wavenumber
/ WAYV-num-ber /
Wavenumber is just a way of counting how many wave crests fit into a centimeter. Picture ripples on a pond: a short, tight ripple packs many crests into a small space, while a long, lazy swell fits only a few. Wavenumber counts those crests per centimeter, so tightly packed (short-wavelength, high-energy) light gets a big number.
More precisely, the wavenumber is the reciprocal of the wavelength, with units of reciprocal centimeters (cm⁻¹). Because it is proportional to energy and frequency, doubling the wavenumber means doubling the photon's energy — unlike wavelength, which runs the other way.
It matters because infrared and Raman spectra are almost always plotted against wavenumber rather than wavelength, since equal steps in wavenumber correspond to equal steps in energy, making vibration positions easy to compare. The honest caveat is that the units trip up newcomers: a higher wavenumber means higher energy, which feels backward if you are used to thinking in wavelength.
A carbonyl stretch appears near 1715 cm⁻¹. To convert, take the reciprocal: 1 ÷ 1715 cm⁻¹ ≈ 5.83 × 10⁻⁴ cm, or about 5830 nm — a wavelength deep in the infrared.
Wavenumber is one over wavelength, rising with energy.
Do not confuse wavenumber with frequency: they are proportional but carry different units. Mid-infrared spectroscopy typically spans roughly 4000 down to 400 cm⁻¹.