When analysing the wave equation $u_{tt} = c^2 u_{xx}$ in my PDE's module, I understand the 'domain of dependence' which is where the value $u(x_0,t_0)$ is only depends on the initial value of $x$ (at $t=0$) in the closed interval $[x_0 - ct_0, x_0 + ct_0]$ and so it forms a triangle on the $x\, \, t$ plane.
Can someone please explain, intuitively, what the 'domain of influence' is? This is apparently the upside down triangle on the $x \, \, t$ plane starting at point $(x_0, 0)$?
Thanks!