The aim of this paper is to use an analytical multi-physical model—electromagnetic, mechanic, and acoustic—in order to predict the electromagnetic noise of a permanent magnet synchronous machine (PMSM). Afterward, the experimental design method, with a particular design: “trellis design,” is used to build response surfaces of the noise with respect to the main factors. These surfaces can be used to find the optimal design or more simply, to avoid unacceptable designs of the machine, in term of noise for a variable speed application.