Wave and Standing wave

Surface waves in water showing water ripples

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

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

Transient analysis of a damped traveling wave reflecting at a boundary

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)

Standing wave in stationary medium. The red dots represent the wave nodes.

Sine, square, triangle and sawtooth waveforms.

A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).

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.

Electric force vector (E) and magnetic force vector (H) of a standing wave.

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.

Standing waves in a string – the fundamental mode and the first 5 harmonics.

The red square moves with the phase velocity, while the green circles propagate with the group velocity

A standing wave on a circular membrane, an example of standing waves in two dimensions. This is the fundamental mode.

A wave with the group and phase velocities going in different directions

A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

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.

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.

In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space.

- Standing wave

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.

- Wave

4 related topics

Wave equation

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).

Hydraulic jump

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

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 happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves.

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

Seismic wave

Velocity of seismic waves in Earth versus depth. The negligible S-wave velocity in the outer core occurs because it is liquid, while in the solid inner core the S-wave velocity is non-zero

The sense of motion for toroidal 0T1 oscillation for two moments of time.

The scheme of motion for spheroidal 0S2 oscillation.Dashed lines give nodal (zero) lines. Arrows give the sense of motion.

The hypocenter/epicenter of an earthquake is calculated by using the seismic data of that earthquake from at least three different locations. The hypocenter/epicenter is found at the intersection of three circles centered on three observation stations, here shown in Japan, Australia and the United States. The radius of each circle is calculated from the difference in the arrival times of P- and S-waves at the corresponding station.

P- and S-waves sharing with the propagation

Seismic waves are waves of energy that travel through Earth's layers, and are a result of earthquakes, volcanic eruptions, magma movement, large landslides and large man-made explosions that give out low-frequency acoustic energy.

Free oscillations of the Earth are standing waves, the result of interference between two surface waves traveling in opposite directions.

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

Resonance

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

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.

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

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.

"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).

Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions.

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