String synthesis has been the subject of a lot of research. In its simplest form, one can model the displacement of a taut string by means of the 1D wave equation. Direct numerical simulation can be employed to simulate a class of phenomena not included in the wave equation alone. Typical examples includes nonlinear contact and collision forces, as well as large geometrical stretching. In the video, a colliding mass (a finger, or a pick) sets a string into motion. Notice the presence of the rigid curved barrier underneath. The blue and red squares are movable pickups, and incredibly organic simulations can be realised. Listen to the example here below ...

Bouncing sphere colliding with a string. The string collides as well with a barrier underneath.

Bouncing Sphere

NONLINEAR STRINGS
A nonlinear string model yields realistic and organic sound synthesis. Here are examples including two stiff strings connected together nonlinearly. The string-plate system is also pretty interesting.

String-String 1
String-String 2
String-String 3
String-Plate 1
String-Plate 2

In this video, a Bach sonata is played using a network of nonlinearly interconnected strings. I steered clear of simulating a given instrument here (e.g. a harpsichord), as a set of nonlinearly interconnected strings is considered instead. However, one can appreciate the sympathetic resonances and double-decay envelopes, all needed for realistic synthesis.