  We consider the Cauchy problem with smooth and compactly supported initial
data for the wave equation in a general class of spherically symmetric
geometries which are globally smooth and asymptotically flat. Under certain
mild conditions on the far-field decay, we show that there is a unique globally
smooth solution which is compactly supported for all times and \emph{decays in
$L^{\infty}_{\text{loc}}$ as $t$ tends to infinity}. Because particlelike
geometries are singularity free, they impose additional difficulties at the
origin. Thus this study requires ideas and techniques not present in the study
of wave equations in black hole geometries. We obtain as a corollary that
solutions to the wave equation in the geometry of particle-like solutions of
the SU(2) Einstein/Yang-Mills equations decay as $t\to \infty$.
