Gabriel's Horn

[Arariel]

This kind of overlaps with math, but what would happen if someone tried to blow Gabriel's Horn?

[KrO2]

It would be difficult, since it's infinitely long. But if they could get to the point (infinity, 0) they'd be blowing into a hole with diameter 0. That would also be difficult. If we pretend that air molecules are infinitely small, they could blow through but the speed the air stream is traveling at would be much smaller as the it reaches the other end. There wouldn't be much of a sound.

[broken_escalator]

Then comes the question that if no one is at the other end (which is infinitely far away from the horn blower) would it still make a sound?

[KrO2]

Maybe after an infinite amount of time? Unless you consider friction, in which case maybe not at all.

[Agent_Irons]

If you could blow into it "backwards" you could accelerate your ideal fluid to infinite speed. That's pretty cool.

[Technical Ben]

Did you just dived by Zero?
On a serious note, if I was ever in charge of maths, I'd put "times infinity" next to "divide by zero" in things not to do.

[doogly]

http://www.youtube.com/watch?v=ITWh1TNoM7c

And times infinity is fine! For example, five times infinity is infinity. Nothing wrong there.

[thoughtfully]

http://www.youtube.com/watch?v=ITWh1TNoM7c

And times infinity is fine! For example, five times infinity is infinity. Nothing wrong there.

There's a joke about physicsists and renormalization in here somewhere..

[doogly]

Oh hush, mathematicians do it too. Infinity - infinity = .58, right?

[poxic]

On an 1993-model Intel chip, yes.

[Agent_Irons]

Did you just dived by Zero?

I'm not entirely sure that I have. Assume an incompressible fluid, conservation of volume, the speed at any finite distance along the neck of the horn is finite. Although much larger than the speed of light.

[Qaanol]

Anyone know how to calculate the resonant frequencies of a partial Gabriel’s horn made of brass, as a function of x, the horizontal distance at which you cut it off (and at which point the air is blown) in meters, and y, the radius of the opening at the big end in meters, and z, the thickness of the brass, which we will take to be constant? We’ll say the Gabriel’s horn part is the size of the hollow interior.

[gorcee]

edit: DAMMIT! There is a filter for the most Chuck of all the Norris's. This was a perfect nerd moment, too.

My day, it is ruined =(

[doogly]

Chuck isn't friends with nerd club anymore. Are you familiar with the mountain of shit that spews from his mouth every time it opens?

[KrO2]

Anyone know how to calculate the resonant frequencies of a partial Gabriel’s horn made of brass, as a function of x, the horizontal distance at which you cut it off (and at which point the air is blown) in meters, and y, the radius of the opening at the big end in meters, and z, the thickness of the brass, which we will take to be constant? We’ll say the Gabriel’s horn part is the size of the hollow interior.

y is constant, since Gabriel's Horn is 1/x from cut off at 1 and rotated around the x-axis. So the opening has a radius of 1, but I still can't help with the harmonics. At least not off the top of my head, and I'm too lazy to try to do work to find it.

[thoughtfully]

Chuck isn't friends with nerd club anymore. Are you familiar with the mountain of shit that spews from his mouth every time it opens?

It's alright, we still have Bruce Sheier!

[webgiant]

Then comes the question that if no one is at the other end (which is infinitely far away from the horn blower) would it still make a sound?

It depends on your profession. For physicists, the answer is "yes", because a sound wave is produced.
For audiophiles, the answer is "no", because sound is what you get when the eardrum vibrates.

[Qaanol]

Anyone know how to calculate the resonant frequencies of a partial Gabriel’s horn made of brass, as a function of x, the horizontal distance at which you cut it off (and at which point the air is blown) in meters, and y, the radius of the opening at the big end in meters, and z, the thickness of the brass, which we will take to be constant? We’ll say the Gabriel’s horn part is the size of the hollow interior.

y is constant, since Gabriel's Horn is 1/x from cut off at 1 and rotated around the x-axis. So the opening has a radius of 1, but I still can't help with the harmonics. At least not off the top of my head, and I'm too lazy to try to do work to find it.

The units aren’t specified, so we can choose any opening radius we want, in meters, and then call that the base unit for our measurement system when graphing 1/x, right? So y is a free variable.

We can then choose how far to the right to cut it off, in meters, so x is a free variable.

We can then choose how thick to make the brass around it, so z is also a free variable.

[frezik]

Did you just dived by Zero?

I'm not entirely sure that I have. Assume an incompressible fluid, conservation of volume, the speed at any finite distance along the neck of the horn is finite. Although much larger than the speed of light.

Somewhere in this, a spherical chicken will emerge.

[Yakk]

If we account for pressure, the speed of the air won't diverge ridiculously. But that is not much fun.

If we ignore pressure and otherwise account for relativity, things could get interesting.

[eternauta3k]

Anyone know how to calculate the resonant frequencies of a partial Gabriel’s horn made of brass, as a function of x, the horizontal distance at which you cut it off (and at which point the air is blown) in meters, and y, the radius of the opening at the big end in meters, and z, the thickness of the brass, which we will take to be constant? We’ll say the Gabriel’s horn part is the size of the hollow interior.

I was writing how to calculate it when I realized, if I simplify it to a uniform width tube, it's not an interesting problem anymore...

[thoughtfully]

We've covered this already
(check out the thread number! Found it googling around)

Anyway, if the horn is truncated to create a mouthpiece, then it's no longer infinite in volume.

[Micali]

Then comes the question that if no one is at the other end (which is infinitely far away from the horn blower) would it still make a sound?

It depends on your profession. For physicists, the answer is "yes", because a sound wave is produced.
For audiophiles, the answer is "no", because sound is what you get when the eardrum vibrates.

To a physicist, not quite. The sound waves propagate outwards like an inverse square function since the cross-sectional area logarithmically increases. It would limit to zero since:
I (is-proportional-to) 1/d^2 so as distance -> infinity, then I (which, lets say represents decibels) would then limit to zero.

[Antimony-120]

Then comes the question that if no one is at the other end (which is infinitely far away from the horn blower) would it still make a sound?

It depends on your profession. For physicists, the answer is "yes", because a sound wave is produced.
For audiophiles, the answer is "no", because sound is what you get when the eardrum vibrates.

To a physicist, not quite. The sound waves propagate outwards like an inverse square function since the cross-sectional area logarithmically increases. It would limit to zero since:
I (is-proportional-to) 1/d^2 so as distance -> infinity, then I (which, lets say represents decibels) would then limit to zero.

They work like that in open space because of the energy propogation. In a confined space you can have some interesting effects. In open space, the area of the expanding wave increases as the area of a sphere, so as it propogates outwards the energy per area goes down as the inverse, which is of order 1/r^2. But that isn't true in general. For example, if you had an infinitely long tube of constant radius, and you blew into one end, ignoring frictional effects, the other end would have the exact same decibel level.

For Gabriel's horn, as the area goes up by a different function. Nonetheless I suspect because he opening has a finite area and the input an infinitesimal one you would still get a limit of zero, but I'm not entirely certain, as you'll have infinite energy per unit area at the infinitesimal end, and I don't feel like working around the infinity over zero issue right now.

[MHD]

Suppose you were blowing it backwards as has been suggested above, but with and ideal gas instead.
Given the shape that would be an interesting thermodynamic system...

[Afif_D]

Actually you will never reach the end of the gabriel's horn where you can blow.

[Arariel]

Actually you will never reach the end of the gabriel's horn where you can blow.

Well, yes, but in the same way, you will never fill up the horn with paint. But of course we assume in the limit of infinity...

[Meteoric]

Not if you use infinitely-divisible theoretical paint, but normal paint made out of atoms could fill the horn to the brim in a finite amount of time.

[Arariel]

Is it truly filling it up, though, if not all of the volume is filled?