# Why does this paper use 1/cm for units of frequency?

Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.

Here is an excerpt: It doesn't seem like wave number, as they clearly call it frequency. What's going on here?

$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic resonance in MnO and NiO." Physical Review 129.4 (1963): 1566.

• Frequency is proportional to wavenumber, it is straightforward to convert kayser to hertz.
– user137289
Jul 17 '18 at 9:22
• @Pieter Why would they call it frequency? Jul 17 '18 at 9:23
• All explained here en.wikipedia.org/wiki/Wavenumber#In_spectroscopy Jul 17 '18 at 9:35
• Per @Farcher suggestions, wikipedia says: "A wavenumber in inverse cm can be converted to a frequency in GHz by multiplying by 29.9792458 (the speed of light in centimeters per nanosecond)." Jul 17 '18 at 9:47
• It's probably also relevant that the unit hertz, with its convenient derived unit of gigahertz, didn't come into wide use until roughly the 1960's. So up to that time you would have had to talk about "kilo megacycles per second" to discuss frequencies in this band, and 10s of inverse cm would have been much more convenient. Even after SI became commonly used, some fields have continued to work in wavenumber rather than GHz or THz. Jul 17 '18 at 14:29

People working in the infrared or optical region tend to sometimes, depending on what school of thought they come from, use a unit called wavenumber, which is the reciprocal wavelength in centimeters, $\frac{1}{\lambda_{centimeter}}$.

This is still a frequency, but instead of oscillations per second, it is oscillations per centimeter.

This unit is also called a Kayser. Wavenumber and Kayser are commonly used when working with spectroscopy/diffraction.

• soooo, why call it frequency? That's my question Jul 17 '18 at 12:27
• @axsvl77 It is still a frequency, but the unit of the frequency is not oscillations per second, but rather oscillations per centimeter. Jul 18 '18 at 4:54

A frequency is a number of oscillations, but you need to specify the unit you're refering to : is it oscillations per a given duration (temporal frequency) or per a given length (spatial frequency). Today "frequency" implies a temporal frequency, and we use the word "wave number" for the spatial frequency, allowing us to go away with the adjective. That was not always the case.

Sometimes physicists use (lenghts)$^{-1}$ to indicate frequencies, expecially in spectroscopy...

As you well now, $\omega = 2\pi \nu$ and $c = \lambda \nu$ so that

$\omega = 2\pi \frac{c}{\lambda}$ which is proportional to $\lambda ^ {-1},$ since $c$ is a constant.

So when one says $\omega_1 = 29 cm^{-1}$ is actually saying $\omega_1 = c_{cgs}29 s^{-1}$ where $c_{cgs}$ is the speed of light in the cgs system

If you suppose c=1, then 'centimetre' is the time it takes for light to cross a centimetre, and a count of cycles per centimetre is something that can be done in nature, and also relates to the frequency in cycles per second.