The Youtube video by
the Physics girl explains some cool things about partial differential equations.
Singing plates - Standing Waves on Chladni plates. These patterns are level curves

f(x,y) = c

of functions f(x,y) which satisfy the Laplace type equation

f_{xx} + f_{yy} = -c^{2} f

which is a partial differential equation. The c to the right is called an
eigenvalue. The function f represents the height of the plate. It is an eigenmode.
The sand on the plates moves to the level curve f(x,y) = 0.
The cool connection with the wave equation

f_{xx} + f_{yy} = f_{tt}

is that now we have

f_{tt} = - c^{2} f

which is solved by f(x,y,0) cos(c t) for example. At a fixed location, the plate now
oscillates up and down. But at the places where the initial function f(x,y,0) is zero,
the plate does not move. This is where the sand rests