This paper formulates and solves the shape optimization problem for the body of a musical instrument such as an acoustic guitar. A coupling system consisting of a linear elastic body surrounded by a compressible fluid is used to define the frequency response problem with respect to an external force applied to the bridge of an acoustic guitar. The acoustic power on an outer boundary within a given frequency range is defined as the objective cost function. The solution of the shape optimization problem is constructed using the $H^1$ gradient method. A numerical example is used to validate this approach.