# Dictionary:Wave

A disturbance that is propagated through the body or on the surface of a medium without involving net movement of material. Waves are usually characterized by periodicity (Figure W-2). The general expression for a plane wave in rectangular coordinates is

where *f* and *g* are any functions and *l*, *m*, *n* are direction cosines for the direction of travel.

For a spherical wave, the general expression is

where *r* is the distance from the point source. **Wave amplitude** is usually defined as the maximum displacement from the equilibrium or null position. The **rms amplitude** is the square root of the mean of the squares of the displacements, which is times the peak amplitude for sinusoidal waves. A wave **peak** or **crest** is a point at which the displacement is greater (in the positive direction) than at adjacent points, and a wave **trough** is a point which is displaced farther than adjacent points in the negative sense. The **wave height** is the difference in displacement between successive peaks and troughs. The **wavelength** () is the distance perpendicular to the wavefront between successive similar points on the wavetrain. The **wavenumber** is the number of cycles per unit distance, the reciprocal of the wavelength (sometimes defined as , which is given the symbol ). **Body waves** propagate through the body of the medium, and *surface* or *interface waves* propagate along a boundary. Body waves may be either *P-waves* (q.v.) or *S-waves* (q.v.). Wave energy that has traveled partly as a P-wave and partly as an S-wave is called a **converted wave**. Surface waves (or interface waves) may travel by several modes, the most common of which are *Rayleigh waves* (q.v.) or pseudo-Rayleigh waves. Other surface waves include *Love waves* (q.v.), hydrodynamic waves, coupled waves, and Stoneley waves. A *tube wave* (q.v.) is a surface wave which travels along the surface of a borehole. See also *wave notation*. Wave motion at a point is often described mathematically in terms of harmonic components:

or in complex notation:

where *C*_{n} is amplitude, *n* is an integer, *f* is frequency, is phase angle, and .