Wave propagation faster than light

It is shown that waves obeying the conventional wave equation del(2)u = (1/c(2))(partial derivative(2)u/partial derivativet(2)) do not necessarily travel with a phase velocity c. The case of spherical waves proceeding from the origin is analysed. For non-spherically symmetric waves, the wave speed is greater than c at distances much shorter than a wavelength. This applies in particular to the fields from oscillating electric and magnetic dipoles. It is shown, however, that a signal in the form of a step travels with speed c.