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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 108 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.

This was last updated in September 2005

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Is the answer a bit ambiguous, or mixed up?
The first sentence relates to the linear wave number (denoted "v" with a tilde above), which indeed is in reciprocal meters, but later the formula 2pi/lambda shows up, which is for the angular wave number (which is denoted "k") and is in radians per meter.
The two different types of wave numbers are separated by a factor of 2pi, meaning Linear Wavenumber is 1 over lambda, and Angular Wavenumber is 2pi over lambda.
To me it's a lit bit like saying the radius and circumference of a circle is the same … eh, no, they're not, they differ by 2pi.
I know the word Wavenumber is used arbitrarily, but when formulas come into play one should distinguish between the two of them.


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