How do transverse waves propagate through a string?

[Deshen]

Hi, Can anybody explain how by giving an vertical impulse to a string you can cause a transverse wave. What is confusing me is that you just give the string an impulse upwards, where does the energy transferr horizontally come from? By picturing that all the Points of the strings are connected you can realize that if one part moves the adjoining part also has to move. But how does this work in more detail?

 

[Simon Bridge]

Hi, Can anybody explain how by giving an vertical impulse to a string you can cause a transverse wave. What is confusing me is that you just give the string an impulse upwards, where does the energy transferr horizontally come from? By picturing that all the Points of the strings are connected you can realize that if one part moves the adjoining part also has to move. But how does this work in more detail?

What do you mean more detail? That's exactly how it happens!

When you pull on one bit of the string, that bit pulls on the bits close by and so on.
The fine details depend on how the string is made - i.e. twine is a lot of twisted fibers - when you pull on it the twist gets tighter, scrunching up the fibers. When you let go, the fibers push the string back to it's full thickness forcing it to return to its start shape, momentum means it passes through that shape, and losses mean that the vibrations eventually die down.

 

[Deshen]

Okay thanks, so all there is to analyze the movement of the string if you give it a wiggle is the tension that one part of the string places on the next? Let's say you just picture the string as an infinite set of points connected to each other. Is it possible to answer the question of how high particle 1 has to move vertically up before particle 2 gives away from the tension between the particles and start to move up? Because particle 2 does not move up right away when particle 1 moves up, it has to build up tension first right?

 

[Simon Bridge]

Lets say you just picture the string as an infinite set of points connected to each other.

Yep - the classical model for a string is to picture it as a lot of very small point masses m connected by massless ideal springs with spring constant k.

You can see that if you lifted one of the masses, that action lifts the other masses and also stretches the springs.
[Left alone, the string also sags slightly in the middle.The smaller k, and the applied tension, the bigger the sag.]

All the wave rules that you are learning can be derived from this model just by considering how pulling on one mass pulls on the others through the springs.

It's the same with longitudinal waves, except you displace a mass "sideways" along the string instead.

It's easier to see if you look at finite numbers of masses first and build up.

 

[Deshen]

Thank you very much, that is really helpful!

 

[Simon Bridge]

No worries :)

 

[sophiecentaur]

The reason that all waves occur is, basically, Delay. It takes time for an effect in one place to have an effect somewhere else. If there were no delay (the string was infinitely rigid) there would be no wave.