  We prove a reducibility result for a class of quasi-periodically forced
linear wave equations on the $d$-dimensional torus $\mathbb{T}^d$ of the form
$$ \partial_{tt} v - \Delta v + \varepsilon {\cal P}(\omega t)[v] = 0 $$ where
the perturbation ${\cal P}(\omega t)$ is a second order operator of the form
${\cal P}(\omega t) = - a(\omega t) \Delta - {\cal R}(\omega t)$, the frequency
$\omega \in {\cal R}^\nu$ is in some Borel set of large Lebesgue measure, the
function $a : \mathbb{T}^\nu \to {\cal R}$ (independent of the space variable)
is sufficiently smooth and ${\cal R}(\omega t)$ is a time-dependent finite rank
operator. This is the first reducibility result for linear wave equations with
unbounded perturbations on the higher dimensional torus $\mathbb{T}^d$. As a
corollary, we get that the linearized Kirchhoff equation at a smooth and
sufficiently small quasi-periodic function is reducible.
