  We propose a new space-time variational formulation for wave equation
initial-boundary value problems. The key property is that the formulation is
coercive (sign-definite) and continuous in a norm stronger than $H^1(Q)$, $Q$
being the space-time cylinder. Coercivity holds for constant-coefficient
impedance cavity problems posed in star-shaped domains, and for a class of
impedance-Dirichlet problems. The formulation is defined using simple Morawetz
multipliers and its coercivity is proved with elementary analytical tools,
following earlier work on the Helmholtz equation. The formulation can be stably
discretised with any $H^2(Q)$-conforming discrete space, leading to
quasi-optimal space-time Galerkin schemes. Several numerical experiments show
the excellent properties of the method.
