# Wavenumber

Wavenumber, k, sometimes called the *propagation number*, is a quantification of spatial scale. It can be thought of as a spatial analog to the temporal frequency, and is often called *spatial frequency*. It is often defined as the number of wavelengths per unit distance, or in terms of wavelength, *λ*:

This is analogous to frequency *f*, which is the reciprocal of period *T*; that is, *f* = 1/*T*. In a sense, period can be thought of as a temporal 'wavelength', and this is obvious when you compare a spatially varying quantity with a temporally varying one:

If you've explored the applications of frequency in geophysics, you'll have noticed that we sometimes don't use ordinary frequency f, in Hertz. Because geophysics deals with oscillating waveforms, ones that vary around a central value (think of a wiggle trace of seismic data), we often use the **circular** or **angular frequency**. In this way, we can also express the close relationship between frequency and phase, which is an angle. So in many geophysical applications, we want the *angular wavenumber*. It is expressed in radians per metre:

The relationship between angular wavenumber and angular frequency is analogous to that between wavelength and ordinary frequency—they are related by the velocity *V*:

It's unfortunate that there are two definitions of *wavenumber*. Some people reserve the term *spatial frequency* for the ordinary wavenumber, or use ν (that's a Greek *nu*, not a vee — another potential source of confusion!), or even *σ* for it. But just as many call it the wavenumber and use *k*, so the only sure way through the jargon is to specify what you mean by the terms you use. As usual!

## External links

- Wavenumber — Wikipedia entry