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

In summary, the vibration in a string is caused by tension force, resulting from the net electrostatic attraction between particles in a solid when it is deformed. Nodes in the string are stationary and transmit movement to string masses on either side by creating tension. The force of tension is a vector and the theory of small oscillations assumes it does not vary in magnitude. Energy is carried in both directions by two progressive waves, which add up to a standing wave.
  • #1
bob900
40
0
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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  • #2
The rope has to have some tension before you start waggling it.

A completely slack string will not oscillate.

Try it and see.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 

1. How do nodes on a string produce tension?

Nodes on a string produce tension through the transfer of energy. When a force is applied to one end of the string, this energy travels along the string and is eventually stopped or reflected at the other end. This stopping or reflection creates a tension force at the nodes, which are points along the string that do not move.

2. Why do nodes on a string stay stationary?

Nodes on a string stay stationary due to the principle of superposition. This means that when two waves meet at a point, their amplitudes add together to create a new wave. At the nodes, the amplitudes of the two waves cancel each other out, resulting in no movement at that point.

3. Can nodes on a string move?

While nodes on a string generally stay stationary, they can move under certain conditions. For example, if the string is not perfectly fixed at the nodes, they may be able to move slightly. Additionally, if the string is vibrating at a high enough frequency, the nodes may appear to move due to the rapid changes in amplitude.

4. How does the number of nodes affect tension on a string?

The number of nodes on a string does not directly affect the tension. However, the distance between nodes can indirectly affect tension by changing the frequency of the string's vibration. A string with more nodes will have a higher frequency, resulting in a higher tension force.

5. Can tension be created without nodes on a string?

Yes, tension can be created without nodes on a string. Tension is created whenever a force is applied to a string, regardless of the presence of nodes. Nodes are simply points where the tension force is equal and opposite on either side, resulting in a stationary point on the string.

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