Resonance

RESONANCE. If any body (e.g., pendulum, string, membrane, tuning fork, column of air, etc.) or generally some system can perform independent oscillations with period T (or with frequency f = number of oscillations per second), then in the case of external oscillations with period T_x (or with frequency f_x = ~\ acting upon it, two oscillations with periods T and T_x (frequencies f and f_x) arise in it. The first of these is called the system's natural oscillation, the second is forced. In the case of equality of periods T and T_x, the system's oscillations become most intense, and this case is called resonance of oscillations. For example, oscillations of a tuning fork excite intense oscillations of the column of air enclosed in a box on which the tuning fork is mounted, if the natural frequency of the air mass in the box coincides with the frequency of the tuning fork; similarly, a string comes into oscillation and produces a sound audible to the ear under the influence of even weak acoustic oscillations of air reaching it, if the frequency of the incoming oscillations is the same as the frequency of the string's natural oscillations. Exactly the same concept of R. is applied not only to mechanical but to any system in which oscillations can arise, e.g., to an electrical oscillatory circuit, i.e., a circuit in which electrical oscillations (rapidly alternating currents) can exist. Electrical oscillations existing in one such circuit excite the most intense oscillations in a second circuit under the condition of equality of the natural periods of oscillation of the circuits, i.e., when the circuits are tuned to resonance. A special case is electromechanical resonance, when under the influence of electrical oscillations of a certain frequency, mechanical oscillations of the same frequency arise or vice versa. This case occurs when using (to create ultrasonic oscillations and in some radio circuits) piezoelectric crystals, in particular quartz; under the influence of an alternating voltage applied to it, the quartz periodically compresses and expands; its natural frequency of mechanical oscillations is determined by its geometric dimensions, and the mechanical oscillations are intense only at the frequency of the applied alternating voltage equal to the natural frequency of the crystal's mechanical oscillations.

The ability of a body to resonate not only at one specific frequency but also at adjacent frequencies can be characterized by the so-called resonance curve (see figure). Along the horizontal axis here are plotted the frequencies of external oscillations acting on the system under consideration, along the vertical axis - the amplitudes of oscillations arising in the system; the natural frequency of the system is marked f_r. Curve A represents the case of 'sharp resonance', in which the system resonates only at frequencies adjacent to its natural frequency, curve B refers to the case of 'blunt' tuning. In the latter case, the system responds to frequencies sufficiently distant from its natural frequency. The sharpness of resonance depends on the damping of oscillations in the given system. In the case where, left to itself, the excited oscillations in a system quickly cease, we say that the system has large damping; the less damping in the system, the longer the oscillations persist in it. The less damping, the sharper the resonance curve and vice versa. An example of a system with small damping can be a tuning fork, which resonates only at a very narrow range of frequencies; an example of strong damping is the soundboard of a piano, which resonates at all frequencies. In many cases of practical acoustics, the phenomenon of R. turns out to be a significant interference. Such is, for example, resonance of membranes in microphones and telephones, due to which certain sound heights are amplified, resonance in loudspeaker horns, etc. According to Helmholtz's theory, the perception by the ear of sounds of different pitches is based on the phenomenon of R. In this case, the resonating system is the fibers of the basilar membrane (membrana basilaris), stretched along the cochlea. Each of the fibers of this membrane is a resonator tuned to a specific frequency. Air oscillations transmitted from the outer ear to the cochlea set into oscillation those fibers that are in resonance with the incoming sound waves (along with these fibers, adjacent fibers also come into oscillation, but their oscillations turn out to be much weaker).