A numerical multi-physical model, electromagnetic , mechanical and acoustic, for an induction motor able to predict the electromagnetic noise at variable speed is firstly presented. Experimental measurements but also finite element simulations validate the model for different type of industrial motors. In a second time, this multi-physical model is employed with the design of experiment method to build response surfaces of the electromagnetic noise with respect to the main factors. The aim of the study is to find an optimal design or more simply, to avoid unacceptable designs of the machine, in term of noise for variable speed applications.