# wave number

The term wave number refers to the number of complete wave cycles of an electromagnetic field (EM field) that exist in one meter (1 m) of linear space. Wave number is expressed in reciprocal meters (m^{-1}).

The wave number for an EM field is equal to 2 pi divided by the wavelength in meters. (In some references, it is defined as the reciprocal of the wavelength in meters; in still others, it is defined as the reciprocal of the wavelength in centimeters.) As the wavelength grows shorter, the wave number becomes larger.

Wave number is usually specified for an EM field in a vacuum, also called free space. In most situations, the air is equivalent to a vacuum. In media other than free space, the wave number for a given EM field may increase. When a ray of light passes from air into water or glass, or a radio signal propagates through a polyethylene dielectric rather than air, the wavelength is shortened because the speed of propagation decreases. This causes the wave number to increase.

In free space, the wave number *k* (in reciprocal meters) is related to the frequency *f* (in hertz) according to the following formula:

*k* = *f*/*c*

where *c* is the speed of EM propagation in free space, approximately equal to 2.99792 x 10^{8} meters per second.

In media other than free space, *c* must be multiplied by a velocity factor *v*. The velocity factor for a particular medium is the ratio of the speed of EM propagation in that medium to the speed of EM propagation in free space. As such, the velocity factor is always greater than 0 and less than or equal to 1. Taking velocity factor into account, the above formula becomes:

*k* = *f*/(*vc*)

See also EM field, frequency, and wavelength.