The dispersion of acoustic waves in the rarefied high-temperature plasma of the solar corona and its role in the propagation of disturbances occurring in the corona are analyzed. We believe that the quasi-periodic oscillations (QPOs) that are recorded when observing propagating disturbances in coronal holes and loops are formed as a result of the combined effect of dispersion and damping of compressive waves. Observations and wavelet analysis show that their spectra are continuous, where the periods are distinguished by corresponding maxima. The shape of spectrum is characteristic of localized disturbances. The study is based on the simple model of non-adiabatic waves in high-temperature plasma, taking into account the properties of thermal conductivity, radiative cooling and constant heating.