Physics · University
Wave equations, normal modes and boundary conditions · revision notes
The ideal one-dimensional wave equation is ytt=c²yxx. The parameter c is propagation speed for this nondispersive model.
Key ideas and conditions
Wave equation
The ideal one-dimensional wave equation is ytt=c²yxx. The parameter c is propagation speed for this nondispersive model.
Boundary data
Fixed endpoints require zero displacement at each end. They permit standing waves whose spatial wave numbers are nπ/L.
Superposition
Solutions of a linear homogeneous wave equation can be added. The result need not resemble one single travelling sinusoid.
Energy
A standing wave can have stationary nodes while its material elements oscillate. Node locations should not be confused with material travelling at wave speed.
Explain without looking
- At a node of an ideal standing transverse wave, what happens to displacement?
- State why an ideal string model may fail at very large displacements.
Further reading and review references
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