PARAMETRIC GENERATION OF ULTRASONIC WAVES: LINEAR AND NONLINEAR PHENOMENA.

The problem of a fluid-filled cavity caused to resonate by an ultrasonic wave is described as a parametric phenomenon. Variations of the cavity dimensions produce instabilities in the liquid. As a result fractional harmonics of the drivers frequency are parametrically generated. The wave equation describing the system is transformed into an ordinary differential equation with varying coefficients. The solution of this differential equation Mathieus equation predicts a frequency spectrum which agrees with that observed experimentally. From the limit of the region of instability of the Mathieu function, a threshold of parametric excitation is obtained. This threshold criterion relates the amplitude and frequency of the driver transducer to the cavity length and to the absorption per wavelength of the medium. The nonlinearity of the medium, although it appears to be responsible for limiting the growth of the parametrically excited ultrasonic wave, does not affect the threshold. Reasonable agreement between theory and experiment is obtained. Examples of parametric phenomena observed in many branches of physics are discussed. Author