Pressure ratios of modern high pressure radial compressors tend to increase along with pressure fluctuations and the excitation potential on the impellers. The vibrational interactions between side cavities, filled with high pressure fluid, and the impeller structure play an important role in designing a machine for reliable operation. However, they are not yet fully understood. Vibrations at frequencies that have been uncritical at lower pressure levels could become critical at a higher pressure level. Additionally, coupling effects between fluid and structure are becoming stronger at higher fluid densities. For a safe and reliable design, the excitation and the damping mechanism of coupled modes has to be better understood. To understand the interaction, especially regarding the damping behavior, of coupled structure and acoustic modes, a comprehension of the behavior of the uncoupled or weakly coupled modes is required. The structural damping ratio is very small and it has been analyzed in existing literature extensively. The damping behavior of uncoupled acoustic modes, however, is not yet well investigated. This paper focuses on the damping behavior of acoustic modes that are weakly coupled to structure modes. Measurement results gathered at the aeroacoustic test rig at the University of Duisburg-Essen are presented. The results show the influence of fluid pressure variations on the damping behavior of acoustic modes. Therefore, the response functions of some selected acoustic modes are evaluated with the Peak-to-Peak method. In general, the damping decreases with increasing fluid pressure. Furthermore, a relationship of the damping ratio, the kinematic viscosity, and the natural frequency of the acoustic modes has been detected.