Differential Equations › Section I · Partial differential equations › Topic I.2
The wave equation
Pluck a guitar string and its shape changes in space and time, but instead of fading smoothly like a temperature profile it swings back and forth. Newton's second law, applied to each tiny piece of the string, gives the wave equation that describes this motion.
In this topic
- A stretched string
- The modelling assumptions
- Newton's second law on a small piece
- The wave equation
- Worked example: wave speed on a string
- Reading the equation
- Initial and boundary conditions
- Travelling waves: d'Alembert's solution
- Worked example: checking a travelling pulse
- Worked example: a pulse released from rest
- Common mistakes to avoid
- Key takeaways
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