  We propose a topology optimisation of acoustic devices that work in a certain
bandwidth. To achieve this, we define the objective function as the
frequency-averaged sound intensity at given observation points, which is
represented by a frequency integral over a given frequency band. It is,
however, prohibitively expensive to evaluate such an integral naively by a
quadrature. We thus estimate the frequency response by the Pad\'{e}
approximation and integrate the approximated function to obtain the objective
function. The corresponding topological derivative is derived with the help of
the adjoint variable method and chain rule. It is shown that the objective and
its sensitivity can be evaluated semi-analytically. We present efficient
numerical procedures to compute them and incorporate them into a topology
optimisation based on the level-set method. We confirm the validity and
effectiveness of the present method through some numerical examples.
