  We consider the wave equation on a product cone and find a joint asymptotic
expansion for solutions near null and future infinities. The rates of decay
seen in the expansion at future infinity are the resonances of a hyperbolic
cone and were computed by the authors in a previous paper. The expansion treats
an asymptotic regime not considered in the influential work of Cheeger and
Taylor. The main result adapts the blueprint laid out in the asymptotically
Minkowski setting with key new elements including propagation estimates near
the conic singularities. The proof of the propagation estimates extends prior
work of Melrose-Vasy-Wunsch and Gannot-Wunsch.
