  We solve for waves in an isothermal, stratified medium with a magnetic field
that points along a direction perpendicular to that of gravity and varies
exponentially in the direction of gravity. We find exact analytical solutions
for two different cases: (a) waves propagating along the direction of the
magnetic field and (b) waves propagating along the direction of the gravity. In
each case, we find solutions in terms of either the hypergeometric functions or
their confluent cousins. We solve the resultant transcendental dispersion
relation numerically. The changes in the eigenfrequencies due to a spatially
inhomogeneous Alfv\'en wave speed are significant -- there are more
oscillations or leaking of nodes of the eigenfunctions in regions of lower
Alfv\'en speed and wave reflection from regions of larger Alfv\'en speed. Such
changes in the dispersion relation and the mode structures may allow detection
of magnetic fields buried in the stellar interior.
