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Wave Equation
Newton's second law
Assumptions
- Lossless
- Linear
- Flexible (no ``Stiffness'')
- Slope
Example One-Dimensional Waveguides
- Any elastic medium displaced along 1D
- Air column of a clarinet or organ pipe
- Vibrating strings
- Really need at least three coupled 1D waveguides:
(Typically 1 or 2 WG per string used in practice)
- Bowed strings also require torsional waves
(Typical: one waveguide per string [plane of the bow])
- Piano requires up to three coupled strings per key
- Two-stage decay
- Aftersound
(Typical: 1 or 2 waveguides per string)
Let's first review the finite difference approximation applied to the ideal string (for comparison purposes):
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Download WaveEquations.pdf
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