What happens when you pluck a guitar string?

[olivermsun]

In the first video for example, doesn't the kink lose it's kinkiness and just a general pattern of up and down oscillation emerge? Or is that still a traveling wave, only that the kink is smoother and less kinky?

The kink slowly becomes a bump but continues to travel back and forth between the ends of the string.

A standing wave doesn't travel, it stands still.

 

[chingel]

The kink slowly becomes a bump but continues to travel back and forth between the ends of the string.

A standing wave doesn't travel, it stands still.

There is still a moving wave near the end of the video, but it seems to me there is some general up and down moving as well happening when the bump is on the other side. Doesn't that mean that there are standing waves evolving? Isn't it the case that the bump is just an illusion created by the sum of the standing waves of the harmonics?

 

[sophiecentaur]

What's in a name? Travelling / standing. The way you would recognise a 'standing wave' would not be obvious if there were multiple waves. What would you expect to see? Certainly not a simple set of nodes and antinodes. But the maths tells you that you will only get combinations of the normal modes. They are the only ones that can exist, I think, so you need to think more layerally and decide what you would look for. Would it be obvious?

 

[chingel]

I think that if the vibrating string is actually the result of a sum of standing waves, the big kink (traveling wave) makes it's roundtrip at the speed of the fundamental, but if the string is actually divided into nodes, the edges (every part actually I think but the edges are easier to discern when the big kink is on the other side) would wobble up an down before the big kink arrives, because the frequency of the nodes is several times higher. I am not too sure but I think that is what I see happening in the high speed videos towards the end.

I am probably sounding stubborn, but I still don't understand why/how does the string divide itself into nodes, why does it vibrate at multiple frequencies simultaneously, if it does so at all?

 

[sophiecentaur]

I think you need to ignore what the movies appear to tell you because they are not ideal. The high frequencies are lost too soon for you to see the pattern - and what pattern would you actually expect to see?
You have to believe the sums, which tell you the only possible solutions to the wave equation. (That could be your problem?)
All the possible modes can exist at once (with respective levels according to the start shape) because superposition is 'allowed'. Intuition can be a problem with this sort of thing an you may need to FIGHT it. ;-)

 

[chingel]

I think you need to ignore what the movies appear to tell you because they are not ideal. The high frequencies are lost too soon for you to see the pattern - and what pattern would you actually expect to see?
You have to believe the sums, which tell you the only possible solutions to the wave equation. (That could be your problem?)
All the possible modes can exist at once (with respective levels according to the start shape) because superposition is 'allowed'. Intuition can be a problem with this sort of thing an you may need to FIGHT it. ;-)

But the overtones are there for as long as the string is vibrating, otherwise wouldn't it's timbre change to a sine wave? I think there should be some vibrating nodes distinguishable from the string if there are nodes, because they vibrate multiple times faster than the big bump is moving.

Do you mean the sums that make up the shape of the bump on the string? But that gives me again the question that the sums making up the shape aren't the same sums making up the pressure waves.

Why does a string decide, when it is pulled to the side, alright, I'll divide myself at this point and make the part on the other side move up while I'm going down and the opposite. What makes it behave like that?

 

[sophiecentaur]

The timber of the attack is very different from that of the sustain.
Each piece only "knows" to follow the net force on it and it has a certain mass. The boundary conditions tell you what each bit will do. Why do you demand that the problem must be solved in 'your way'? You could do a simulation, I suppose, which would look at each element in turn. But, as an analytical solution exists, why not use it?

 

[chingel]

The timber of the attack is very different from that of the sustain.
Each piece only "knows" to follow the net force on it and it has a certain mass. The boundary conditions tell you what each bit will do. Why do you demand that the problem must be solved in 'your way'? You could do a simulation, I suppose, which would look at each element in turn. But, as an analytical solution exists, why not use it?

How and what forces apply to make nodes happen? How do the boundary conditions tell the nodes what to do?

I am just trying to understand why/how does a string divide itself into nodes.

 

[sophiecentaur]

Assuming that you accept that multiple modes can exist (superposition) then you can consider each overtones separately.
Every time a wave travels towards an end, a wave will be reflected and it will be in antiphase. One half wavelength away from the end, the incident and reflected waves will again be in antiphase. This is a node and part of an interference pattern, on ANY string and for ANY wave. If the string happens to be an integer number of half waves long the interference patterns for both ends coincide and you get resonance.

 

[chingel]

Do I understand correctly that if I only consider one overtone, when the wave is half the wavelength away from the end, the string is straight for that overtone?

How do the interference patterns give me the resonance? Are there waves on both ends at the same time and they need to be in sync? What would happen if the string isn't a multiple of half waves long, how would they interfere? Why do the overtones appear in the first place?

 

[sophiecentaur]

How could the string be straight all the time. Do you actually have a proper picture in your mind of what a standing wave looks like over time?

 

[sophiecentaur]

How do the interference patterns give me the resonance? Are there waves on both ends at the same time and they need to be in sync? What would happen if the string isn't a multiple of half waves long, how would they interfere? Why do the overtones appear in the first place?

You are still having problems, aren't you?
You need to appreciate that this all takes time to establish. Enough time for waves of the highest frequency to have traveled back and forth and to have formed an interference pattern.
A stable interference pattern cannot be established for any waves but those allowed modes _ the overtones and fundamental.
When you get down to it, you have a system that can only vibrate at certain frequencies so it can't oscillate any other way if it is left to itself.
Imagine a mass on a spring. There is only one frequency for it to vibrate at once you let it go. Now try adding another mass, hanging on the bottom on another spring. More complex but you could still only get vibrations at a limited set of natural frequencies. The masses will go up and down and together and apart. You could choose any setup to start with and you'd only get those normal modes of vibration. (Violent disturbance so they collide is not allowed, of course) I don't think you could argue with it so far.
A taught string is just another system that can oscillate in certain modes. Once it's been let go it cannot vibrate in any other way but in a combination of these modes. Before you try to argue against the why's and wherefores of traveling waves, nodes and standing waves you just HAVE TO accept the above.
This means there can only be certain waves on the string. These have to have lengths which actually fit into the space between the ends of the string.

I think it's time for you to do more thinking, reading round and not to keep coming back more questions. You need to cut the apron strings.
:-)