Wavenumber Units: Standard or Free-for-All?

[JesseC]

Hi there, quick question about units.

I know wavenumber can be defined as 1/λ or 2π/λ, the latter sometimes being termed 'angular' wavenumber. Is there an agreed upon way of distinguishing between these two definitions when displaying units on, for example, a graph or paper?

I've seen units such as (m-1) which is ambiguous or (cpm) which I presume to mean cycles per metre and thus refer to angular version, but also (rad m-1).

Is there a standard that should be followed? Or is it a free for all?

Cheers,
Jesse

 

[olivermsun]

It's a bit of a free for all. You can often tell by context, but sometimes it's quite confusing.

E.g., if waves are referred to as $\cos kx,$ then $k = 2\pi / \lambda$ (radians/m).

Using cpm (analogous to Hz = cps) whenever you mean cycles, not radians, is a good habit.

If you are working with both wave number and frequency, you definitely want to stick to the same convention for both.

 

[Matterwave]

I think which one you like to use is probably dependent on the field you are working in. In physics, because we almost always express waves like $\cos(kx)$ or $e^{ikx}$, we almost always use angular wave number, and $1/\lambda$ is very very rarely used.