Ultrasonic attenuation spectra between 100 kHz and 500 MHz, mutual diffusion coefficients and shear viscosities of the triethylamine/water mixture of critical composition have been measured at various temperatures near the critical one. The broadband ultrasonic spectra reveal two relaxation terms with discrete relaxation time and a term that is subject to a broad relaxation time distribution. The former have been discussed to be due to a protolysis reaction and a structural isomerization. The latter term has been evaluated in the light of the Bhattacharjee-Ferrell dynamic scaling theory, relating the sonic spectrum to fluctuations in the local mixture concentrations. The relaxation rate of the Bhattacharjee-Ferrell term follows power law behavior. However, its amplitude (Gamma(0)=45x10(9) s(-1)) is considerably smaller than that derived from the dynamic light scattering and shear viscosity measurements (Gamma(0)=96x10(9) s(-1)). This result is assumed to be due to a shear viscosity relaxation. Using density and heat capacity measurements from the literature, the adiabatic coupling constant g of the triethylamine/water system has been derived from the amplitude of the Bhattacharjee-Ferrell term in the ultrasonic spectra and from a thermodynamic relation as well. Again, a discrepancy is found. The ultrasonic spectra yield g=0.19, whereas g=0.98 follows otherwise. This difference in the g values is taken as an indication of the limitations of the Bhattacharjee-Ferrell model. It had been derived assuming a small amplitude in the singular part of the heat capacity, a precondition which is clearly not fulfilled with the triethylamine/water system.