Are Pendulum Waves Truly Waves Without Physical Connections?

[DaTario]

Hi All,

I use to teach wave theory and I like to discuss the example of pendulum waves, which is easy to find at internet,

for instance, ).

My question has to do with stating that this pendulum waves are not waves, for there is no physical connection between the oscillators, although there is no matter transport involved. In my explanation I stress the point that a true wave must have some kind of physical connection which is responsible for providing typically strong correlations between neighbor parts of the system.

Is this idea correct ?

Best wishes,

DaTario

 

[Dale]

I would say that a wave is something which obeys: $\frac{\partial^2}{\partial t^2}f=c^2 \frac{\partial^2}{\partial x^2}f$

The pendulum wave doesn't seem to do that.

 

[Vanadium 50]

I stress the point that a true wave must have some kind of physical connection which is responsible for providing typically strong correlations between neighbor parts of the system.

I don't know if I would use that. Look at an AC current in a wire - the individual electrons are only weakly coupled, as evidenced by their small drift velocity. I like Dale's answer.

 

[DaTario]

Thanks for the answers,

DaleSpan, you gave the north with a clean definition, but is it really simple like this? Bellow I present some provocative reasoning on this point...

Concerning the pendulum wave, I agree with you, but considering the video attatched at times from 0:29 to 0:34, one is tempted to say that a wave solution may be a good approximation. Not to mention that if one build an array of, say, twenty independent and identical pendula, with an appropriate initial condition, a wave like patern will show up. I would say, before the present discussion, that their behavior do not constitute a wave manifestation. Essencially because the components are completely independent of each other.

Vanadium 50, if a man carries, horizontally, at constant speed and over his head, a roof tile like the one shown bellow

this would correspond to a nicely defined plane wave, but this would not be a wave, would it?

Another question: Is the AC current phenomenon, in classical electrodynamics, a wave like manifestation?

Best wishes,

DaTario

 

[sophiecentaur]

There are two distinct instances where the maths of wave propagation apply. Some waves actually carry energy and others do not. That is a very relevant distinction but it doesn't mean that a Mexican Wave is not a 'real' Wave. One shouldn't get too wound up with classifying things too rigidly. It tends to add confusion and not resolve it.
If you happen to have a teacher for whom that is important then you are just stuck with it and you have to indulge them - but you can move on, eventually.

 

[Vanadium 50]

I would call it a wave, since you can write the wave equation to give you the height of the roof tile at a given position and time. But we're getting to the point of semantics and any minute now someone will talk about "real waves" and then later "really real waves". These seldom lead anywhere good.

 

[Dale]

DaleSpan, you gave the north with a clean definition, but is it really simple like this?

I tend to prefer simple clean definitions. In the end, I don't think that the label means too much. If a set of pendulums or a corrugated sheet gets classified as a "wave" because of the definition, then does that really matter? It doesn't change what they are.

However, if I were interested in making a more complicated definition of a wave then I would still start with the wave equation, but I would also set some constraints on the boundary conditions. Such constraints could enforce that things called "waves" exhibit properties like reflection and transmission, and thereby exclude pendulum waves and corrugated sheet waves.

 

[DaTario]

I tend to prefer simple clean definitions. In the end, I don't think that the label means too much. If a set of pendulums or a corrugated sheet gets classified as a "wave" because of the definition, then does that really matter? It doesn't change what they are.

However, if I were interested in making a more complicated definition of a wave then I would still start with the wave equation, but I would also set some constraints on the boundary conditions. Such constraints could enforce that things called "waves" exhibit properties like reflection and transmission, and thereby exclude pendulum waves and corrugated sheet waves.

Do you think that using the idea that in waves we do not have matter transport is a good approach?

Best wishes,

DaTario

 

[Dale]

Do you think using the idea that in waves we do not have matter transport is a good one?

That would exclude the corrugated sheet wave but not the pendulum wave.

I just don't think that it is important. If you have a physical law that you can show leads to the wave equation under relatively general conditions, then you have something physically interesting which you may choose to label as a "wave". If you have something that also leads to the wave equation but only under some specific and restrictive conditions, then you have something much less interesting which you may or may not also choose to label as a "wave". I don't think that choosing to label the "coincidental" waves and the "general" waves with the same label detracts from the general waves nor does it add additional stature to the coincidental waves.

 

[DaTario]

That would exclude the corrugated sheet wave but not the pendulum wave.

I just don't think that it is important. If you have a physical law that you can show leads to the wave equation under relatively general conditions, then you have something physically interesting which you may choose to label as a "wave". If you have something that also leads to the wave equation but only under some specific and restrictive conditions, then you have something much less interesting which you may or may not also choose to label as a "wave". I don't think that choosing to label the "coincidental" waves and the "general" waves with the same label detracts from the general waves nor does it add additional stature to the coincidental waves.

I agree that the pendulum wave are not filtered by this criteria. In order to do so I was using the criteria of "coupling" or "non-independence". But I guess I understand your point. The main reason which led me to this discussion was my attempt to clearly define oscillations and waves to my students.

Thank you.

Best wishes,

DaTario

 

[DaTario]

I was considering this discussion finished with reasonably good arguments in favor of not going to far with classifications. But an idea appeared and it seems that it will be nice to add this. According to classical notions, the movement of translation of a rigid body may be seen as a geometrical shape with constant velocity. Thus, with appropriate definition of the surfaces which demark the shape of the body, we could say that the inertial movement of a rigid body fits in the definition of a wave for it may be described by functions of the form f(r - vt) and f(r + vt).

Is it correct ?

Best wishes,

DaTario