  We deal with an initial-boundary value problem for the multidimensional
acoustic wave equation, with the variable speed of sound. For a three-level
semi-explicit in time higher-order vector compact scheme, we prove stability
and derive 4th order error bound in the enlarged energy norm. This scheme is
three-point in each spatial direction, and it exploits additional sought
functions which approximate 2nd order non-mixed spatial derivatives of the
solution to the equation. At the first time level, a similar two-level in time
scheme is applied, with no derivatives of the data. No iterations are required
to implement the scheme. We also present results of various 3D numerical
experiments that demonstrate a very high accuracy of the scheme for smooth
data, its advantages in the error behavior over the classical explicit 2nd
order scheme for nonsmooth data as well and an example of the wave in a layered
medium initiated by the Ricker-type wavelet source function.
