  We investigate heating of the cool core of a galaxy cluster through the
dissipation of sound waves excited by the activities of the central active
galactic nucleus (AGN). Using a weak shock theory, we show that this heating
mechanism alone cannot reproduce observed temperature and density profiles of a
cluster, because the dissipation length of the waves is much smaller than the
size of the core and thus the wave energy is not distributed to the whole core.
However, we find that if it is combined with thermal conduction from the hot
outer layer of the cluster, the wave heating can reproduce the observational
results.
