I State space of a standing wave?

AI Thread Summary
A state can be defined by the minimum independent variables needed to describe a system, exemplified by the (q,p)-phase-space for point masses and Hilbert-space for quantum states. The discussion explores the possibility of defining a 'state-space' for frequencies in a standing wave, such as fundamental and harmonic frequencies. It suggests that the concept of phase space is indeed related to wave and harmonic oscillator motions. The conversation leads to the consideration of writing a governing equation for the motion of a standing wave in a string. This highlights the connection between frequency states and their mathematical representation in physical systems.
pliep2000
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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.?
 
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Doesn't the original concept behind "phase space" pretty much come from wave/harmonic oscillator motions?
 
Do i interpret your answer correctly as: yes probably?
 
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?
 
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