Frequency and wavelength prediction of ultrasonic induced liquid surface waves

A theoretical investigation of parametric excitation of liquid free surface by a high frequency sound wave is preformed, using potential flow theory. Pressure and velocity distributions, resembling the sound wave, are applied to the free surface of the liquid. It is found that for impinging wave two distinct capillary frequencies will be excited: One of them is the same as the frequency of the sound wave, and the other is equal to the natural frequency corresponding to a wavenumber equal to the horizontal wavenumber of the sound wave. When the wave propagates in vertical direction, mathematical formulation leads to an equation, which has resonance frequency equal to half of the excitation frequency. This can explain an important contradiction between the frequency and the wavelength of capillary waves in the two cases of normal and inclined interaction of the sound wave and the free surface of the liquid.