State space of a standing wave?

[pliep2000]

Lets say a state is defined by the minimal amount of independent variables to completely describe a system.
One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states.

Consider the very simple case of a standing wave in string where f₁, f₂ etc are the fundamental and the harmonics.

Question: Could one define a 'state-space' of the frequencies f₁, f₂ etc.?

 

[olivermsun]

Doesn't the original concept behind "phase space" pretty much come from wave/harmonic oscillator motions?

 

[pliep2000]

Do i interpret your answer correctly as: yes probably?

 

[olivermsun]

Well, maybe you can think of it this way:
Suppose you were to write down a governing equation for the motion of the standing wave in a string. What would such an equation look like?