  In this paper we continue to study the shock formation for the
$3$-dimensional quasilinear wave equation \begin{align}\label{main eq}
-(1+3G"(0)(\partial_{t}\phi)^{2})\partial^{2}_{t}\phi+\Delta\phi=0,\tag{\textbf{$\star$}}
\end{align} with $G"(0)$ being a non-zero constant. Since \eqref{main eq}
admits global-in-time solution with small initial data, to present shock
formation, we consider a class of large data. Moreover, no symmetric assumption
is imposed on the data. Compared to our previous work [18], here we pose data
on the hypersurface $\{(t,x)|t=-r_{0}\}$ instead of $\{(t,x)|t=-2\}$, with
$r_{0}$ being arbitrarily large. We prove an a priori energy estimate
independent of $r_{0}$. Therefore a complete description of the solution
behavior as $r_{0}\rightarrow\infty$ is obtained. This allows us to relax the
restriction on the profile of initial data which still guarantees shock
formation. Since \eqref{main eq} can be viewed as a model equation for
describing the propagation of electromagnetic waves in nonlinear dielectric,
the result in this paper reveals the possibility to use wave pulse with weak
intensity to form electromagnetic shocks in laboratory. A main new feature in
the proof is that all estimates in the present paper do \emph{not} depend on
the parameter $r_{0}$, which requires different methods to obtain energy
estimates. As a byproduct, we prove the existence of semi-global-in-time
solutions which lead to shock formation by showing that the limits of the
initial energies exist as $r_{0}\rightarrow\infty$. The proof combines the
ideas in [5] where the the formation of shocks for 3-dimensional relativistic
compressible Euler equations with small initial data is established, and the
short pulse method introduced in [6] and generalized in [15], where the
formation of black holes in general relativity is proved.
