Wavenumber-frequency diagram
Encyclopedia
A wavenumber–frequency diagram is a plot
displaying the relationship between the wavenumber
(spatial frequency) and the frequency
(temporal frequency) of certain phenomena. Usually frequencies are placed on the vertical axis, while wavenumbers are placed on the horizontal axis.
In the atmospheric sciences, these plots are a common way to visualize atmospheric wave
s.
In the geosciences, especially seismic data analysis, these plots also called f-k plot, in which energy density within a given time interval is contoured on a frequency-versus-wavenumber basis. They are used to examine the direction and apparent velocity of seismic waves and in velocity-filter design.
λ, frequency
ν, and the phase velocity
vp of a sinusoidal wave is:
Since the wavenumber
k, is the inverse of wavelength (k = 1/λ) the previous equation can be rewritten as
On the other hand, the group velocity
is equal to the slope of the wavenumber–frequency diagram:
Analyzing such relationships in detail often yields information on the physical properties
of the medium
, such as density
, composition
, etc.
Plot (graphics)
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a mechanical or electronic plotter. Graphs are a visual representation of the relationship between variables, very useful for...
displaying the relationship between the wavenumber
Wavenumber
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...
(spatial frequency) and the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
(temporal frequency) of certain phenomena. Usually frequencies are placed on the vertical axis, while wavenumbers are placed on the horizontal axis.
In the atmospheric sciences, these plots are a common way to visualize atmospheric wave
Atmospheric wave
An atmospheric wave is a periodic disturbance in the fields of atmospheric variables which may either propagate or not . Atmospheric waves range in spatial and temporal scale from large-scale planetary waves to minute sound waves...
s.
In the geosciences, especially seismic data analysis, these plots also called f-k plot, in which energy density within a given time interval is contoured on a frequency-versus-wavenumber basis. They are used to examine the direction and apparent velocity of seismic waves and in velocity-filter design.
Origins
In general, the relationship between wavelengthWavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
λ, frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
ν, and the phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
vp of a sinusoidal wave is:
Since the wavenumber
Wavenumber
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...
k, is the inverse of wavelength (k = 1/λ) the previous equation can be rewritten as
On the other hand, the group velocity
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
is equal to the slope of the wavenumber–frequency diagram:
Analyzing such relationships in detail often yields information on the physical properties
Physical property
A physical property is any property that is measurable whose value describes a physical system's state. The changes in the physical properties of a system can be used to describe its transformations ....
of the medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
, such as density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, composition
Composition
Composition may refer to:* Composition , in which one assumes that a whole has a property solely because its various parts have that property* Compounding is also known as composition in linguistic literature* in computer science...
, etc.