Difference Between Wavelength and Wavenumber

Wavelength vs Wavenumber
 

Wavelength and wavenumber are two very important concepts discussed in physics and various other fields. Wavelength is the distance between two consecutive points which are in the same phase. Wavenumber is the number of wavelengths in a given distance along the propagation of the wave. These concepts are very important in fields such as electromagnetics, analytical chemistry, physical chemistry, waves and vibrations and various other fields. In this article, we are going to discuss what wavelength and wave number are, their definitions, and finally the difference between wavelength and wavenumber.

Wavelength

Wavelength is a concept discussed under waves. The wavelength of a wave is the length where the shape of the wave starts to repeat itself. This can be also defined using the wave equation. For a time dependent wave equation ψ(x,t), in a given time, if ψ(x,t) is equal for two x values and there are no points between the two values having the same ψ value, the difference of x values are known as the wavelength of the wave.

Another definition for wavelength can be given using the phase. Wavelength is the distance between two consecutive points of the wave that are in the same phase.

The relationship between wavelength, frequency, and velocity of a wave is given by v = f λ where f is the frequency of the wave and λ is the wavelength. For a given wave, since the wave velocity is constant, the wavelength becomes inversely proportional to the frequency.

Wavenumber

Wavenumber is another very important property of a wave. Wavenumber is defined as the number of wavelengths in a given distance. There are two main wavenumber measurements. First one is the number of wavelengths per 2π meters. This is widely used in physics and mathematical models of the wave as well as quantum mechanics. This wavenumber is denoted using “k” and it is also known as the angular wavenumber.

The other form is the number of wavelengths per 1 cm. This definition is widely used in chemistry. This wavenumber is usually denoted by “ν” (the Greek letter Nu), and it is known as the spectroscopic wavenumber.

The units of the wavenumber vary depending on the definition used. If the first definition is used, it is measured in radians per meter. If the second definition is used, the wavenumber is measured in per centimeter.

Wavelength vs Wavenumber

  • Wavelength has only one definition whereas wavenumber has two different definitions for angular wavenumber and spectroscopic wavenumber.
  • Wavelength is measured in distance units, but wavenumber is measured in reciprocal distance units or radians per distance units.
  • The wavelength and wavenumber are two forms, which describe the same entity. In some places, it is more convenient to use one form instead of the other.