The activation of a radical polymerization using ultrasound in water is an eco-friendly way to produce synthetic latexes, as it avoids using radical initiators and surfactants that negatively impact the environment. Such an experiment can be achieved by exciting a water bath (so-called generator) in which the reaction vessel is immersed with an ultrasonic transducer. Following data from the literature, several frequency bands may be used, but the present setup uses the 480-500 kHz range. Prior experiments by the same team and others have shown that such an excitation successfully fosters polymerization. The question now pertains to optimizing the setup geometry for a more efficient reaction. In the framework of linear acoustics, the experimental setup can be described as nested cavities and the pressure field in the different domains is modeled with modal theory. By describing the cavities with parameters related to their shape and position, this contribution aims at determining optimized sets of parameters to enhance the radicals generation rate and connect it to the stable or transient cavitation activity produced by sonication. The data from the linear model are compared with some experimental data at high frequencies and high intensity.