Wave equation visualiser

This app demonstrates one central idea from the one-dimensional wave equation:

$$ u_{tt}=c^2u_{xx}. $$

A starting shape does not merely sit still. In the zero-initial-velocity case, it splits into two equal travelling copies:

$$ u(x,t)=\frac12\phi(x-ct)+\frac12\phi(x+ct). $$

Use the sliders to see how the same formula explains snapshots, motion through time, and the PDE derivative check.