4. In the acute triangle $\triangle A B C$, $2 \angle B=\angle C, A B: A C$ the range of values ( ).
A. $(0,2)$
B. $(0, \sqrt{2})$
C. $(\sqrt{2}, 2)$
D. $(\sqrt{2}, \sqrt{3})$
4. D.

Since $A B=2 R \sin \angle C, A C=2 R \sin \angle B$, then $A B: A C=\frac{\sin \angle C}{\sin \angle B}=2 \cos \angle B$. And $\angle B+ \angle C=3 \angle B>90^{\circ}$, and $\angle C=2 \angle B<90^{\circ}, 30^{\circ}<\angle B<45^{\circ}$, so $\sqrt{2}<2 \cos \angle B<\sqrt{3}$.