Novel propulsion systems have been studied in literature to reduce aircraft emissions with hydrogen or other electrical energy sources. Hybrid Electric Propulsion (HEP) system consists of electric machines as an alternative way to provide power for propulsion resulting in the reduction of aircraft fuel consumption. While reduction of emission is the main driver of new HEP designs, aircraft noise reduction and performance improvement will also need to be investigated. Much quieter electrified aircraft than conventional aircraft is explored with considering the benefits of coupled design between the propeller and electric machines. In this study, several electric machine designs have been explored and coupled with the propeller design to study the trade-off between the aerodynamic and acoustic performance of the propeller. Aerodynamic optimization is used as a baseline to minimize the energy consumption to find the aerodynamics optimum subject to constraints on the thrust levels during the mission. The propeller aerodynamic optimizer considers the electric machine efficiency map, which is a function of propeller torque and rotational speed, to find the optimum combination of propeller and electric machine designs. The objective function of the acoustic optimizations is to reduce the cumulative noise level over the entire mission. It is shown that a wider envelope of peak motor efficiency in the efficiency map provides acoustics and aerodynamic performance benefits. The trade-offs between reducing noise or increasing aerodynamic efficiency to reduce energy consumption are demonstrated.