What is Wavenumber?

Wavenumber definition: Wave motion is a disturbance that travels from its point of origin. The physical characteristics required to describe a wave are its amplitude and wavelength (see figure 1).

Amplitude and Wavelength

The amplitude of a wave is the maximum distance from the equilibrium position, i.e., the distance between the central line and the peak of the crest or bottom of the trough.

The wavelength of a wave is the length of one wave, i.e., the distance between two crests or two troughs.

SI Unit of Wavenumber

The SI unit of wavenumber is m⁻¹. We define wavenumber as the number of wavelengths per unit distance, i.e., wavenumber = 1/ wavelength. The SI unit of wavelength is meter or m. Hence the SI unit of wavenumber is m⁻¹.

Calculating Wavenumber and Frequency of Yellow Radiation

To calculate the wavenumber and frequency of yellow radiation (wavelength, λ = 5800 × 10⁻¹⁰ m), follow the given instructions:

1. Using the wavenumber formula, wavenumber = 1 / wavelength, determine the wavenumber as:

wavenumber = 1/(5800 × 10⁻¹⁰ m) = 1.724 × 10⁶ m⁻¹.

2. Using the formula, frequency = speed of light / wavelength, calculate the frequency as:

frequency = (3 × 10⁸ m/s) / (5800 × 10⁻¹⁰ m) = 5.172 × 10¹⁴ s⁻¹.