Date: Wed, 8 Feb 2012 11:45:27 -

Author: Paul Nord

Subject: Re: Waves on a heavy chain - What should the wave speed be?

Post:


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Cliff,

Got it. The low-resolution image makes it difficult to see the chain in =
some places. At first glance it appears that you are seeing the same =
thing that I see. The wave initially moves slowly and then speeds up =
before slowing down again near the floor. It may even speed up and slow =
down a couple of times.

Paul


On Feb 8, 2012, at 9:26 AM, Cliff Bettis wrote:

> Paul,
> =20
> I emailed it separately. It is 16 MB in size so I hope it doesn=92t =
clog your interweb pipe thingies ;-)
> =20
> Cliff
> =20
> From: tap-l-owner@lists.ncsu.edu [mailto:tap-l-owner@lists.ncsu.edu] =
On Behalf Of Paul Nord
> Sent: Wednesday, February 08, 2012 9:16 AM
> To: tap-l@lists.ncsu.edu
> Cc: Paul Nord
> Subject: Re: [tap-l] Waves on a heavy chain - What should the wave =
speed be?
> =20
> Cliff,
> =20
> Do you have a video?
> =20
> Your summer intern project sounds interesting. Let me know how I can =
help.
> =20
> Paul
> =20
> =20
> On Feb 8, 2012, at 8:18 AM, Cliff Bettis wrote:
>=20
>=20
> Paul,
> =20
> I was using a heavier chain and did have mine firmly fixed at the top =
end. I also tried a couple of different ways of exciting the chain. I am =
thinking that this might make for a nice project for a summer high =
school inter. If you would like to collaborate let me know.
> =20
> Cliff
> =20
> From: tap-l-owner@lists.ncsu.edu [mailto:tap-l-owner@lists.ncsu.edu] =
On Behalf Of Paul Nord
> Sent: Tuesday, February 07, 2012 3:44 PM
> To: tap-l@lists.ncsu.edu
> Cc: Paul Nord
> Subject: Re: [tap-l] Waves on a heavy chain - What should the wave =
speed be?
> =20
> Cliff,
> =20
> I think that we're on the same page here. There is some analogy to =
ocean waves on the shore. The wave front slows on a slanted beach and =
the wave itself lowers the water in front of it.
> =20
> We're seeing the tension in the chain changing dramatically as it =
bounces up and down. And this bouncing is coupled to the wave. Is it =
possible to disentangle these two effects on a hanging chain? Most of =
the things I can think of to try would result in a smaller wave. This =
might not be observable on video. Even here we can see that the energy =
in a small wave at the top results in a large whip-like motion at the =
bottom. =20
> =20
> Ideas:
> * Leaving a coil of free chain at the bottom might change =
the effect.
> * Fixing the top more rigidly to the ceiling would =
eliminate the sway in the support
> * A heavier chain
> * A longer chain
> * starting the motion from the bottom
> * could try driving a resonance to see a standing wave
> * could try to match the frequency of the "bouncing" wave =
and the transverse wave
> ... or do they feedback on each other making =
the system inherently chaotic?
> =20
> Paul
> =20
> =20
> =20
> On Feb 7, 2012, at 1:34 PM, Cliff Bettis wrote:
>=20
>=20
>=20
> Paul,
> =20
> I haven=92t digitized our video yet but it looks like what you saw. I =
am thinking that the tension gradient in the chain is responsible: the =
rear part of the pulse over takes the slower moving leading edge as the =
wave goes down the chain making the group velocity faster than the local =
wave speed. I want to think about that more before I really accept it. =
If that=92s so, it might make for a nice demonstration of group =
velocity.
> =20
> Cliff
> =20
> From: tap-l-owner@lists.ncsu.edu [mailto:tap-l-owner@lists.ncsu.edu] =
On Behalf Of Paul Nord
> Sent: Monday, February 06, 2012 5:21 PM
> To: tap-l pira
> Cc: Paul Nord
> Subject: [tap-l] Waves on a heavy chain - What should the wave speed =
be?
> =20
> Here's the video:
> Waves on a Heavy Chain - YouTube
>=20
> Can you explain it?
> =20
> There is a curious effect here. You would expect the wave speed on a =
chain to be proportional to the tension. If the end of the chain is =
hanging free the tension will change from a maximum at the top to nearly =
zero at the bottom. You would expect a fast wave speed at the top which =
then slows down as it reaches the bottom.
>=20
> Attempting to measure this we observe that the wave seems to speed up =
and slow down a couple of times. The wavelength is compressed as it =
reaches the bottom. And it's possible that there are several waves =
traveling at once. The pileup may produce the effect seen here.
>=20
> Another explanation is that the tension changes dramatically as a =
compression wave first jerks the chain up and then drops it again. We're =
observing the transverse wave. Evidence of a compression wave is seen =
only by the position of the free end of the chain.
> =20
> Paul


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Cliff,Got it. The =
low-resolution image makes it difficult to see the chain in some places. =
At first glance it appears that you are seeing the same thing that =
I see. The wave initially moves slowly and then speeds up before =
slowing down again near the floor. It may even speed up and slow =
down a couple of =
times.PaulOn Feb 8, 2012, at 9:26 AM, Cliff Bettis wrote:I =
emailed it separately. It is 16 MB in size so I hope it doesn=92t clog =
your interweb pipe thingies ;-)From: tap-l-owner@lists.ncsu.edu =
[mailto:tap-l-owner@lists.ncsu.edu] On Behalf Of Paul =
NordSent: Wednesday, February 08, =
2012 9:16 AMTo: tap-l@lists.ncsu.eduCc: Paul =
NordSubject: Re: [tap-l] Waves on a =
heavy chain - What should the wave speed =
be?Do you have a =
video?Your summer intern =
project sounds interesting. Let me know how I can =
help.On Feb 8, 2012, at 8:18 =
AM, Cliff Bettis wrote:I was using a heavier chain and did have mine firmly =
fixed at the top end. I also tried a couple of different ways of =
exciting the chain. I am thinking that this might make for a nice =
project for a summer high school inter. If you would like to collaborate =
let me know. On Behalf Of Paul =
NordSent: Tuesday, February 07, 2012 =
3:44 PMTo: Paul =
NordSubject: Re: [tap-l] Waves on a =
heavy chain - What should the wave speed =
be? Cliff, I think that we're on the same page here. There =
is some analogy to ocean waves on the shore. The wave front slows =
on a slanted beach and the wave itself lowers the water in front of =
it.We're seeing =
the tension in the chain changing dramatically as it bounces up and =
down. And this bouncing is coupled to the wave. Is it =
possible to disentangle these two effects on a hanging chain? Most =
of the things I can think of to try would result in a smaller wave. =
This might not be observable on video. Even here we can see =
that the energy in a small wave at the top results in a large whip-like =
motion at the bottom. Ideas: &=
nbsp; * Leaving a coil of =
free chain at the bottom might change the =
effect. &=
nbsp; * Fixing the top more =
rigidly to the ceiling would eliminate the sway in the =
support &=
nbsp; * A heavier =
chain &=
nbsp; * A longer =
chain &=
nbsp; * starting the motion from =
the bottom &=
nbsp; * could try driving a =
resonance to see a standing =
wave &=
nbsp; * could try to match the =
frequency of the "bouncing" wave and the transverse =
wave &=
nbsp; &nb=
sp; ... or do they feedback on =
each other making the system inherently =
chaotic?On Feb 7, 2012, at 1:34 PM, Cliff Bettis =
wrote:I haven=92t digitized our video =
yet but it looks like what you saw. I am thinking that the tension =
gradient in the chain is responsible: the rear part of the pulse over =
takes the slower moving leading edge as the wave goes down the chain =
making the group velocity faster than the local wave speed. I want to =
think about that more before I really accept it. If that=92s so, it =
might make for a nice demonstration of group =
velocity.From: tap-l-owner@lists.ncsu.edu On Behalf Of Paul =
NordSent: Monday, February 06, 2012 =
5:21 PMTo: tap-l =
piraCc: Paul =
NordSubject: [tap-l] Waves on a heavy =
chain - What should the wave speed =
be? Here's the video:Waves on a Heavy Chain - =
YouTubeCan you explain =
it?There is a curious effect here. You would expect the =
wave speed on a chain to be proportional to the tension. If the end of =
the chain is hanging free the tension will change from a maximum at =
the top to nearly zero at the bottom. You would expect a fast wave speed =
at the top which then slows down as it reaches the =
bottom.Attempting to measure this we observe that the wave seems =
to speed up and slow down a couple of times. The wavelength =
is compressed as it reaches the bottom. And it's possible that =
there are several waves traveling at once. The pileup may produce the =
effect seen here.Another explanation is that the tension =
changes dramatically as a compression wave first jerks the chain up and =
then drops it again. We're observing the transverse wave. Evidence =
of a compression wave is seen only by the position of the free end of =
the =
chain.

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