5.2 Comparison with D'Alembert
The example problem of the previous section was also solved in chapter
4 using D'Alembert. It is interesting to compare the
The separation of variables solution took the form:
Some of its nice features are:
- It shows the natural frequencies (tones) to be ,
- It shows the energy, so the strength, of each harmonic.
- The method is not restricted to the one-dimensional wave
The D’Alembert solution took the form
Some of its nice features are
- The pressure can be evaluated at any point without doing infinite
- It shows how wave fronts propagate.
- It shows regions of influence and dependence.
In short, each method has its advantages and disadvantages.