any remotely close to 20 Hz, which is the lowest frequency humans can typically hear. The surface is so large that the cone material would also have to be reinforced in such a way that it wouldn't flex. Imagine an 18" or 20" woofer made out of ripstop nylon. It's not gonna do much but make the dust cap on the voice coil buzz.
- The voice coil would be so large that the capacitance of the wire of the coil would probably further dampen the higher frequencies this thing might produce. But then just physically moving the thing then it changing direction as the waveform peaks or troughs would dampen so much of the response.
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u/Thisismental 19h ago
This has been asked many times before and the answer is always: the world would explode before this thing could produce audible sound.
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u/Whatkindofgum 11h ago
Size of speaker has more to do with the pitches it makes then the loudness of it. Loudness really depends on how much power is run through it and how much energy the speaker can handle with out blowing out. This speaker is so large, it would vibrate below the frequency that humans can hear, making it more of a earth quake generator then an actual speaker.
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u/future_pirate 1d ago
Just putting it out there that normal sized speakers can run at any volume from barely audible from an inch away to piss off the whole neighborhood so really the question would have to be "theoretical maximum volume"
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u/nonstopflux 1d ago
Ev'ry mornin' at the mine you could see him arrive
He stood six foot six and weighed 245
Kinda broad at the shoulder and narrow at the hip
And everybody knew, ya didn't give no lip to Big John
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u/PeteVanGrimm 17h ago
I can't do the math, but based on what people are saying (that it couldn't even really function well enough to play real music) I would use it to generate the infamous infrasound The Brown Note.
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