# reciprocal meter

The reciprocal meter is the standard unit of wave number for electromagnetic field s (EM fields). In terms of International Units ( SI ), the reciprocal meter is equal to m ^{-1} . The wave number is the number of complete wave cycles that exist in a linear span of 1 meter (m).

At the speed of light in free space, 2.99792 x 10 ^{8} m/s, the frequency *f* in hertz ( Hz ) is related to the wave number *y* in reciprocal meters (m ^{-1} ) according to the following formula:

*y* = *f* / (2.99792 x 10 ^{8} )

To cite a few examples, an EM wave at 300 megahertz (MHz) in free space has a wave number of almost exactly 1 m ^{-1} . If the frequency is doubled to 600 MHz, the wave number also doubles, to 2 m ^{-1} . If the frequency becomes 1/10 as great, that is, it is decreased to 30 MHz, then the wave number is reduced to 0.1 m ^{-1} . As a point of reference, it is easy to remember that the wave number of a 300-MHz signal in free space is very close to 1 m ^{-1} .

In general, if the speed of propagation in meters per second for a specific medium is given by *c* , then:

*y* = *f* / *c*

where *y* is in reciprocal meters, and *f* is in hertz.

In radio-frequency ( RF ) transmission lines such as coaxial cable s and waveguide s, the speed of propagation is less than 2.99792 x 10 ^{8} m/s. This increases the wave number, although it has no effect on the frequency.

Also see frequency , electromagnetic field , meter , wavelength , and International System of Units ( SI ).