  Decorated membrane, comprising a thin layer of elastic film with small rigid
platelets fixed on top, has been found to be an efficient absorber of low
frequency sound. In this work we consider the problem of sound absorption from
a perspective aimed at deriving upper bounds under different scenarios, i.e.,
whether the sound is incident from one side only or from both sides, and
whether there is a reflecting surface on the back side of the membrane. By
considering the negligible thickness of the membrane, usually on the order of a
fraction of one millimeter, we derive a relation showing that the sum of the
incoming sound waves' (complex) pressure amplitudes, averaged over the area of
the membrane, must be equal to that of the outgoing waves. By using this
relation, and without going to any details of the wave solutions, it is shown
that the maximum absorption achievable from one-side incident is 50%, while the
maximum absorption with a back reflecting surface can reach 100%. The latter
was attained by the hybridized resonances. All the results are shown to be in
excellent agreement with the experiments. This generalized perspective, when
used together with the Green function formalism, can be useful in gaining
insights and delineating the constraints on what are achievable in scatterings
and absorption by thin film structures.
