• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

A Physics Question

kaisersean

New Blood
K
Joined
Oct 22, 2004
Messages
22
Ok, I'm merely a humble history major, and so this isn't my field. Nonetheless, I've been mulling over a physics thought experiment that's been bothering me, and hopefully someone can explain where I'm going wrong.

Picture the following, if you would:

A metal bar with two pencils attached perpendicular to it on either end, such that the tips touch paper on either end (sort of like a seismograph does in the movies). Now, a man takes one end in his hand and writes a message; the other end moves with it and writes the same message because the same impulses are transmitted through the inflexible bar.

(An illustration, crudely drawn)

...........--------------------------------------------------------
..........|********************BAR********************|
...........--------------------------------------------------------
..........| |...<------...................Pencils..................------->..| |
..........| |........................................................................| |
...........\/.........................................................................\/
.......________..............................................................________

Now, it would appear that both pencils are simultaneously writing the same message. However, if it were truly precisely simultaneous, this would appear to be transmitting information from one end of the bar faster than light, thus (to my understanding) violating special relativity.

I know there's a simple explanation- no, I assume there is one. However, I can't figure it out- I sincerely doubt that no one has thought of this before. So any assistance anyone could lend would be helpful.

Thanks!
 
kaisersean said:
Now, a man takes one end in his hand and writes a message; the other end moves with it and writes the same message because the same impulses are transmitted through the inflexible bar.
Click to expand...
The explaination lies in this section. We can't assume an inflexibe bar as nothing is completed rigid. So the impulses are transmitted at a finite speed, the speed of sound in the material.

Walt
 
Walter's explanation is correct.

I like to think of it on the atomic scale. When the atoms on the end of the bar are moved, they exert an attractive force on the neighbouring atoms which cause them to follow. These atoms, in turn, cause their neighbours to follow. This movement cascades through the bar at the speed of sound in the metal, until the jiggling reaches the pencil.

It blows my mind whenever I think about this - it's really how all objects move. There isn't any such thing as a "solid" object.
 
It should be pointed out that the speed of sound in a metal bar is several thousand m/s, so for any bar short enough to do this with the transmission time is such a small fraction of a second that it almost immeasurable.
 
You can modify that setup and it gets a little more interesting.

If you put a handle exactly in the middle of the bar and move both pencils with the handle the time it takes for a movement of the handle to get to the two pencils (traveling with the speed of sound) would be the same. So when you see one tip moving, you can guess that the other one is moving at exactly the same time.

But you wouldn't be transmiting information from one tip to the other. You couldn't even be sure that the second tip moved at all, someone might have cut off the bar or something.
 
At least it wil take more than an average stop-watch ;). Actually, all you need to do is place a sound source at one end and a microphone at the other, feed it a tone and note the phase-shift. Change the frequency till you have a 180 deg phase-shift, and the transmission time will be 1/(f*2).

ETA: There will be some interesting resonance phenomena.

Hans
 
ospalh said:
If you put a handle exactly in the middle of the bar and move both pencils with the handle the time it takes for a movement of the handle to get to the two pencils (traveling with the speed of sound) would be the same. So when you see one tip moving, you can guess that the other one is moving at exactly the same time.
Click to expand...

Not to make this overly confusing, but that's only true if you are in the same reference frame as the handle/bar arrangement. If you were in some vehicle traveling past the bar along its length, the writing would not be simultaneous; one end would write before the other -- and it would be correct to conclude that. If one traveled in the exact opposite direction the writing sequence would be reversed -- and to that observer that would be correct as well.
 
Sorry Hans, I should have said, "immeasurable without specialised equipment." :oldroll:
 
Ok, that's actually kind of what I was thinking- it's effectively a wave, right? So just as sound moves more slowly through air than water, and more slowly through water than steel, it would move more quickly as density increases (I'm guessing).

What is the theoretical maximum? I presume that neutronium would be the most dense material that could be effectively modeled. Anyone know how to calculate the speed of sound through it?

As I understand it, waves can travel faster than light, but only in certain circumstances that preclude actual transmission of information. Still, I'm curious to know just how fast we could get it moving.
 
kaisersean said:
Ok, that's actually kind of what I was thinking- it's effectively a wave, right? So just as sound moves more slowly through air than water, and more slowly through water than steel, it would move more quickly as density increases (I'm guessing).
Click to expand...
Exactly right. There are actually two types of sound waves in solids - transverse and longitudinal. The longitudinal waves are like the sound waves that travel through fluids (liquids and gases), i.e. compression waves, whilst the longitudinal waves are what most people would envision as a wave, with the particles only moving at right angles to the direction of propogation. Longitudinal waves travel faster than transverse waves in a solid, and transverse waves cannot propogate in a fluid.

What is the theoretical maximum? I presume that neutronium would be the most dense material that could be effectively modeled. Anyone know how to calculate the speed of sound through it?

As I understand it, waves can travel faster than light, but only in certain circumstances that preclude actual transmission of information. Still, I'm curious to know just how fast we could get it moving.
Click to expand...
Not quite. Sound waves cannot travel faster than light travels in a vacuum. They can, however, travel faster than light in a given medium.
 
kaisersean said:
Ok, that's actually kind of what I was thinking- it's effectively a wave, right? So just as sound moves more slowly through air than water, and more slowly through water than steel, it would move more quickly as density increases (I'm guessing)..
Click to expand...

Not quite. The figure of merit is the ratio of stiffness to density. So a very stiff substance that has a low density (like carbon fiber) would have a high speed of sound.
 
wollery said:
Not quite. Sound waves cannot travel faster than light travels in a vacuum. They can, however, travel faster than light in a given medium.
Click to expand...

Right. That's absolutely true, but I actually was referring to instances where the phase velocity of a wave propagates faster than light- which the article I read likens to a group of people standing in a line, each shouting "I'm here!" at a particular time according to their watch. It may appear that the wave of shouts is proceeding faster than light, but it required the information to already have been transmitted (at a slower than light speed). Not sure if this analogy is correct (came off of Wikipedia, so my info on this is iffy) but it's what I'm working with.

At any rate, I glanced through some websites talking about the speed of sound through solids. Apparently this requires knowledge of their elastic property and inertial property, which I'm uncertain how to calculate. Again, according to wikipedia (I know, shouldn't rely on this for info- but this is for fun) the density of a neutron star is from 8×10^13 to 2×10^15 g/cm^3. However, apparently there is debate over just what neutron stars are composed of.

Anyway, anyone know how to at least approximate the speed of sound through such a substance?

Edited for exactness.
 
kaisersean said:
At any rate, I glanced through some websites talking about the speed of sound through solids. Apparently this requires knowledge of their elastic property and inertial property, which I'm uncertain how to calculate. Again, according to wikipedia (I know, shouldn't rely on this for info- but this is for fun) the density of a neutron star is from 8×10^13 to 2×10^15 g/cm^3. However, apparently there is debate over just what neutron stars are composed of.

Anyway, anyone know how to at least approximate the speed of sound through such a substance?

Edited for exactness.
Click to expand...
Neutron stars are composed of neutron degenerate material, which doesn't act in the same way as a solid. The closest analogy would be a super dense fluid, but its physical properties are governed as much by quantum mechanics as anything else.

From THE ASTROPHYSICAL JOURNAL, 470:L61L64, 1996 October 10, Kalogera & Baym, Maximum Neutron Star Mass (©1996. The American Astronomical Society. All rights reserved. Printed in U.S.A.) (Link)

The set of fundamental constraints, independent of the detailed physical properties of neutron matter, imposed on the equation of state of the inner core are the following: (i) the mass density, {rho}0, is non-negative, i.e., gravity is attractive; (ii) the pressure, P, at zero temperature is a function of {rho}0 only, i.e., neutron matter is a fluid; (iii) dP/d{rho}>0, so that the zero-frequency sound speed of neutron matter (dP/d{rho})1/2 is real and matter is stable against microscopic collapse; (iv) the sound speed does not exceed the speed of light, i.e., dP/d{rho}<c2, hence signals cannot be superluminal and causality is satisfied.
Click to expand...

I think that the important part in there as far as you are concerned is (dP/d{rho})1/2 which is the zero-frequency sound speed. Suggests to me that the sound speed is dependent on the frequency of the sound. Hmmm, interesting.
 
wollery said:
I think that the important part in there as far as you are concerned is (dP/d{rho})1/2 which is the zero-frequency sound speed. Suggests to me that the sound speed is dependent on the frequency of the sound. Hmmm, interesting.
Click to expand...

Does this mean a neutron star would act as a sonic prism?
 
Huntsman said:
Great, now you've done it.

Next week we'll start seeing "Neutra-Sound: Neutron matter speaker cables! Seperate your sound and remove only the unwanted noise with our exclusive "sonic prism" technology!" on all the audiophile websites!
Click to expand...
:dl:

I'd love to see how they'd claim to create stable neutron degenerate matter in an earthbound cable!! :D
 
Huntsman said:
Great, now you've done it.

Next week we'll start seeing "Neutra-Sound: Neutron matter speaker cables! Seperate your sound and remove only the unwanted noise with our exclusive "sonic prism" technology!" on all the audiophile websites!
Click to expand...

:D
 
Huntsman said:
Great, now you've done it.

Next week we'll start seeing "Neutra-Sound: Neutron matter speaker cables! Seperate your sound and remove only the unwanted noise with our exclusive "sonic prism" technology!" on all the audiophile websites!
Click to expand...
I'll buy any technology so long as it uses the now obligatory "Death Photons"®
 
kaisersean
Now, a man takes one end in his hand and writes a message; the other end moves with it and writes the same message because the same impulses are transmitted through the inflexible bar.
Click to expand...

Question: Is Walter Wayne’s interpretation is correct, i.e. can we assume that the bar is not rigid, e.g. if the bar was one light year long, and I pushed it longitudinally (ignoring all the physics of metal strength, and the amount of force required), would the other end of the bar move instantly or would the bar compress and a wave of movement travel along it’s length? How fast?
 
You must log in or register to reply here.

Back
Top Bottom