  We consider the global existence and blow up of solutions of the Cauchy
problem of the quasilinear wave equation: $\partial_{t}^2 u = \partial_x(c(u)^2
\partial_x u)$, which has richly physical backgrounds. Under the assumption
that $c(u(0,x))\geq \delta$ for some $\delta>0$, we give sufficient conditions
for the existence of global smooth solutions and the occurrence of two types of
blow-up respectively. One of the two types is that $L^{\infty}$-norm of
$\partial_t u$ or $\partial_x u$ goes up to the infinity. The other type is
that $c(u)$ vanishes, that is, the equation degenerates.
