phase

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phase

mechanics

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Related Topics:: wave; phase velocity; polyphase current; multiphase current; phase angle

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phase, in mechanics of vibrations, the fraction of a period (i.e., the time required to complete a full cycle) that a point completes after last passing through the reference, or zero, position. For example, the reference position for the hands of a clock is at the numeral 12, and the minute hand has a period of one hour. At a quarter past the hour the minute hand has a phase of one-quarter period, having passed through a phase angle of 90°, or π/2 radians. In this example the motion of the minute hand is a uniform circular motion, but the concept of phase also applies to simple harmonic motion such as that experienced by waves and vibrating bodies.

If the position y of a point or particle changes according to a simple harmonic law, then it will change in time t according to the product of the amplitude, or maximum displacement, r, of the particle and a sine or cosine function composed of its angular speed, symbolized by the Greek letter omega (ω), the time t, and what is called the angle, symbolized by the Greek letter epsilon (ε): y = r sin (ωt + ε). The angle (ωt + ε) is called the phase angle at time t, which at zero time is equal to ε. Phase itself is a fractional value—the ratio of elapsed time t to the period T, or t/T—and is equal to the ratio of the phase angle to the angle of the complete cycle, 360°, or 2π radians. Thus, phase for uniform circular or harmonic motion has the value (ωt + ε)/2π. Applying this expression to the example of the moving minute hand cited above, ε is zero (zero phase angle at zero time), angular speed is 2π radians per hour, and time t is 1/4 hour, giving a phase of 1/4.

When comparing the phases of two or more periodic motions, such as waves, the motions are said to be in phase when corresponding points reach maximum or minimum displacements simultaneously. If the crests of two waves pass the same point or line at the same time, then they are in phase for that position; however, if the crest of one and the trough of the other pass at the same time, the phase angles differ by 180°, or π radians, and the waves are said to be out of phase (by 180° in this case).

wave motion

physics

Also known as: wave propagation

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wave motion, propagation of disturbances—that is, deviations from a state of rest or equilibrium—from place to place in a regular and organized way. Most familiar are surface waves on water, but both sound and light travel as wavelike disturbances, and the motion of all subatomic particles exhibits wavelike properties. The study of waves therefore forms a topic of central importance in all physical science and engineering.

The simplest types of wave motion are vibrations of elastic media, such as air, crystalline solids, or stretched strings. If, for example, the surface of a metal block is struck a sharp blow, the deformation of the surface material compresses the metal in the vicinity of the surface, and this transmits the disturbance to the layers beneath. The surface relaxes back to its initial configuration, and the compression propagates on into the body of the material at a speed determined by the stiffness of the material. This is an example of a compression wave. The steady transmission of a localized disturbance through an elastic medium is common to many forms of wave motion.

In most systems of interest, two or more disturbances of small amplitude may be superimposed without modifying one another. Conversely, a complicated disturbance may be analyzed into several simple components. In radio transmission, for example, a high-frequency signal can be superimposed on a low-frequency carrier wave and then filtered out intact on reception.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

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In the simplest waves, the disturbance oscillates periodically with a fixed frequency and wavelength. These sinusoidal oscillations form the basis for the study of almost all forms of linear wave motion. In sound, for instance, a single sine wave produces a pure tone, and the distinctive timbre of different musical instruments playing the same note results from the admixture of sine waves of different frequencies. In electronics, the natural rhythmic oscillations of electric currents in tuned circuits are used to produce sinusoidal radio waves.

electromagnetic spectrumThe electromagnetic spectrum.

Although the mathematical properties of all linear waves are common, the waves exhibit various physical manifestations. One important class—electromagnetic waves—represents oscillations of the electromagnetic field. These include infrared radiation, visible light, radio and television, microwave, ultraviolet, X-rays, and gamma rays. Electromagnetic waves are produced by moving electric charges and varying currents, and they can travel through a vacuum. Unlike sound waves, they are not, therefore, disturbances in any medium. Another difference between electromagnetic and sound waves is that the former are transverse, that is, the disturbance occurs in a direction perpendicular to that in which the wave is propagating. Sound waves are longitudinal: they vibrate along the path of their propagation.

prismAs white light is refracted, or bends, when it passes through a prism, it separates into its constituent colours. This happens because each colour has a different wavelength and each wavelength bends at a different angle.

The propagation of a wave through a medium will depend on the properties of the medium. For example, waves of different frequencies may travel at different speeds, an effect known as dispersion. In the case of light, dispersion leads to the unscrambling of colours and is the mechanism whereby a prism of glass can produce a spectrum. In geophysics, the dispersive propagation of seismic waves can provide information about the constitution of Earth’s interior.

Two important characteristics of all waves are the phenomena of diffraction and interference. When a wave disturbance is directed toward a small aperture in a screen or other obstacle, it emerges traveling in a range of directions. Thus, light rays, which normally follow straight paths, can bend upon passing through a small hole: this is the phenomenon known as diffraction.

Understanding wave interference through sound experimentsOverview of interference using the example of sound waves.
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Interference occurs when two waves are combined and the disturbances overlap. If the waves arrive at a point in phase, enhancement occurs and the disturbance is large. Where the waves are out of phase, their opposing motions cancel and the disturbance is small or nonexistent. The net effect is therefore a distinctive interference pattern of large and small disturbances.

Mathematically less tractable is the study of nonlinear waves, which can be very important in many applications. These usually display a more complicated structure and behaviour; for example, water waves in a shallow channel can develop a humplike formation known as a soliton, which propagates as a coherent entity. Nonlinear waves are important in systems as diverse as nerve networks and the spiral arms of galaxies.

The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen.