A Variety of String Vibration Examples

There are some standard layouts which give various insights into the vibrations of a string, some of which will be discussed as examples.

1. uniform string with fixed ends,
2. uniform string with unrestrained ends,
3. two half-strings joined in the middle,
4. two half-strings with an impedance-matching joint,
5. a diatomic string - one with two masses alternating heavy, light,
6. a string with a point defect, say a discrepant mass,
7. a string with an insert larger than a point, of a different material,
8. a whip, with mass continuously varying from one end to the other.
9. a disordered string, whose masses and elastic constants are chosen at random from a probability distribution.