How do nodes on a string produce tension if they are stationary?

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Discussion Overview

The discussion revolves around the mechanics of tension in a vibrating string, particularly focusing on how tension is produced at stationary nodes within the context of standing waves. Participants explore the relationship between tension, movement, and energy transmission in oscillating strings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that tension in a string arises from the electrostatic attraction between particles when the string is deformed, questioning how tension can exist at stationary nodes where no movement occurs.
  • Another participant asserts that a string must have some initial tension to oscillate, emphasizing that a slack string will not produce oscillations.
  • A follow-up post clarifies that while tension is necessary for oscillation, the participant is specifically inquiring about the transmission of force through stationary nodes during oscillation.
  • It is noted that energy does not pass through a node in a standing wave, which is characterized by the stationary nature of nodes, yet energy is still flowing past each node due to the interaction of progressive waves.
  • One participant mentions that the tension in the string varies during oscillation, indicating that it can range from zero to a maximum value at different points in the cycle.

Areas of Agreement / Disagreement

Participants express differing views on the nature of tension and energy transmission at stationary nodes, with no consensus reached on how these concepts interact within the framework of standing waves.

Contextual Notes

The discussion highlights assumptions regarding the behavior of tension in oscillating strings and the definitions of energy transmission in the context of standing waves, which remain unresolved.

bob900
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The vibration in a string is caused by the tension force on point masses inside the string :

23ih4wg.png


The tension force itself results from "the net electrostatic attraction between the particles in a solid when it is deformed so that the particles are further apart from each other than when at equilibrium" (source).

But a node in the string (when two waves cancel each other) is stationary. To transmit movement to string masses on either side of the node, shouldn't the node have to move (deform) to produce tension?

For example, in the following picture

2qsxao3.png


At node B, the red wave traveling to the right, has to create tension to transmit its upward to the string mass immediately to the right of B. Analogously, the green wave has to create tension to transmit its downward movement to the string mass on the left of B. But if the mass element at B itself does not move, how are these tension forces produced?
 
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The rope has to have some tension before you start waggling it.

A completely slack string will not oscillate.

Try it and see.
 
Studiot said:
The rope has to have some tension before you start waggling it.

A completely slack string will not oscillate.

Try it and see.

I know that you need tension to start oscillating. What I'm asking is that when it is oscillating already, how is force/tension/anything transmitted through the stationary nodes, if they don't move at all? On a microscopic, electrostatic force level.
 
What I'm asking is that when it is oscillating already, how is force/tension/anything transmitted through the stationary nodes,

As I indicated a vibrating string is already under tension throughout.

Energy does not pass a node. That is why this type of wave is called a stationary (or standing) wave.

The force of tension is a vector.
The theory of small oscillations assumes the tension does not vary in magnitude along the string, just in direction.
 
Studiot said:
As I indicated a vibrating string is already under tension throughout.

Energy does not pass a node. That is why this type of wave is called a stationary (or standing) wave.

The force of tension is a vector.
The theory of small oscillations assumes the tension does not vary in magnitude along the string, just in direction.

Energy is flowing past each node - it's just that energy is being carried in both directions by two progressive waves, which add up to a standing wave. You need to remember that the (extra) tension in the string varies from zero to a maximum during each half of the oscillation.
 

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