A report on Resonance and Standing wave

Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator.
Animation of a standing wave ( red ) created by the superposition of a left traveling ( blue ) and right traveling ( green ) wave
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.
Longitudinal standing wave
An RLC series circuit
Transient analysis of a damped traveling wave reflecting at a boundary
A mass on a spring has one natural frequency, as it has a single degree of freedom
Standing wave in stationary medium. The red dots represent the wave nodes.
A standing wave (in black), created when two waves moving from left and right meet and superimpose
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).
Standing waves in a string – the fundamental mode and the first 5 harmonics.
Electric force vector (E) and magnetic force vector (H) of a standing wave.
School resonating mass experiment
Standing waves in a string – the fundamental mode and the first 5 harmonics.
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).
A standing wave on a circular membrane, an example of standing waves in two dimensions. This is the fundamental mode.
NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2-tesla field, the proton resonance is at 900 MHz.
A higher harmonic standing wave on a disk with two nodal lines crossing at the center.
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).

The most common cause of standing waves is the phenomenon of resonance, in which standing waves occur inside a resonator due to interference between waves reflected back and forth at the resonator's resonant frequency.

- Standing wave

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

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

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A standing wave in a rectangular cavity resonator

Resonator

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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

A resonator is a device or system that exhibits resonance or resonant behavior.

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 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.

Light confined in the cavity reflects multiple times, producing standing waves for certain resonance frequencies.

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.

They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string.

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.

Resonance