Animation of a standing wave formed by components from a free end

[pkc111]

TL;DR

What does an animation of a standing wave formation from its component travelling waves at a free-end look like?

This is not a homework question, it is for my understanding so please do not answer this question with a question.

I have found this great animated gif but it appears to be for a fixed end (notice wave inversions at the end). Has anyone seen a similar one for a free end?



Many Thanks

 

[A.T.]

I have found this great animated gif but it appears to be for a fixed end (notice wave inversions at the end). Has anyone seen a similar one for a free end?

The ends aren't "fixed", they just remain stationary for the resultant stationary wave, because they were chosen to be at its nodes.

 

[pkc111]

The ends aren't "fixed", they just remain stationary for the resultant stationary wave, because they were chosen to be at its nodes.

Nevertheless it would be the same animation for a blue wave reflecting from a fixed end creating the pink wave reflection, right?

 

[A.T.]

Nevertheless it would be the same animation for a blue wave reflecting from a fixed end creating the pink wave reflection, right?

What do you mean by "fixed end"? No point of the blue wave is actually fixed to a stationary position.

 

[kuruman]

Just put a red dot at a point one-quarter wavelength short of the “tied” end, omit showing the remaining string to the tied end and, presto, you have an animation of a standing wave with one end “free”.

 

[pkc111]

Wow..thank you that's what I needed

 

[sophiecentaur]

What do you mean by "fixed end"? No point of the blue wave is actually fixed to a stationary position.

I think you are being a bit minimalist about this. The solution to a wave equation is only plottable if the boundary conditions are known and the 'other wave' will only exist to give a standing wave if they are appropriate. A string, left to itself and untethered would not necessarily do what the animation shows. Convention assumes that either the end points are fixed or the resonator is constrained in some way - by a periodic driving force or the end effects such as the air resonating in an open ended tube.

Initial treatment of standing waves leaves out a lot - like the fact that there is a driving source and a loss mechanism. The sort of standing wave that's shown in typical animations ignores this. With no loss mechanism, the wave would build up in amplitude for ever. For a wave of constant amplitude, that loss must be included in the driver system.

 

[A.T.]

A string, left to itself and untethered would not necessarily do what the animation shows.

Who said it's a string? The blue and red could be water waves traveling in opposite directions.

 

[sophiecentaur]

Who said it's a string? The blue and red could be water waves traveling in opposite directions.

That would imply that there were other boundary conditions - defined somewhere else. You are trying to answer the OP question in terms that don't really fit the type of (concrete) question.
Either the wave is 'as shown' with two ends at the fixed points shown or the situation is too open ended to be worth discussing. If you think it's a 'bad' question then perhaps you could have asked for some clarification from the OP about what the diagram actually represents. I suspect the OP requires some help for that too, in order to relate it to real life (which is how we all start our Physics learning.)

 

[A.T.]

I suspect the OP requires some help...

The OP was apparently confused by the way the animation is cropped exactly at the nodes, but that was cleared up already.

 

[sophiecentaur]

The OP was apparently confused by the way the animation is cropped exactly at the nodes, but that was cleared up already.

I didn't read the OP that way at all. People don't ask that sort of question wanting a discussion of a mathematical function or an abstract concept. The animation was made to look pretty but does it really provide answers about physical waves? The fact that the OP has the term "Fixed ends" in it implies (to me, at least) that a physical answer is needed.
How may people look at standing waves in terms of two independent waves moving against each other? The model is of a wave reflected at each end, producing an interference pattern. If there is an 'open ended tube' or equivalent, there is a 100% reflection of the wave at the (antinode) boundary.

 

[A.T.]

I didn't read the OP that way at all.

I read post #6 as problem solved.

But god forbid a PF thread ends after just 6 posts, so let's talk about all the things that the animation doesn't show. Who made these waves? Where are they coming from and where are they going to?