All waves have a wavelength λ that represents the distance over which the wave repeats itself, such as from peak to peak. For instance, if the distance from one water ripple to another is 0.12 meters, then λ = .12 meters. On the other hand, you can talk about a wavenumber n, which is the number of full waves in a given unit of length. The two are related by n = 1/λ. In physics, one frequently sees the angular wave number k = 2π/λ. If the wave travels with a velocity v, and frequency f, then k = 2πf/v.
Graphical Method for Spatial Waves
Find an image of a spatial wave. Ripples on water works well.
Find two neighboring peaks on the wave. These would be high points on the ripples.
Measure the distance between them. This is the wavelength λ.
Calculate the wavenumber using n = 1/λ. Using the aforementioned example of water ripples, 1 / .12 = 8.34. This means that there are eight and one third waves per meter of rippling water.
Write down the frequency of the wave. The frequency for the visible color red is around 4.3×10^15 Hertz.
Use reference 3 to find the speed of light: c = 3.0×10^8 meters per second.
Multiply the frequency by 2π and divide by the speed of light to get the angular wavenumber k = 2π4.3×10^15/3.0×10^8 = 9×10^7 meters^-1.
Sometimes, k is used for the standard wavenumber, not the angular wavenumber.