The ultrasonic vibration potential (UVP) and the electrokinetic sonic amplitude (ESA) are described in terms of equilibrium time-correlation functions using the linear response theory. The reciprocal relationship between UVP and ESA is shown based on the formulation. By introducing the generalized Langevin theory and taking the hydrodynamic limit, it is discussed how the effective volume of ions in the UVP measurement is related to their partial molar thermodynamic quantities. The effective volume is proven exactly equal to the isothermal partial molar volume in the isothermal formulation. The effect of the adiabaticity of sound wave is also investigated. (C) 2003 American Institute of Physics.