Faraday wave
Encyclopedia
Faraday waves, also known as Faraday ripples, named after Michael Faraday
, are nonlinear
standing wave
s that appear on liquids enclosed by a vibrating receptacle. When the vibration frequency exceeds a critical value, the flat hydrostatic surface becomes unstable. This is known as the Faraday instability
. Faraday first described them in an appendix to an article in the Philosophical Transactions of the Royal Society of London in 1831.
If a layer of liquid is placed on top of a vertically oscillating piston, a pattern of standing wave
s appears which oscillates at half the driving frequency, given certain criteria of instability
. This relates to the problem of parametric resonance
. The waves can take the form of stripes, close-packed hexagons, or even squares
or quasiperiodic
patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wineglass that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a singing bowl
.
The Faraday wave and its wavelength
is analogy of the de Broglie wave with the de Broglie wavelength in quantum mechanics
.
Michael Faraday
Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....
, are nonlinear
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...
standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
s that appear on liquids enclosed by a vibrating receptacle. When the vibration frequency exceeds a critical value, the flat hydrostatic surface becomes unstable. This is known as the Faraday instability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
. Faraday first described them in an appendix to an article in the Philosophical Transactions of the Royal Society of London in 1831.
If a layer of liquid is placed on top of a vertically oscillating piston, a pattern of standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
s appears which oscillates at half the driving frequency, given certain criteria of instability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
. This relates to the problem of parametric resonance
Parametric oscillator
A parametric oscillator is a harmonic oscillator whose parameters oscillate in time. For example, a well known parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size of the swing's oscillations. The varying of the parameters drives the system...
. The waves can take the form of stripes, close-packed hexagons, or even squares
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
or quasiperiodic
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wineglass that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a singing bowl
Singing bowl
Singing bowls are a type of bell, specifically classified as a standing bell. Rather than hanging inverted or attached to a handle, singing bowls sit with the bottom surface resting...
.
The Faraday wave and its wavelength
Wavelength
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...
is analogy of the de Broglie wave with the de Broglie wavelength in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.