  In this paper, we compute an explicit analytic expression for the Green
function of the wave operator on the $2$-regular lattice called the "Bethe
lattice" equipped with its standard metric. In particular, we exhibit a
phenomena of abnormal speed of propagation for waves: the effective speed of
propagation of energy for large time is $c_*=2\sqrt 2/3 <1$, and there exists a
true propagation at any speed $c<c_*$.
