Physically-based sound rendering enriches 3D animation. However, it is difficult to make an object with a given shape produce a specific sound using physically-based sound rendering because the user would need to define appropriate internal material distribution. To address this, we propose an example-based method to design physically-based sound for a 3D model. Our system optimizes the material distribution inside the 3D model so that physically-based sound rendering produces sounds similar to the target sounds specified by the user. A problem is that modal analysis required for this optimization is prohibitively expensive. In order to run the optimization at an interactive rate, we present fast approximate modal analysis that enables three orders of magnitude acceleration of the eigenproblem computation compared to standard modal analysis for an elastic object. It consists of data-driven online coarsening of the mesh and hierarchical component mode synthesis with efficient error correction. We demonstrate the feasibility of the method with a set of comparisons and examples.