The possibility of resonance always exists wherever there is periodic motion, movement that is repeated at regular intervals called periods, and/or harmonic motion, the repeated movement of a particle about a position of equilibrium or balance. Many examples of resonance involve large objects: a glass, a child on a swing, a bridge. But resonance also takes place at a level invisible to the human eye using even the most powerful optical microscope.
All molecules exert a certain electromagnetic attraction toward each other, and generally speaking, the less the attraction between molecules, the greater their motion relative to one another. This, in turn, helps define the object in relation to its particular phase of matter.
A substance in which molecules move at high speeds, and therefore hardly attract one another at all, is called a gas. Liquids are materials in which the rate of motion, and hence of intermolecular attraction, is moderate. In a solid, on the other hand, there is little relative motion, and therefore molecules exert enormous attractive forces. Instead of moving in relation to one another, the molecules that make up a solid tend to vibrate in place.
Due to the high rate of motion in gas molecules, gases possess enormous internal kinetic energy. The internal energy of solids and liquids is much less than in gases, yet, as we shall see, the use of resonance to transfer energy to these objects can yield powerful results.
In colloquial terms, oscillation is the same as vibration, but, in more scientific terms, oscillation can be identified as a type of harmonic motion, typically periodic, in one or more dimensions. All things that oscillate do so either along a more or less straight path, like that of a spring pulled from a position of stable equilibrium; or they oscillate along an arc, like a swing or pendulum.
In the case of the swing or pendulum, stable equilibrium is the point at which the object is hanging straight downward—that is, the position to which gravitation force would take it if no other net forces were acting on the object. For a spring, stable equilibrium lies somewhere between the point at which the spring is stretched to its maximum length and the point at which it is subjected to maximum compression without permanent deformation.
A cycle of oscillation involves movement from a certain point in a certain direction, then a reversal of direction and a return to the original point. It is simplest to treat a cycle as the movement from a position of stable equilibrium to one of maximum displacement, or the furthest possible point from stable equilibrium.
The amount of time it takes to complete one cycle is called a period, and the number of cycles in one second is the frequency of the oscillation. Frequency is measured in Hertz. Named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894), a single Hertz (Hz)—the term is both singular and plural—is equal to one cycle per second.
The amplitude of a cycle is the maximum displacement of particles during a single period of oscillation. When an oscillator is at maximum displacement, its potential energy is at a maximum as well. From there, it begins moving toward the position of stable equilibrium, and as it does so, it loses potential energy and gains kinetic energy. Once it reaches the stable equilibrium position, kinetic energy is at a maximum and potential energy at a minimum.
As the oscillating object passes through the position of stable equilibrium, kinetic energy begins to decrease and potential energy increases. By the time it has reached maximum displacement again—this time on the other side of the stable equilibrium position—potential energy is once again at a maximum.
The particles in a mechanical wave (a wave that moves through a material medium) have potential energy at the crest and trough, and gain kinetic energy as they move between these points. This is just one of many ways in which wave motion can be compared to oscillation. There is one critical difference between oscillation and wave motion: whereas oscillation involves no net movement, but merely movement in place, the harmonic motion of waves carries energy from one place to another. Nonetheless, the analogies than can be made between waves and oscillations are many, and understandably so: oscillation, after all, is an aspect of wave motion.
A periodic wave is one in which a uniform series of crests and troughs follow one after the
Again, the wave itself experiences net movement, but within the wave—one of its defining characteristics, as a matter of fact—are oscillations, which (also by definition) experience no net movement. In a transverse wave, which is usually easier to visualize than a longitudinal wave, the oscillation is from the crest to the trough and back again. At the crest or trough, potential energy is at a maximum, while kinetic energy reaches a maximum at the point of equilibrium between crest and trough. In a longitudinal wave, oscillation is a matter of density fluctuations: the greater the value of these fluctuations, the greater the energy in the wave.
The maximum value of the pressure change between waves is the amplitude of a longitudinal wave. In fact, waves can be described according to many of the same parameters used for oscillation—frequency, period, amplitude, and so on. The definitions of these terms vary somewhat, depending on whether one is discussing oscillation or wave motion; or, where wave motion is concerned, on whether the subject is a transverse wave or a longitudinal wave.
For the present purposes, however, it is necessary to focus on just a few specifics of harmonic motion. First of all, the type of motion with which we will be concerned is oscillation, and though wave motion will be mentioned, our principal concern is the oscillations within the waves, not the waves themselves. Second, the two parameters of importance in understanding resonance are amplitude and frequency.
Resonance can be defined as the condition in which force is applied to an oscillator at the point of maximum amplitude. In this way, the motion of the outside force is perfectly matched to that of the oscillator, making possible a transfer of energy.
As its name suggests, resonance is a matter of one object or force "getting in tune with" another object. One literal example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible.
The same can be true of soldiers walking across a bridge, or of winds striking the bridge at a resonant frequency—that is, a frequency that matches that of the bridge. In such situations, a large structure may collapse under a force that would not normally destroy it, but the effects of resonance are not always so dramatic. Sometimes resonance can be a simple matter, like pushing a child in a swing in such a way as to ensure that the child gets maximum enjoyment for the effort expended.