Differential Equations › Section I · Partial differential equations › Topic I.8
The vibrating string
A guitar string fixed at both ends sounds a definite note, along with fainter higher notes that give it its character. Solving the wave equation by separation of variables shows exactly where those notes come from and how the way a string is set moving decides their mix.
In this topic
- The problem to solve
- The normal modes
- Frequencies and harmonics
- Matching both initial conditions
- Worked example: a guitar string
- Worked example: a string plucked at its centre
- Worked example: a struck string
- Timbre: how the start shapes the sound
- Standing waves from travelling waves
- Common mistakes to avoid
- Key takeaways
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