A report on Standing wave

Animation of a standing wave ( red ) created by the superposition of a left traveling ( blue ) and right traveling ( green ) wave
Longitudinal standing wave
Transient analysis of a damped traveling wave reflecting at a boundary
Standing wave in stationary medium. The red dots represent the wave nodes.
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).
Electric force vector (E) and magnetic force vector (H) of a standing wave.
Standing waves in a string – the fundamental mode and the first 5 harmonics.
A standing wave on a circular membrane, an example of standing waves in two dimensions. This is the fundamental mode.
A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

Wave that oscillates in time but whose peak amplitude profile does not move in space.

- Standing wave
Animation of a standing wave ( red ) created by the superposition of a left traveling ( blue ) and right traveling ( green ) wave

16 related topics with Alpha

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Surface waves in water showing water ripples

Wave

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Propagating dynamic disturbance of one or more quantities.

Propagating dynamic disturbance of one or more quantities.

Surface waves in water showing water ripples
Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.
Wavelength λ, can be measured between any two corresponding points on a waveform
Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)
Sine, square, triangle and sawtooth waveforms.
Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.
Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.
The red square moves with the phase velocity, while the green circles propagate with the group velocity
A wave with the group and phase velocities going in different directions
Standing wave. The red dots represent the wave nodes
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
Schematic of light being dispersed by a prism. Click to see animation.
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Formation of a shock wave by a plane.
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A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.
Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles
One-dimensional standing waves; the fundamental mode and the first 5 overtones.
A two-dimensional standing wave on a disk; this is the fundamental mode.
A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave.

Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator.

Resonance

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Applied periodic force is equal or close to a natural frequency of the system on which it acts.

Applied periodic force is equal or close to a natural frequency of the system on which it acts.

Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator.
Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate.
An RLC series circuit
A mass on a spring has one natural frequency, as it has a single degree of freedom
A standing wave (in black), created when two waves moving from left and right meet and superimpose
Standing waves in a string – the fundamental mode and the first 5 harmonics.
School resonating mass experiment
Animation illustrating electrical resonance in a tuned circuit, consisting of a capacitor (C) and an inductor (L) connected together. Charge flows back and forth between the capacitor plates through the inductor. Energy oscillates back and forth between the capacitor's electric field (E) and the inductor's magnetic field (B).
NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2-tesla field, the proton resonance is at 900 MHz.
High and low Q factor
"Universal Resonance Curve", a symmetric approximation to the normalized response of a resonant circuit; abscissa values are deviation from center frequency, in units of center frequency divided by 2Q; ordinate is relative amplitude, and phase in cycles; dashed curves compare the range of responses of real two-pole circuits for a Q value of 5; for higher Q values, there is less deviation from the universal curve. Crosses mark the edges of the 3 dB bandwidth (gain 0.707, phase shift 45° or 0.125 cycle).

In many cases these systems have the potential to resonate at certain frequencies, forming standing waves with large-amplitude oscillations at fixed positions.

A standing wave. The red dots are the wave nodes

Node (physics)

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A standing wave. The red dots are the wave nodes
Pattern of two waves' interference (from up to down). The point represents the node.

A node is a point along a standing wave where the wave has minimum amplitude.

A standing wave in a rectangular cavity resonator

Resonator

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Device or system that exhibits resonance or resonant behavior.

Device or system that exhibits resonance or resonant behavior.

A standing wave in a rectangular cavity resonator
An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator.
RF cavities in the linac of the Australian Synchrotron are used to accelerate and bunch beams of electrons; the linac is the tube passing through the middle of the cavity.
A sport motorcycle, equipped with exhaust resonator, designed for performance
A Dobro-style resonator guitar

The oppositely moving waves interfere with each other, and at its resonant frequencies reinforce each other to create a pattern of standing waves in the resonator.

A raft encountering a hydraulic jump on Canolfan Tryweryn in Wales.

Hydraulic jump

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Phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways.

Phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways.

A raft encountering a hydraulic jump on Canolfan Tryweryn in Wales.
Figure 2: A common example of a hydraulic jump is the roughly circular stationary wave that forms around the central stream of water. The jump is at the transition between the point where the circle appears still and where the turbulence is visible.
Figure 3: A tidal bore in Alaska showing a turbulent shock-wave-like front. At this point the water is relatively shallow and the fractional change in elevation is large.
Figure 4: An undular front on a tidal bore. At this point the water is relatively deep and the fractional change in elevation is small.
Figure 5: Series of roll waves moving down a spillway, where they terminate in a stationary hydraulic jump.
Naturally occurring hydraulic jump observed on the Upper Spokane Falls north channel.
Saint Anthony Falls on the Mississippi River showing a pronounced hydraulic jump.
Supercritical flow down the Cleveland Dam spillway at the head of the Capilano River in North Vancouver, British Columbia, Canada.
Energy dissipation using hydraulic jump.
Kayak playing on the transition between the turbulent flow and the recirculation region in the pier wake.

When this occurs, the water slows in a rather abrupt rise (a step or standing wave) on the liquid surface.

Surfer on the Eisbach, Englischer Garten, Munich, Germany.

River surfing

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Surfer on the Eisbach, Englischer Garten, Munich, Germany.
Surfing a standing wave on the Eisbach.
Surfers on the Severn bore

River surfing is the sport of surfing either standing waves, tidal bores or upstream waves in rivers.

A glass nanoparticle is suspended in an optical cavity

Optical cavity

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A glass nanoparticle is suspended in an optical cavity
Types of two-mirror optical cavities, with mirrors of various curvatures, showing the radiation pattern inside each cavity.
Stability diagram for a two-mirror cavity. Blue-shaded areas correspond to stable configurations.
Alignment of a folded cavity using an autocollimator

An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves.

Incident wave (blue) is fully reflected (red wave) out of phase at short-circuited end of transmission line, creating a net voltage (black) standing wave. Γ = −1, SWR = ∞.

Standing wave ratio

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Measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide.

Measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide.

Incident wave (blue) is fully reflected (red wave) out of phase at short-circuited end of transmission line, creating a net voltage (black) standing wave. Γ = −1, SWR = ∞.
Standing waves on transmission line, net voltage shown in different colors during one period of oscillation. Incoming wave from left (amplitude = 1) is partially reflected with (top to bottom) Γ = 0.6, −0.333, and 0.8 ∠60°. Resulting SWR = 4, 2, 9.
Example of estimated bandwidth of antenna according to the schedule VSWR by the help of the Ansys HFSS
Slotted line. The probe moves along the line to measure the variable voltage. SWR is the maximum divided by the minimum voltage
A directional wattmeter using a rotatable directional coupler element.

Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line.

French scientist Jean-Baptiste le Rond d'Alembert discovered the wave equation in one space dimension.

Wave equation

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French scientist Jean-Baptiste le Rond d'Alembert discovered the wave equation in one space dimension.
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1-d standing wave as a superposition of two waves traveling in opposite directions
Swiss mathematician and physicist Leonhard Euler (b. 1707) discovered the wave equation in three space dimensions.
Cut-away of spherical wavefronts, with a wavelength of 10 units, propagating from a point source.
Figure 1: Three consecutive mass points of the discrete model for a string
A solution of the wave equation in two dimensions with a zero-displacement boundary condition along the entire outer edge.

The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves).

Standing waves, in which each immobile point represents a node.

Franz Melde

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German physicist and professor.

German physicist and professor.

Standing waves, in which each immobile point represents a node.

Standing waves were first discovered by Melde, who coined the term "standing wave" (stehende Welle) around 1860.