Astrophysics (Index)About


(ν, spatial frequency)
(reciprocal of wavelength)

A wave's wavenumber (or spatial frequency) is the reciprocal of its wavelength, the number of cycles per unit distance, a convenient quantity in the analysis and modeling of waves including EMR and sound waves. An example unit is 1/cm, 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 three waves, you could cite the average wavenumber as 0.3 1/m. 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 one cycle of the wave to pass.) 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 to distinguish it.

The angular wavenumber is 2π × the wavenumber.

Further reading:

Referenced by pages:
detective quantum efficiency (DQE)
Kolmogorov spectrum