[amelius]

This simulates the displacement of the string, but the hard part seems to be to simulate how that string affects the air and induces a sound.

[IsTom]

Considering that there's a pickup in the model, air doesn't matter. And in typical string instruments the loud part you mostly hear is coming from sound box through bridge, not from strings themselves.

[lagrange77]

Why is that harder? Because require solving PDEs, aren't they?