Question about instantaneous travel of information on a solid

[LazerStallion]

I hope this isn't a common question, and that I'm not breaking any rules of posting - please let me know if I am, as I'm new here.

So, to describe what I'm trying to ask: Picture a very long rod, say, one light-year long. Imagine it's in space, and is free of gravitational interactions (and all other ideal requirements are met). If I were to push one end of this rod away from me, would it take one year for the information regarding the push to reach the other end of the rod? Or would that end move instantaneously?

I think that should be a simple enough description to convey what I'm trying to ask - thanks to anyone that has any input on this!

 

[Bandersnatch]

Hi LazerStallion, welcome to PF.

It's a perfectly good question, one that is often asked.

When you push one end of the rod, you bring closer together(compress) the molecules at this particular place. These molecules push on the molecules farther down the rod, and so on until the wave of interactions reaches the far end of the rod.
These interactions between molecules are not instantenous, but take a finite amount of time, depending on the type of material from which the rod is made. The speed the signal travels along the rod is called the, wait for it, speed of sound. :P

So, the answer is neither of the two options you've provided. The information doesn't travel instantenously, nor does it travel at the speed of light, but at a much slower speed.

 

[LazerStallion]

Ah, thanks Bandersnatch - that makes sense. Do you know if there are any real-life instances in engineering or other settings in which this delay is noticeable? Just curious!

 

[mfb]

Earthquakes.

Most musical instruments do not use the speed of sound in their material, but I think some of them do.
I am sure there are more applications.

 

[russ_watters]

Guitars? Anything that transmits vibration.

 

[Simon Bridge]

Earthquakes.

Most musical instruments do not use the speed of sound in their material, but I think some of them do.
I am sure there are more applications.

Any stringed instrument for instance.
The speed of sound in the string is essential to the note played.

You'll notice that instruments made of different materials sound different even when playing the same note?

But you can just get someone to hit a long steel beam with a hammer, while you listen at the other end, to notice the speed of sound in the beam is much slower than light. Look up the speed of sound in different solids and work out your own experiment.

The thing to realize about rigid bodies, which is what is actually being discussed here, is that they are an approximation that works for small scales.
IRL there is no such thing as "rigid", and you should think of solids as behaving more like a kind of stiff jelly.

 

[mfb]

Vibrating strings do not oscillate so much in longitudinal direction - their wave propagation speed is not the speed of sound in that material, it depends on the linear density and tension only (to a good approximation).

 

[Simon Bridge]

Oh I see what you mean... right-oh.
Cavity instruments do use the speed of sound (in air) - but we are interested in solids here.
What about a bell?

Still I think the string is a reasonable example here - a displacement at one end take longer than light to reach the other end.

I think the proposed experiment holds up too - have to hit the bar end-on.

 

[Bandersnatch]

Speed of sound in steel is ~6km/s, so it'd have to be a really long beam to notice the lag. Maybe a section of a railway?

Anyway, can't we say all cases of vibration in solids are expressions of the effect? As far as I understand, bells, tuning forks etc., all wouldn't work if the propagation of internal stresses were instantenous. And if it were close to speed of light, then the vibrations would be too rapid for human ear to pick up any sound.

 

[mfb]

What about a bell?

Same issue, but at least the restoring force comes from the material itself.
The basic problem (for instruments) is the fast speed of sound:

Speed of sound in steel is ~6km/s

To get a frequency of 500 Hz, you need a length of at least 3m. In addition, the coupling between sound waves in steel and air is bad.

Still I think the string is a reasonable example here - a displacement at one end take longer than light to reach the other end.

That is true, of course.

 

[nasu]

Ah, thanks Bandersnatch - that makes sense. Do you know if there are any real-life instances in engineering or other settings in which this delay is noticeable? Just curious!

This how nondestructive testing by ultrasound works.
Measuring the delay you can tell how deep are the defects in metallic parts or the thickness of the parts, etc.
This is a very real-life instance in engineering. You'll find it in any car assembly plant, I suppose.

 

[PAllen]

There is also a method of testing behavior of ceramics that involves striking a 1 meter rod at one end and observing propagation delay to the other end - just one meter away - using high speed circuitry. This is supplemented by increasing the force of the strike until fracture occurs and observing (using very high speed photography) the crack propagation along the rod. The first variant, especially, directly observes the time delay between striking one end and the other end moving over just one meter of a rigid ceramic rod.

 

[nasu]

A similar method is used in New Zealand to test trees. They hit one end of the (cut) tree with a hammer and measure the time it takes for the wave to go along the tree.

 

[Simon Bridge]

A similar method is used in New Zealand to test trees. They hit one end of the (cut) tree with a hammer and measure the time it takes for the wave to go along the tree.

I'd like to see a reference for that.

Lumber mills will pay considerably more for high density logs to be cut for structural timbers (for those who don't know, almost all houses in NZ are timber-framed - and they have to withstand earthquakes) so the people cutting the forests want to be able to tell which logs to send where.

Fletcher Challenge offer a "sonic testing" service to test the wood density of logs, and I found http://www.nzffa.org.nz/farm-forestry-model/resource-centre/tree-grower-articles/tree-grower-may-2007/measuring-radiata-pine-and-forecasting-yields/ for use on living trees - works by directly comparing the time of travel for sound (in the wood) and light (in air) over the same distance.

I have seen lumberjacks whack the end of a log with a big hammer to test "soundness" - usually by listening to the resonance - you can tell if there are gross defects in the log, like if it is rotten someplace in the middle, without having to inspect every inch. However, I have been unable to find a reference.

 

[nasu]

I'd like to see a reference for that.

Lumber mills will pay considerably more for high density logs to be cut for structural timbers (for those who don't know, almost all houses in NZ are timber-framed - and they have to withstand earthquakes) so the people cutting the forests want to be able to tell which logs to send where.

Here is a pdf, attached. It seems to be used in UK too.
Seems to be the similar (or identical) to the family of devices shown in your link.

I was talking about the manufacturers from NZ. I found about the method when talking to one of their researchers.
He also mentioned the adaptation for standing trees, shown in your link.

It may be that they use a resonance method rather that time of flight, for fallen logs, you are right.
I will correct my post.

 

[Simon Bridge]

@nasu: cool, thanks :)

 

[bobc2]

Elastlic Wave Speeds in a Rod

This afternoon I walked out in the lab and found a 110-inch aluminum extrusion with a 2" x 2" cross-section, set it up on my desk (two foam rubber supports for dynamic decoupling from desk). I attached a tri-axis accelerometer on the far end of the beam and applied a 0.3 milli-second force transient (approximate short half-sine pulse) to the other end. The force was applied to one corner of the beam end, hoping to get good excitation of the transverse modes of the beam as well as the longitudinal modes. A force transducer was attached to the hammer head. The force and accelerometer transducers were connected to a USB data acquisition module with parallel analog-to-digital conversion at 52.1 thousand samples per second. Here are plots of the four data channels. "As one would expect" the longitudinal pulse (axial) arrives before the transverse pulses.

The interpretation of the reflected pulses is not trivial--the normal mode theory must be applied with understanding of superposition principles, etc. The slight oscillations in the force signal following termination of the half-sine pulse is due to resonant vibration of the transducer-hammer head (the hammer continues to vibrate at very small amplitudes after losing contact with the beam). Maybe one of these days I'll repeat the test using a smaller diameter solid cylindrical rod with higher frequency response transducers (resonance freq of the accel was 50KHz) and lighter hammer head (shorter force pulse duration).

It took 0.540 milli-seconds for the initial stress pulse to travel from one end to the other. (By the way, the X-accelerometer was mounted with negative orientation, i.e., positive +G on the plot is actually -G, sorry).

Homework problem for LazerStallion: Compute the longitudinal speed of sound in this aluminum specimen.

 

[Simon Bridge]

Very cool Bobc2, thanks :D

 

[bobc2]

Post Respose

Very cool Bobc2, thanks :D

Thanks for noticing, Simon Bridge. It was inspired by your excellent comments along with the others.

 

[Dale]

This afternoon I walked out in the lab

Excellent post! I have linked to it from the FAQ.

https://www.physicsforums.com/showthread.php?t=536289

 

[bobc2]

Got to thinking that there is no way the X-axis (longitudinal) accelerometer should respond with an initial negative going pulse, so double checked the polarity and found that the plot of Gx vs. time is correct as plotted. There was no error in the orientation of the accelerometer after all. Sorry for first sorry.
---bobc2

 

[russ_watters]

Awesome: people keep asking to see that test. Nice to see it done.

 

[bobc2]

Young's Modulus from Velocity

The boss walked by my office a couple of times casting puzzling looks in my direction, so I decided to do the next test at home (now, with the apparatus set up in the living room, my wife is giving me puzzling looks). I used a solid cylindrical aluminum bar, 36”-long and 0.49” diameter. Using a miniature hammer with a really small force transducer (incredible technology), it was possible to produce a force pulse of just 90 micro-second duration. The main reason for repeating the experiment with the aluminum rod was to allow a measurement of Young’s Modulus for this particular aluminum alloy (didn’t want to mess with the cross-section area measurement for the extrusion used previously—and also have more confidence working with a solid circular cross-section). The velocity equation for a longitudinal elastic wave in a solid is

v = SQRT(E/r) where E is Young's modulus (psi) and r is mass density (lbm/in^3)

The rod was weighed and volume calculated, giving a weight density of 0.0998 lb/in^3, or
2.5828 x 10^-4 lbm/in^3. From the stress pulse travel time shown in the data plotted below and the 36 inch rod length, the velocity in aluminum (our particular alloy) is 213,018 in/sec (17,751 ft/sec). From the above equation we have for the Young’s modulus:

E = (mass density) x (velocity^2)

E = 11.72 x 10^6 psi

This value is on the high end of the range for aluminum alloys. A popular alloy, 2014 T-6, is 10.6 x 10^6 psi.

 

[bobc2]

Resonance Frequencies

Appologies for dragging this out (and straying further from special relativity)--but just wanted to close it out with a presentation of the resonance frequencies and vibration patterns induced with the hammer impact. A frequency response function (FRF) has been computed for the longitudinal vibration response and the transverse vibration response. The FRF is formed as the ratio of the Fourier transform of acceleration-time divided by the Fourier transform of the Force-time. The resonance frequencies correspond to the peaks in the FRF plot. Longitudinal standing wave patterns are associated with the longitudinal resonances and transverse vibration patterns are associated with the transverse resonance frequencies. The FRF was computed over a 0.32 sec time period with 16,384 points sampled. The maximum frequency available in the Fourier transform is 1/2 of the 51.2 KHz sample rate. The frequency resolution corresponds to one cycle covering the 0.32 second time period (3.125 Hz). Notice we have a kind of uncertainty principle here--to locate one cycle of oscillation in a precise small time period means we must accept a large uncertainty in the frequency (dF = 1/T).

 

[Simon Bridge]

This experiment may warrant a more formal workup to be placed elsewhere.

The only niggle I'd have with it is that it's a bit black-boxey - but that cannot be avoided on this scale.

It is pretty much everything a scientific demonstration needs to be - including warts-and-all data-sets ... which is why it lends itself so readily to further analysis. (I like the first data set better for demonstration since it is messier .. but the whole example lends itself to a discussion lesson from senior high level upwards.)

Anybody can reproduce the experiment - or just reality-check it against stuff they have - so there is a high level of confidence in the outcomes. Considering the amount of pseudoscience that comes my way, it's great to have an unambiguous example.

 

[bobc2]

Einstein's Book

Thanks, Simon Bridge. My favorite is the second example, because Einstein's relativity book on the coffee table was caught in the photo. (Trying to stay on topic?)