Energy stored in a standing wave

[kasse]

I'm trying to find the energy stored in a standing wave on a string. My book suggests to find the maximum kinetic energy for a small segment of the sting, and then integrate over the string.

I find this strange, because the kinetic energy is certainly not at its maximum all over the string at the same time. Can anyone explain?

Edit: I've been thinking for a while now. Maybe it's because when the kinetic energy is not at its max, the rest of the total energy of the segment is stored as potential energy, and that the kinetic energy is at its max when the potential energy is zero?

 

[Pere Callahan]

That is true.