Nonlinear Standing Waves, Resonance Phenomena and Frequency Characteristics of Distributed Systems

Abstract

Resonance is one of the most interesting and fundamental phenomena in the physics of oscillations and waves. Resonance manifests itself clearly when the dependence of the amplitude of induced oscillations on frequency (frequency response of the system) has a sharp maximum. In these cases, the ratio of the central frequency ω0 of the spectral line, representing a response, to the characteristic width of this line is a large value. This ratio, called the quality- or Q-faetor, is used as a “quality” measure of the resonance system. At large values of Q, the system may contain a high energy density, since the ratio of the amplitude of induced oscillations to the amplitude of oscillations of the external source providing an influx of energy to the system is also equal to Q. In high-Q systems, approaching a state of equilibrium is slow process with a characteristic relaxation time on the order of Q/ω0. The buildup time of oscillations (or their attenuation after the source is switched off) occurs over the course of many periods, the number of which is ~ Q. Excitation of strong oscillations during resonance may lead to the appearance of nonlinear effects, the most well-known of which is destruction of the system. On the other hand, high-Q systems are used for taking high-precision physical measurements.