Conceptual Standing Wave Question

[MyNewPony]

Homework Statement

If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat.

What has happened to the energy of the wave at those instants?

The Attempt at a Solution

I'm assuming that nothing has happened to the energy. At that instant in time, even if the displacement of the wave is zero, it does not imply that the wave is stationary, therefore, it still has a velocity. Thus, there remains kinetic energy in the wave.

Am I on the right track?

 

[alphysicist]

Hi MyNewPony,

Homework Statement

If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat.

What has happened to the energy of the wave at those instants?

The Attempt at a Solution

I'm assuming that nothing has happened to the energy. At that instant in time, even if the displacement of the wave is zero, it does not imply that the wave is stationary, therefore, it still has a velocity. Thus, there remains kinetic energy in the wave.

Am I on the right track?

Yes, that sounds right to me.

 

[nlightner]

Yes, you are on the right track. The energy of a standing wave does not change at any point in time, including the instants when the string is flat. This is because the energy of a standing wave is a combination of potential energy, due to the tension in the string, and kinetic energy, due to the motion of the string. Even though the string may appear to be flat at certain instants, it is still moving and therefore has kinetic energy. The potential energy also remains constant throughout the standing wave. Therefore, the energy of the wave remains the same at all instants in time.