  We consider in this paper blow-up solutions of the semilinear wave equation
in one space dimension, with an exponential source term. Assuming that initial
data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times
L^{\infty}$, we derive the blow-up rate near a non-characteristic point in the
smaller space, and give some bounds near other points. Our result generalize
those proved by Godin under high regularity assumptions on initial data.
