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A wave's wavenumber (or spatial frequency) is the reciprocal of its wavelength which is the number of wavelengths per unit distance, a useful quantity in the analysis and modeling of waves such as EMR and sound waves. An example unit is 1/cm, aka cm-1. which means "number of complete waves in a cm" (or "fraction of a complete wave that spans a cm"). If you viewed the ocean and noticed that at some instant, over a distance of 10 meters, there were four waves (for an average wavelength of 2.5 meters), you could cite the average wavenumber as 0.4 m-1. Pattern regarding wave terms:
time | space | |
quantity | wave period | wavelength |
reciprocal | frequency | wave number |
(the wave period or period being the length of time it takes a complete oscillation of the wave to pass some point in space.) Relations between the terms (given compatible base units, e.g., m and 1/m):
wavelength × wavenumber = 1 frequency × period = 1 wavelength × frequency = wave speed For EMR: wavelength × frequency = c
The symbol ν is sometimes used for the wavenumber, but also often for frequency. Sometimes, for wavenumbers, a tilda (~) is placed over ν (i.e., ṽ) to distinguish it.
The angular wavenumber is 2π times the wavenumber.