The distances over which magnetohydrodynamic waves will propagate in a
non-ideal, magnetic, compressible medium, representing the solar coro
na structured by the presence of loops of denser material, are conside
red. The waves are damped by ion viscosity and electron heat conductio
n in a radiating, optically thin atmosphere. Waves which lose their en
ergy of propagation in distances of less than our criterion value of 4
x 10(9) cm are regarded as candidates for contributing towards corona
l heating. Alfvenic-type waves only dissipate in this way in weak (les
s than or similar to 15 G) magnetic fields and when they have periods
of a few seconds (2-10 s). Acoustic-type waves can also be dissipated
and we give typical values of magnetic field strength, density and tem
perature for which the dissipation could occur. Dissipating acoustic-t
ype waves have periods that range from tens to hundreds of seconds (15
-225 s). Calculations show that reliable measurements of velocity ampl
itudes will be invaluable in deciding whether these dissipating waves
can contribute to heating the corona. We suggest that the waves that s
urvive dissipation may account for some of the observed coronal oscill
ations.