Much attention has recently been paid to musical sound
synthesis using partial differential equation models.
Compared to the conventional signal-processing approach,
the parameters in the PDE models have physical interpretation.
This enables appropriate parameter fitting and the design of
more realistic models.
The research on this approach is still at the beginning and
there remain many interesting mathematical problems.
In this talk, recent developments on piano simulations are
exemplarily presented. Some mathematical challenges are also
shown.