Undergrad State space of a standing wave?

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SUMMARY

The discussion centers on defining a 'state-space' for the frequencies of a standing wave in a string, specifically the fundamental frequency (f1) and its harmonics (f2, etc.). Participants explore the relationship between phase space concepts and wave mechanics, noting that the original idea of phase space is rooted in harmonic oscillator motions. The conversation emphasizes the importance of governing equations in describing the motion of standing waves, suggesting that such equations can effectively represent the state-space of these frequencies.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with phase space concepts in classical mechanics
  • Knowledge of harmonic oscillators and their governing equations
  • Basic principles of quantum mechanics and Hilbert space
NEXT STEPS
  • Research the governing equations for standing waves in strings
  • Explore the mathematical formulation of phase space in classical mechanics
  • Study the relationship between harmonic oscillators and wave functions
  • Investigate the application of Hilbert space in quantum mechanics
USEFUL FOR

Physicists, students of wave mechanics, and anyone interested in the mathematical modeling of wave phenomena and their applications in both classical and quantum contexts.

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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