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
   fxx + fyy  = -c2 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
    fxx + fyy  = ftt
is that now we have
    ftt = - c2 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