A periodic disturbance, either continuous or transient, that is propagated through a medium or through space and in which the displacement from a mean value is a function of time or position or both. Sound waves, water waves, and mechanical waves involve small displacements of particles in the medium; these displacements return to zero after the disturbance has passed. With electromagnetic waves (see electromagnetic radiation) it is changes in the intensities of the associated magnetic and electric fields that represent the disturbance and a medium is not required for propagation of the wave.
The instantaneous values of the periodically varying quantity plotted against time gives a graphical representation of the wave that is known as the waveform. If the waveform is sinusoidal in shape it is usually described as undistorted; a nonsinusoidal waveform is distorted. The wavefront is the imaginary surface over which the displacements are all of the same phase. The amplitude of the wave is the peak value of the displacements relative to the equilibrium state or to some arbitrary reference level, usually zero. If a wave suffers attenuation the amplitude of successive periods is continuously reduced (see also propagation coefficient).
The wavelength is the distance between two displacements of the same phase along the direction of propagation. If v is the velocity of the wave and λ its wavelength, then the frequency of vibration, f, is given by
The frequency is the reciprocal of the period, T, of the wave. The frequency (or wavelength) of electromagnetic radiation is commonly used to describe particular regions of the electromagnetic spectrum, such as the visible or radio regions (see also frequency band).
An alternating current propagated through a long chain network or filter behaves as if it were a wave. Elementary particles, such as electrons, have associated wavelike characteristics. See also Doppler effect.