The similar origin of the sound absorption due to thermal relaxation processes in ultrasonic experiments and the frequency-dependent complex heat capacity measured by temperature-modulated calorimetric (TMC) experiments is reviewed. Furthermore, the similarities and limitations of the two experimental methods for investigations of the glass relaxation and the relaxation of composition fluctuations near a second-order critical point are discussed. The theories for the ultrasonic attenuation near a second-order phase transition, which include the description of the complex frequency-dependent heat capacity, are referred to and illustrated with some examples. It has been shown that, for those relaxation processes the ultrasonic spectroscopy can be considered as a high-frequency extension of the TMC.