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• We developed a new topology optimisation method to design wide-band acoustic devices. • The method is based on the Padé approximation of acoustic response. • The analytical expression for the frequency integral of the approximated response and its sensitivity is obtained. • Some numerical examples of wide-band acoustic devices are presented. 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 Padé 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 as well as 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. [ABSTRACT FROM AUTHOR]