Sunspots are known to behave as efficient sinks of acoustic wave energ
y, absorbing almost 50% of the energy from the acoustic waves impingin
g on them. The physical properties of the flux tube that forms the sun
spot are believed to be responsible for the absorption. We show that t
he absorption coefficient is closely connected not only to the physica
l properties of the sunspot flux tube, but also to its geometry beneat
h the surface. Using geometric acoustics, we show that a sunspot with
a monolithic fluxtube structure mixes acoustic modes; energy in an inc
oming mode, at any horizontal wavenumber k(h), gets dispersed into a w
ide range of wavenumbers. We also predict the observational signatures
of mode mixing in sunspots.