  In this paper we obtain some new Strichartz estimates for the wave propagator
$e^{it\sqrt{-\Delta}}$ in the context of Wiener amalgam spaces. While it is
well understood for the Schr\"odinger case, nothing is known about the wave
propagator. This is because there is no such thing as an explicit formula for
the integral kernel of the propagator unlike the Schr\"odinger case. To
overcome this lack, we instead approach the kernel by rephrasing it as an
oscillatory integral involving Bessel functions and then by carefully making
use of cancellation in such integrals based on the asymptotic expansion of
Bessel functions. Our approach can be applied to the Schr\"odinger case as
well. We also obtain some corresponding retarded estimates to give applications
to nonlinear wave equations where Wiener amalgam spaces as solution spaces can
lead to a finer analysis of the local and global behavior of the solution.
