Wavenumber is defined as the number of complete wave cycles per unit length of a linear space. It can also be referred to as the spatial frequency of the waves represented in radians per unit distance, or cycles per unit distance. It is usually measured in units of reciprocal centimeters (cm-1) and reciprocal meters (m-1).
Wavenumber is usually denoted for an electromagnetic field in a vacuum or free space. Under most of the conditions, air is equivalent to vacuum. The wave number of a given electromagnetic field tends to increase in any media other than free space.
When a light beam is transmitted from an air medium to a glass or water medium, or when a radio signal is propagated via a polyethylene dielectric medium, the wavelength is shortened as the propagation speed decreases. As a result, the wavenumber tends to increase.
In vacuum or free space, the wavenumber represented by the letter “k” is defined as the function of frequency f based on the formula:
k = f/c
where c is the speed of propagation of light waves in free space, which is equal to 2.99792 x 108 m/s.
In a medium other than free space, c is multiplied by velocity of the light wave, v. The velocity of the wave in a particular medium is defined as the ratio of speed of the light wave passing via the medium to the speed of light wave passing through the free space. In most cases, the velocity factor is greater than 0 or less than or equal to 1. The wavenumber in such a medium is given by the formula:
k = f/(vc)