The achievable rotational frequency of acoustically levitated particles is limited by the suspension stability and the achievable driving torque. In this work, a spherical ring arrangement of piezoelectric transducers and an improved excitation concept are presented to increase the rotational speed of an acoustically levitated particle by more than a factor of 10 compared to previously published results. A maximum rotational frequency of 3.6 kHz using asymmetric expanded polystyrene (EPS) particles is demonstrated. At such rotational speeds, high-frequency resonances of the transducers cause disturbances of the acoustic field which present a previously unexplored limit to the achievable manipulation rate of the particle. This limit is investigated in this work by means of calculations based on an analytical model and high precision measurements of the transducer characteristics beyond the conventional frequency range.