# Article

# Article

- Physics
- Theoretical physics
- Phase velocity

# Phase velocity

Article By:

**Williams, S. A. **Department of Physics, Iowa State University, Ames, Iowa.

Last reviewed:2014

DOI:https://doi.org/10.1036/1097-8542.506200

**The velocity of propagation of a pure sine wave of infinite extent.** In one dimension, for example, the form of the disturbance for such a wave is *y*(*x*,*t*) = *A* sin [2π(*x*/λ − *t*/*T*)]. Here *x* is the position at which the disturbance *y*(*x*,*t*) exists at time *t*, λ is the wavelength, *T* is the period which is related to the wave frequency by *T* = 1/*f*, and *A* is the disturbance amplitude. The argument of the sine function is called the phase. The phase velocity is the speed with which a point of constant phase can be said to move. Thus *x*/λ − *ft* = constant, so the phase velocity υ_{p} is given by *dx*/*dt* = υ_{p} = λ*f*. This is the basic relationship connecting phase velocity, wavelength, and frequency.* See also: ***Phase (periodic phenomena)**; **Sine wave**; **Wave motion**

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