Question

Difference between wavelength and wavenumber

Answer 1

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.

Answer 2

wavelength is distance between two creast and trough.
wavenumber is inverse of wavelength