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Standing wave

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. The peak amplitude of the wave oscillations at any point in space is constant with respect to time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes.

Standing waves were first described scientifically by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container. Franz Melde coined the term "standing wave" (German: stehende Welle or Stehwelle) around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings.

This phenomenon can occur because the medium is moving in the direction opposite to the movement of the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. 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.

For waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

Moving medium
As an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee of mountain ranges. Such waves are often exploited by glider pilots.

Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom. A requirement for this in river currents is a flowing water with shallow depth in which the inertia of the water overcomes its gravity due to the supercritical flow speed (Froude number: 1.7 – 4.5, surpassing 4.5 results in direct standing wave ) and is therefore neither significantly slowed down by the obstacle nor pushed to the side. Many standing river waves are popular river surfing breaks.

Opposing waves
As an example of the second type, a standing wave in a transmission line is a wave in which the distribution of current, voltage, or field strength is formed by the superposition of two waves of the same frequency propagating in opposite directions. The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. Such a standing wave may be formed when a wave is transmitted into one end of a transmission line and is reflected from the other end by an impedance mismatch, i.e., discontinuity, such as an open circuit or a short. The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion.

In practice, losses in the transmission line and other components mean that a perfect reflection and a pure standing wave are never achieved. The result is a partial standing wave, which is a superposition of a standing wave and a traveling wave. The degree to which the wave resembles either a pure standing wave or a pure traveling wave is measured by the standing wave ratio (SWR).

Another example is standing waves in the open ocean formed by waves with the same wave period moving in opposite directions. These may form near storm centres, or from reflection of a swell at the shore, and are the source of microbaroms and microseisms.

Mathematical description
This section considers representative one- and two-dimensional cases of standing waves. First, an example of an infinite length string shows how identical waves traveling in opposite directions interfere to produce standing waves. Next, two finite length string examples with different boundary conditions demonstrate how the boundary conditions restrict the frequencies that can form standing waves. Next, the example of sound waves in a pipe demonstrates how the same principles can be applied to longitudinal waves with analogous boundary conditions.

Standing waves can also occur in two- or three-dimensional resonators. With standing waves on two-dimensional membranes such as drumheads, illustrated in the animations above, the nodes become nodal lines, lines on the surface at which there is no movement, that separate regions vibrating with opposite phase. These nodal line patterns are called Chladni figures. In three-dimensional resonators, such as musical instrument sound boxes and microwave cavity resonators, there are nodal surfaces. This section includes a two-dimensional standing wave example with a rectangular boundary to illustrate how to extend the concept to higher dimensions.

Standing wave on an infinite length string
To begin, consider a string of infinite length along the x-axis that is free to be stretched transversely in the y direction.

For a harmonic wave traveling to the right along the string, the string's displacement in the y direction as a function of position x and time t is
 * $$ y_\text{R}(x,t) = y_\text{max}\sin \left({2\pi x \over \lambda} - \omega t \right). $$

The displacement in the y-direction for an identical harmonic wave traveling to the left is
 * $$ y_\text{L}(x,t) = y_\text{max}\sin \left({2\pi x \over \lambda} + \omega t \right), $$

where
 * ymax is the amplitude of the displacement of the string for each wave,
 * ω is the angular frequency or equivalently 2π times the frequency f,
 * λ is the wavelength of the wave.

For identical right- and left-traveling waves on the same string, the total displacement of the string is the sum of yR and yL,
 * $$ y(x,t) = y_\text{R} + y_\text{L} = y_\text{max}\sin \left({2\pi x \over \lambda} - \omega t \right) + y_\text{max}\sin \left({2\pi x \over \lambda} + \omega t \right). $$

Using the trigonometric sum-to-product identity $$\sin a + \sin b = 2\sin \left({a+b \over 2}\right)\cos \left({a-b \over 2}\right)$$,

Equation ($$) does not describe a traveling wave. At any position x, y(x,t) simply oscillates in time with an amplitude that varies in the x-direction as $$2y_\text{max}\sin \left({2\pi x \over \lambda}\right)$$. The animation at the beginning of this article depicts what is happening. As the left-traveling blue wave and right-traveling green wave interfere, they form the standing red wave that does not travel and instead oscillates in place.

Because the string is of infinite length, it has no boundary condition for its displacement at any point along the x-axis. As a result, a standing wave can form at any frequency.

At locations on the x-axis that are even multiples of a quarter wavelength,
 * $$x = \ldots, -{3\lambda \over 2}, \; -\lambda, \; -{\lambda \over 2}, \; 0, \; {\lambda \over 2}, \; \lambda, \; {3\lambda \over 2}, \ldots $$

the amplitude is always zero. These locations are called nodes. At locations on the x-axis that are odd multiples of a quarter wavelength
 * $$x = \ldots, -{5\lambda \over 4}, \; -{3\lambda \over 4}, \; -{\lambda \over 4}, \; {\lambda \over 4}, \; {3\lambda \over 4}, \; {5\lambda \over 4}, \ldots $$

the amplitude is maximal, with a value of twice the amplitude of the right- and left-traveling waves that interfere to produce this standing wave pattern. These locations are called anti-nodes. The distance between two consecutive nodes or anti-nodes is half the wavelength, λ/2.

Standing wave on a string with two fixed ends
Next, consider a string with fixed ends at and. The string will have some damping as it is stretched by traveling waves, but assume the damping is very small. Suppose that at the fixed end a sinusoidal force is applied that drives the string up and down in the y-direction with a small amplitude at some frequency f. In this situation, the driving force produces a right-traveling wave. That wave reflects off the right fixed end and travels back to the left, reflects again off the left fixed end and travels back to the right, and so on. Eventually, a steady state is reached where the string has identical right- and left-traveling waves as in the infinite-length case and the power dissipated by damping in the string equals the power supplied by the driving force so the waves have constant amplitude.

Equation ($$) still describes the standing wave pattern that can form on this string, but now Equation ($$) is subject to boundary conditions where at  and  because the string is fixed at  and because we assume the driving force at the fixed  end has small amplitude. Checking the values of y at the two ends,
 * $$ y(0,t) = 0, $$
 * $$ y(L,t) = 2y_\text{max}\sin \left({2\pi L \over \lambda} \right) \cos(\omega t) = 0. $$

This boundary condition is in the form of the Sturm–Liouville formulation. The latter boundary condition is satisfied when $$ \sin \left({2\pi L \over \lambda} \right) = 0 $$. L is given, so the boundary condition restricts the wavelength of the standing waves to

 * $$n = 1, 2, 3, \ldots $$

Waves can only form standing waves on this string if they have a wavelength that satisfies this relationship with L. If waves travel with speed v along the string, then equivalently the frequency of the standing waves is restricted to
 * $$ f = \frac{v}{\lambda} = \frac{nv}{2L}. $$

The standing wave with oscillates at the fundamental frequency and has a wavelength that is twice the length of the string. Higher integer values of n correspond to modes of oscillation called harmonics or overtones. Any standing wave on the string will have n + 1 nodes including the fixed ends and n anti-nodes.

To compare this example's nodes to the description of nodes for standing waves in the infinite length string, Equation ($$) can be rewritten as
 * $$ \lambda = \frac{4L}{n}, $$
 * $$ n = 2, 4, 6, \ldots $$

In this variation of the expression for the wavelength, n must be even. Cross multiplying we see that because L is a node, it is an even multiple of a quarter wavelength,
 * $$ L = \frac{n\lambda}{4}, $$
 * $$ n = 2, 4, 6, \ldots $$

This example demonstrates a type of resonance and the frequencies that produce standing waves can be referred to as resonant frequencies.

Standing wave on a string with one fixed end

Next, consider the same string of length L, but this time it is only fixed at. At, the string is free to move in the y direction. For example, the string might be tied at to a ring that can slide freely up and down a pole. The string again has small damping and is driven by a small driving force at.

In this case, Equation ($$) still describes the standing wave pattern that can form on the string, and the string has the same boundary condition of at. However, at where the string can move freely there should be an anti-node with maximal amplitude of y. Equivalently, this boundary condition of the "free end" can be stated as ∂y/∂x = 0 at, which is in the form of the Sturm–Liouville formulation. The intuition for this boundary condition ∂y/∂x = 0 at is that the motion of the "free end" will follow that of the point to its left.

Reviewing Equation ($$), for the largest amplitude of y occurs when ∂y/∂x = 0, or
 * $$ \cos \left({2\pi L \over \lambda}\right) = 0. $$

This leads to a different set of wavelengths than in the two-fixed-ends example. Here, the wavelength of the standing waves is restricted to
 * $$ \lambda = \frac{4L}{n}, $$
 * $$ n = 1, 3, 5, \ldots $$

Equivalently, the frequency is restricted to
 * $$ f = \frac{nv}{4L}. $$

In this example n only takes odd values. Because L is an anti-node, it is an odd multiple of a quarter wavelength. Thus the fundamental mode in this example only has one quarter of a complete sine cycle–zero at and the first peak at –the first harmonic has three quarters of a complete sine cycle, and so on.

This example also demonstrates a type of resonance and the frequencies that produce standing waves are called resonant frequencies.

Standing wave in a pipe
Consider a standing wave in a pipe of length L. The air inside the pipe serves as the medium for longitudinal sound waves traveling to the right or left through the pipe. While the transverse waves on the string from the previous examples vary in their displacement perpendicular to the direction of wave motion, the waves traveling through the air in the pipe vary in terms of their pressure and longitudinal displacement along the direction of wave motion. The wave propagates by alternately compressing and expanding air in segments of the pipe, which displaces the air slightly from its rest position and transfers energy to neighboring segments through the forces exerted by the alternating high and low air pressures. Equations resembling those for the wave on a string can be written for the change in pressure Δp due to a right- or left-traveling wave in the pipe.
 * $$ \Delta p_\text{R}(x,t) = p_\text{max}\sin \left({2\pi x \over \lambda} - \omega t \right), $$
 * $$ \Delta p_\text{L}(x,t) = p_\text{max}\sin \left({2\pi x \over \lambda} + \omega t \right), $$

where
 * pmax is the pressure amplitude or the maximum increase or decrease in air pressure due to each wave,
 * ω is the angular frequency or equivalently 2π times the frequency f,
 * λ is the wavelength of the wave.

If identical right- and left-traveling waves travel through the pipe, the resulting superposition is described by the sum
 * $$ \Delta p(x,t) = \Delta p_\text{R}(x,t) + \Delta p_\text{L}(x,t) = 2p_\text{max}\sin \left({2\pi x \over \lambda} \right) \cos(\omega t).$$

This formula for the pressure is of the same form as Equation ($$), so a stationary pressure wave forms that is fixed in space and oscillates in time.

If the end of a pipe is closed, the pressure is maximal since the closed end of the pipe exerts a force that restricts the movement of air. This corresponds to a pressure anti-node (which is a node for molecular motions, because the molecules near the closed end cannot move). If the end of the pipe is open, the pressure variations are very small, corresponding to a pressure node (which is an anti-node for molecular motions, because the molecules near the open end can move freely). The exact location of the pressure node at an open end is actually slightly beyond the open end of the pipe, so the effective length of the pipe for the purpose of determining resonant frequencies is slightly longer than its physical length. This difference in length is ignored in this example. In terms of reflections, open ends partially reflect waves back into the pipe, allowing some energy to be released into the outside air. Ideally, closed ends reflect the entire wave back in the other direction.

First consider a pipe that is open at both ends, for example an open organ pipe or a recorder. Given that the pressure must be zero at both open ends, the boundary conditions are analogous to the string with two fixed ends,
 * $$ \Delta p(0,t) = 0,$$
 * $$ \Delta p(L,t) = 2p_\text{max}\sin \left({2\pi L \over \lambda} \right) \cos(\omega t) = 0,$$

which only occurs when the wavelength of standing waves is
 * $$ \lambda = \frac{2L}{n}, $$
 * $$ n = 1, 2, 3, \ldots, $$

or equivalently when the frequency is
 * $$ f = \frac{nv}{2L},$$

where v is the speed of sound.

Next, consider a pipe that is open at (and therefore has a pressure node) and closed at  (and therefore has a pressure anti-node). The closed "free end" boundary condition for the pressure at can be stated as ∂(Δp)/∂x = 0, which is in the form of the Sturm–Liouville formulation. The intuition for this boundary condition ∂(Δp)/∂x = 0 at is that the pressure of the closed end will follow that of the point to its left. Examples of this setup include a bottle and a clarinet. This pipe has boundary conditions analogous to the string with only one fixed end. Its standing waves have wavelengths restricted to
 * $$ \lambda = \frac{4L}{n}, $$
 * $$ n = 1, 3, 5, \ldots, $$

or equivalently the frequency of standing waves is restricted to
 * $$ f = \frac{nv}{4L}.$$

For the case where one end is closed, n only takes odd values just like in the case of the string fixed at only one end.

So far, the wave has been written in terms of its pressure as a function of position x and time. Alternatively, the wave can be written in terms of its longitudinal displacement of air, where air in a segment of the pipe moves back and forth slightly in the x-direction as the pressure varies and waves travel in either or both directions. The change in pressure Δp and longitudinal displacement s are related as
 * $$ \Delta p = -\rho v^2 \frac{\partial s}{\partial x}, $$

where ρ is the density of the air. In terms of longitudinal displacement, closed ends of pipes correspond to nodes since air movement is restricted and open ends correspond to anti-nodes since the air is free to move. A similar, easier to visualize phenomenon occurs in longitudinal waves propagating along a spring.

We can also consider a pipe that is closed at both ends. In this case, both ends will be pressure anti-nodes or equivalently both ends will be displacement nodes. This example is analogous to the case where both ends are open, except the standing wave pattern has a $$ phase shift along the x-direction to shift the location of the nodes and anti-nodes. For example, the longest wavelength that resonates–the fundamental mode–is again twice the length of the pipe, except that the ends of the pipe have pressure anti-nodes instead of pressure nodes. Between the ends there is one pressure node. In the case of two closed ends, the wavelength is again restricted to
 * $$ \lambda = \frac{2L}{n}, $$
 * $$ n = 1, 2, 3, \ldots, $$

and the frequency is again restricted to
 * $$ f = \frac{nv}{2L}.$$

A Rubens tube provides a way to visualize the pressure variations of the standing waves in a tube with two closed ends.

2D standing wave with a rectangular boundary
Next, consider transverse waves that can move along a two dimensional surface within a rectangular boundary of length Lx in the x-direction and length Ly in the y-direction. Examples of this type of wave are water waves in a pool or waves on a rectangular sheet that has been pulled taut. The waves displace the surface in the z-direction, with defined as the height of the surface when it is still.

In two dimensions and Cartesian coordinates, the wave equation is
 * $$\frac{\partial^2 z}{\partial t^2} \;=\; c^2 \left(\frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial y^2}\right), $$

where
 * z(x,y,t) is the displacement of the surface,
 * c is the speed of the wave.

To solve this differential equation, let's first solve for its Fourier transform, with
 * $$ Z(x,y,\omega) = \int_{-\infty}^{\infty}z(x,y,t) e^{-i\omega t}dt.$$

Taking the Fourier transform of the wave equation,
 * $$ \frac{\partial^2 Z}{\partial x^2} + \frac{\partial^2 Z}{\partial y^2} = -\frac{\omega^2}{c^2}Z(x,y,\omega). $$

This is an eigenvalue problem where the frequencies correspond to eigenvalues that then correspond to frequency-specific modes or eigenfunctions. Specifically, this is a form of the Helmholtz equation and it can be solved using separation of variables. Assume
 * $$ Z = X(x)Y(y).$$

Dividing the Helmholtz equation by Z,
 * $$ \frac{1}{X(x)}\frac{\partial^2 X}{\partial x^2} + \frac{1}{Y(y)}\frac{\partial^2 Y}{\partial y^2} + \frac{\omega^2}{c^2} = 0. $$

This leads to two coupled ordinary differential equations. The x term equals a constant with respect to x that we can define as
 * $$ \frac{1}{X(x)}\frac{\partial^2 X}{\partial x^2} = (ik_x)^2.$$

Solving for X(x),
 * $$ X(x) = A_{k_x} e^{i k_x x} + B_{k_x}e^{-i k_x x}.$$

This x-dependence is sinusoidal–recalling Euler's formula–with constants Ak x and Bk x determined by the boundary conditions. Likewise, the y term equals a constant with respect to y that we can define as
 * $$ \frac{1}{Y(y)}\frac{\partial^2 Y}{\partial y^2} = (ik_y)^2 = k_x^2-\frac{\omega^2}{c^2},$$

and the dispersion relation for this wave is therefore
 * $$ \omega = c \sqrt{k_x^2 + k_y^2}.$$

Solving the differential equation for the y term,
 * $$ Y(y) = C_{k_y} e^{i k_y y} + D_{k_y}e^{-i k_y y}.$$

Multiplying these functions together and applying the inverse Fourier transform, z(x,y,t) is a superposition of modes where each mode is the product of sinusoidal functions for x, y, and t,
 * $$ z(x,y,t) \sim e^{\pm i k_x x}e^{\pm i k_y y}e^{\pm i \omega t}.$$

The constants that determine the exact sinusoidal functions depend on the boundary conditions and initial conditions. To see how the boundary conditions apply, consider an example like the sheet that has been pulled taut where z(x,y,t) must be zero all around the rectangular boundary. For the x dependence, z(x,y,t) must vary in a way that it can be zero at both and  for all values of y and t. As in the one dimensional example of the string fixed at both ends, the sinusoidal function that satisfies this boundary condition is
 * $$\sin{k_x x},$$

with kx restricted to
 * $$k_x = \frac{n \pi}{L_x}, \quad n = 1, 2, 3, \dots$$

Likewise, the y dependence of z(x,y,t) must be zero at both and, which is satisfied by
 * $$\sin{k_y y}, \quad k_y = \frac{m \pi}{L_y}, \quad m = 1, 2, 3, \dots$$

Restricting the wave numbers to these values also restricts the frequencies that resonate to
 * $$\omega = c \pi \sqrt{\left(\frac{n}{L_x}\right)^2 + \left(\frac{m}{L_y}\right)^2}.$$

If the initial conditions for z(x,y,0) and its time derivative ż(x,y,0) are chosen so the t-dependence is a cosine function, then standing waves for this system take the form
 * $$ z(x,y,t) = z_{\text{max}}\sin \left(\frac{n\pi x}{L_x}\right) \sin \left(\frac{m\pi y}{L_y}\right) \cos \left(\omega t\right). $$
 * $$ n = 1, 2, 3, \dots \quad m = 1, 2, 3, \dots$$

So, standing waves inside this fixed rectangular boundary oscillate in time at certain resonant frequencies parameterized by the integers n and m. As they oscillate in time, they do not travel and their spatial variation is sinusoidal in both the x- and y-directions such that they satisfy the boundary conditions. The fundamental mode, and, has a single antinode in the middle of the rectangle. Varying n and m gives complicated but predictable two-dimensional patterns of nodes and antinodes inside the rectangle.

From the dispersion relation, in certain situations different modes–meaning different combinations of n and m–may resonate at the same frequency even though they have different shapes for their x- and y-dependence. For example, if the boundary is square,, the modes and ,  and , and  and  all resonate at
 * $$\omega = \frac{c \pi}{L_x} \sqrt{50}.$$

Recalling that ω determines the eigenvalue in the Helmholtz equation above, the number of modes corresponding to each frequency relates to the frequency's multiplicity as an eigenvalue.

Standing wave ratio, phase, and energy transfer
If the two oppositely moving traveling waves are not of the same amplitude, they will not cancel completely at the nodes, the points where the waves are 180° out of phase, so the amplitude of the standing wave will not be zero at the nodes, but merely a minimum. Standing wave ratio (SWR) is the ratio of the amplitude at the antinode (maximum) to the amplitude at the node (minimum). A pure standing wave will have an infinite SWR. It will also have a constant phase at any point in space (but it may undergo a 180° inversion every half cycle). A finite, non-zero SWR indicates a wave that is partially stationary and partially travelling. Such waves can be decomposed into a superposition of two waves: a travelling wave component and a stationary wave component. An SWR of one indicates that the wave does not have a stationary component – it is purely a travelling wave, since the ratio of amplitudes is equal to 1.

A pure standing wave does not transfer energy from the source to the destination. However, the wave is still subject to losses in the medium. Such losses will manifest as a finite SWR, indicating a travelling wave component leaving the source to supply the losses. Even though the SWR is now finite, it may still be the case that no energy reaches the destination because the travelling component is purely supplying the losses. However, in a lossless medium, a finite SWR implies a definite transfer of energy to the destination.

Examples
One easy example to understand standing waves is two people shaking either end of a jump rope. If they shake in sync the rope can form a regular pattern of waves oscillating up and down, with stationary points along the rope where the rope is almost still (nodes) and points where the arc of the rope is maximum (antinodes).

Acoustic resonance
Standing waves are also observed in physical media such as strings and columns of air. Any waves traveling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a vibrating string or air column's natural frequency, a standing wave is created, allowing harmonics to be identified. Nodes occur at fixed ends and anti-nodes at open ends. If fixed at only one end, only odd-numbered harmonics are available. At the open end of a pipe the anti-node will not be exactly at the end as it is altered by its contact with the air and so end correction is used to place it exactly. The density of a string will affect the frequency at which harmonics will be produced; the greater the density the lower the frequency needs to be to produce a standing wave of the same harmonic.

Visible light
Standing waves are also observed in optical media such as optical waveguides and optical cavities. Lasers use optical cavities in the form of a pair of facing mirrors, which constitute a Fabry–Pérot interferometer. The gain medium in the cavity (such as a crystal) emits light coherently, exciting standing waves of light in the cavity. The wavelength of light is very short (in the range of nanometers, 10−9 m) so the standing waves are microscopic in size. One use for standing light waves is to measure small distances, using optical flats.

X-rays
Interference between X-ray beams can form an X-ray standing wave (XSW) field. Because of the short wavelength of X-rays (less than 1 nanometer), this phenomenon can be exploited for measuring atomic-scale events at material surfaces. The XSW is generated in the region where an X-ray beam interferes with a diffracted beam from a nearly perfect single crystal surface or a reflection from an X-ray mirror. By tuning the crystal geometry or X-ray wavelength, the XSW can be translated in space, causing a shift in the X-ray fluorescence or photoelectron yield from the atoms near the surface. This shift can be analyzed to pinpoint the location of a particular atomic species relative to the underlying crystal structure or mirror surface. The XSW method has been used to clarify the atomic-scale details of dopants in semiconductors, atomic and molecular adsorption on surfaces, and chemical transformations involved in catalysis.

Mechanical waves
Standing waves can be mechanically induced into a solid medium using resonance. One easy to understand example is two people shaking either end of a jump rope. If they shake in sync, the rope will form a regular pattern with nodes and antinodes and appear to be stationary, hence the name standing wave. Similarly a cantilever beam can have a standing wave imposed on it by applying a base excitation. In this case the free end moves the greatest distance laterally compared to any location along the beam. Such a device can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology.

Seismic waves
Standing surface waves on the Earth are observed as free oscillations of the Earth.

Faraday waves
The Faraday wave is a non-linear standing wave at the air-liquid interface induced by hydrodynamic instability. It can be used as a liquid-based template to assemble microscale materials.

Seiches
A seiche is an example of a standing wave in an enclosed body of water. It is characterised by the oscillatory behaviour of the water level at either end of the body and typically has a nodal point near the middle of the body where very little change in water level is observed. It should be distinguished from a simple storm surge where no oscillation is present. In sizeable lakes, the period of such oscillations may be between minutes and hours, for example Lake Geneva's longitudinal period is 73 minutes and its transversal seiche has a period of around 10 minutes, while Lake Huron can be seen to have resonances with periods between 1 and 2 hours. See Lake seiches.

Waves
• Index of wave articles:

• Amphidromic point

• Clapotis

• Longitudinal mode

• Mode-locking

• Metachronal rhythm

• Resonant room modes

• Seiche

• Trumpet

• Kundt's tube

• Wave Equation

• One-Way Wave Equation

Electronics
• Index of electronics articles:

• Cavity resonator

• Characteristic impedance

• Cymatics

• Impedance

• Normal mode

title: Standing wave


text:
Standing wave ratio

In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. 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.

Voltage standing wave ratio (VSWR) (pronounced "vizwar" ) is the ratio of maximum to minimum voltage on a transmission line. For example, a VSWR of 1.2 means a peak voltage 1.2 times the minimum voltage along that line, if the line is at least one half wavelength long.

A SWR can be also defined as the ratio of the maximum amplitude to minimum amplitude of the transmission line's currents, electric field strength, or the magnetic field strength. Neglecting transmission line loss, these ratios are identical.

The power standing wave ratio (PSWR) is defined as the square of the VSWR, however, this deprecated term has no direct physical relation to power actually involved in transmission.

SWR is usually measured using a dedicated instrument called an SWR meter. Since SWR is a measure of the load impedance relative to the characteristic impedance of the transmission line in use (which together determine the reflection coefficient as described below), a given SWR meter can interpret the impedance it sees in terms of SWR only if it has been designed for the same particular characteristic impedance as the line. In practice most transmission lines used in these applications are coaxial cables with an impedance of either 50 or 75 ohms, so most SWR meters correspond to one of these.

Checking the SWR is a standard procedure in a radio station. Although the same information could be obtained by measuring the load's impedance with an impedance analyzer (or "impedance bridge"), the SWR meter is simpler and more robust for this purpose. By measuring the magnitude of the impedance mismatch at the transmitter output it reveals problems due to either the antenna or the transmission line.

Impedance matching
SWR is used as a measure of impedance matching of a load to the characteristic impedance of a transmission line carrying radio frequency (RF) signals. This especially applies to transmission lines connecting radio transmitters and receivers with their antennas, as well as similar uses of RF cables such as cable television connections to TV receivers and distribution amplifiers. Impedance matching is achieved when the source impedance is the complex conjugate of the load impedance. The easiest way of achieving this, and the way that minimizes losses along the transmission line, is for the imaginary part of the complex impedance of both the source and load to be zero, that is, pure resistances, equal to the characteristic impedance of the transmission line. When there is a mismatch between the load impedance and the transmission line, part of the forward wave sent toward the load is reflected back along the transmission line towards the source. The source then sees a different impedance than it expects which can lead to lesser (or in some cases, more) power being supplied by it, the result being very sensitive to the electrical length of the transmission line.

Such a mismatch is usually undesired and results in standing waves along the transmission line which magnifies transmission line losses (significant at higher frequencies and for longer cables). The SWR is a measure of the depth of those standing waves and is, therefore, a measure of the matching of the load to the transmission line. A matched load would result in an SWR of 1:1 implying no reflected wave. An infinite SWR represents complete reflection by a load unable to absorb electrical power, with all the incident power reflected back towards the source.

It should be understood that the match of a load to the transmission line is different from the match of a source to the transmission line or the match of a source to the load seen through the transmission line. For instance, if there is a perfect match between the load impedance $Z$load and the source impedance $Z$source = $Z$*load, that perfect match will remain if the source and load are connected through a transmission line with an electrical length of one half wavelength (or a multiple of one half wavelengths) using a transmission line of any characteristic impedance $Z$0. However the SWR will generally not be 1:1, depending only on $Z$load and $Z$0. With a different length of transmission line, the source will see a different impedance than $Z$load which may or may not be a good match to the source. Sometimes this is deliberate, as when a quarter-wave matching section is used to improve the match between an otherwise mismatched source and load.

However typical RF sources such as transmitters and signal generators are designed to look into a purely resistive load impedance such as 50Ω or 75Ω, corresponding to common transmission lines' characteristic impedances. In those cases, matching the load to the transmission line, $Z$load = $Z$0, always ensures that the source will see the same load impedance as if the transmission line weren't there. This is identical to a 1:1 SWR. This condition ($Z$load = $Z$0) also means that the load seen by the source is independent of the transmission line's electrical length. Since the electrical length of a physical segment of transmission line depends on the signal frequency, violation of this condition means that the impedance seen by the source through the transmission line becomes a function of frequency (especially if the line is long), even if $Z$load is frequency-independent. So in practice, a good SWR (near 1:1) implies a transmitter's output seeing the exact impedance it expects for optimum and safe operation.

Relationship to the reflection coefficient
The voltage component of a standing wave in a uniform transmission line consists of the forward wave (with complex amplitude $$V_f$$) superimposed on the reflected wave (with complex amplitude $$V_r$$).

A wave is partly reflected when a transmission line is terminated with an impedance unequal to its characteristic impedance. The reflection coefficient $$\Gamma$$ can be defined as:

 * $$\Gamma = \frac{V_r}{V_f}.$$

or

 * $$\Gamma = {Z_L - Z_o\over Z_L + Z_o}$$

$$\Gamma$$ is a complex number that describes both the magnitude and the phase shift of the reflection. The simplest cases with $$\Gamma$$ measured at the load are:
 * $$\Gamma = -1$$: complete negative reflection, when the line is short-circuited,
 * $$\Gamma = 0$$: no reflection, when the line is perfectly matched,
 * $$\Gamma = +1$$: complete positive reflection, when the line is open-circuited.

The SWR directly corresponds to the magnitude of $$\Gamma$$.

At some points along the line the forward and reflected waves interfere constructively, exactly in phase, with the resulting amplitude $$V_\text{max}$$ given by the sum of those waves' amplitudes:

 * $$\begin{align}

|V_\text{max}| &= |V_f| + |V_r| \\ &= |V_f| + |\Gamma V_f| \\ &= (1 + |\Gamma|) |V_f|. \end{align}$$

At other points, the waves interfere 180° out of phase with the amplitudes partially cancelling:

 * $$\begin{align}

|V_\text{min}| &= |V_f| - |V_r| \\ &= |V_f| - |\Gamma V_f| \\ &= (1 - |\Gamma|) |V_f|. \end{align}$$

The voltage standing wave ratio is then

 * $$\text{VSWR} = \frac{|V_\text{max}|}{|V_\text{min}|} = \frac{1 + |\Gamma|}{1 - |\Gamma|}.$$

Since the magnitude of $$\Gamma$$ always falls in the range [0,1], the SWR is always greater than or equal to unity. Note that the phase of Vf and Vr vary along the transmission line in opposite directions to each other. Therefore, the complex-valued reflection coefficient $$\Gamma$$ varies as well, but only in phase. With the SWR dependent only on the complex magnitude of $$\Gamma$$, it can be seen that the SWR measured at any point along the transmission line (neglecting transmission line losses) obtains an identical reading.

Since the power of the forward and reflected waves are proportional to the square of the voltage components due to each wave, SWR can be expressed in terms of forward and reflected power:

 * $$\text{SWR} = \frac{1 + \sqrt{P_r/P_f}}{1 - \sqrt{P_r/P_f}}.$$

By sampling the complex voltage and current at the point of insertion, an SWR meter is able to compute the effective forward and reflected voltages on the transmission line for the characteristic impedance for which the SWR meter has been designed. Since the forward and reflected power is related to the square of the forward and reflected voltages, some SWR meters also display the forward and reflected power.

In the special case of a load $R$L, which is purely resistive but unequal to the characteristic impedance of the transmission line $Z$0, the SWR is given simply by their ratio:

 * $$\text{SWR} = \max \left\{ \frac{R_\text{L}}{\,Z_\text{0}\,} \,, \frac{\,Z_\text{0}\,}{R_\text{L}} \right\}$$

with the ratio or its reciprocal is chosen to obtain a value greater than unity.

The standing wave pattern
Using complex notation for the voltage amplitudes, for a signal at frequency $f$, the actual (real) voltages V$actual$ as a function of time $t$ are understood to relate to the complex voltages according to:

 * $$ V_\mathsf{actual} = \mathcal{R_e} (e^{i 2 \pi f t} V) ~.$$

Thus taking the real part of the complex quantity inside the parenthesis, the actual voltage consists of a sine wave at frequency $f$ with a peak amplitude equal to the complex magnitude of $V$, and with a phase given by the phase of the complex $V$. Then with the position along a transmission line given by $x$, with the line ending in a load located at $x$$o$, the complex amplitudes of the forward and reverse waves would be written as:

 * $$\begin{align}

V_\mathsf{fwd}(x) &= e^{-i k(x-x_\mathsf{o})} A \\ V_\mathsf{rev}(x) &= \Gamma e^{i k(x-x_\mathsf{o})} A \end{align}$$

for some complex amplitude $A$ (corresponding to the forward wave at $x$$o$ that some treatments use phasors where the time dependence is according to $$e^{ -i 2 \pi f t }$$ and spatial dependence (for a wave in the $+x$ direction) of $$\ e^{+i k(x - x_\mathsf{o})} ~.$$ Either convention obtains the same result for $V$$actual$.

According to the superposition principle the net voltage present at any point $x$ on the transmission line is equal to the sum of the voltages due to the forward and reflected waves:

 * $$\begin{align}

V_\mathsf{net}(x) &= V_\mathsf{fwd}(x) + V_\mathsf{rev}(x) \\ &= e^{-i k(x - x_\mathsf{o})} \left( 1 + \Gamma e^{i 2k(x - x_\mathsf{o})}\right ) A \end{align}$$

Since we are interested in the variations of the magnitude of $V$$net$ along the line (as a function of $x$), we shall solve instead for the squared magnitude of that quantity, which simplifies the mathematics. To obtain the squared magnitude we multiply the above quantity by its complex conjugate:

 * $$\begin{align}

|V_\mathsf{net}(x)|^2 &= V_\mathsf{net}(x) V^*_\mathsf{net}(x) \\ &= e^{-i k \left(x - x_\mathsf{o}\right)} \left(1 + \Gamma e^{i 2 k \left(x - x_\mathsf{o}\right)}\right) A \, e^{+i k\left(x - x_\mathsf{o}\right)} \left(1 + \Gamma^* e^{-i 2 k \left(x - x_\mathsf{o}\right)}\right) A^* \\ &= \left[\ 1 + |\Gamma|^2 + 2\ \operatorname\mathcal{R_e} \left(\Gamma e^{i 2 k \left(x - x_\mathsf{o}\right)} \right)\ \right] |A|^2 \end{align}$$

Depending on the phase of the third term, the maximum and minimum values of $V$$net$ (the square root of the quantity in the equations) are $$\ \left(1 + |\Gamma|\right) |A|\ $$ and $$\ \left(1 - |\Gamma|\right) |A|\ ,$$ respectively, for a standing wave ratio of:

 * $$ \boldsymbol\mathsf{SWR} = \frac{|V_\mathsf{max}|}{|V_\mathsf{min}|} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$

 * $$ \left|\Gamma\right| = \frac{\ \boldsymbol\mathsf{SWR} - 1\ }{\boldsymbol\mathsf{SWR} + 1}$$

as earlier asserted. Along the line, the above expression for $$\ |V_\mathsf{net}(x)|^2\ $$ is seen to oscillate sinusoidally between $$\ |V_\mathsf{min}|^2\ $$ and $$\ |V_\mathsf{max}|^2\ $$ with a period of $2π⁄2k$. This is half of the guided wavelength $λ$ = $2π⁄k$ for the frequency $f$. That can be seen as due to interference between two waves of that frequency which are travelling in opposite directions.

For example, at a frequency $f$ = 20 MHz (free space wavelength of 15 m) in a transmission line whose velocity factor is 0.67, the guided wavelength (distance between voltage peaks of the forward wave alone) would be $λ$ = 10 m. At instances when the forward wave at $x$ = 0 is at zero phase (peak voltage) then at $x$ = 10 m it would also be at zero phase, but at $x$ = 5 m it would be at 180° phase (peak negative voltage). On the other hand, the magnitude of the voltage due to a standing wave produced by its addition to a reflected wave, would have a wavelength between peaks of only $1⁄2$$λ$ = 5 m. Depending on the location of the load and phase of reflection, there might be a peak in the magnitude of $V$$net$ at $x$ = 1.3 m. Then there would be another peak found where $V$$net$ at $V$ = 6.3 m, whereas it would find minima of the standing wave $max$net at $x$ = 3.8 m, 8.8 m, etc.

Practical implications of SWR
The most common case for measuring and examining SWR is when installing and tuning transmitting antennas. When a transmitter is connected to an antenna by a feed line, the driving point impedance of the antenna must match the characteristic impedance of the feed line in order for the transmitter to see the impedance it was designed for (the impedance of the feed line, usually 50 or 75 ohms).

The impedance of a particular antenna design can vary due to a number of factors that cannot always be clearly identified. This includes the transmitter frequency (as compared to the antenna's design or resonant frequency), the antenna's height above and quality of the ground, proximity to large metal structures, and variations in the exact size of the conductors used to construct the antenna.

When an antenna and feed line do not have matching impedances, the transmitter sees an unexpected impedance, where it might not be able to produce its full power, and can even damage the transmitter in some cases. The reflected power in the transmission line increases the average current and therefore losses in the transmission line compared to power actually delivered to the load. It is the interaction of these reflected waves with forward waves which causes standing wave patterns, with the negative repercussions we have noted.

Matching the impedance of the antenna to the impedance of the feed line can sometimes be accomplished through adjusting the antenna itself, but otherwise is possible using an antenna tuner, an impedance matching device. Installing the tuner between the feed line and the antenna allows for the feed line to see a load close to its characteristic impedance, while sending most of the transmitter's power (a small amount may be dissipated within the tuner) to be radiated by the antenna despite its otherwise unacceptable feed point impedance. Installing a tuner in between the transmitter and the feed line can also transform the impedance seen at the transmitter end of the feed line to one preferred by the transmitter. However, in the latter case, the feed line still has a high SWR present, with the resulting increased feed line losses unmitigated.

The magnitude of those losses are dependent on the type of transmission line, and its length. They always increase with frequency. For example, a certain antenna used well away from its resonant frequency may have an SWR of 6:1. For a frequency of 3.5 MHz, with that antenna fed through 75 meters of RG-8A coax, the loss due to standing waves would be 2.2 dB. However the same 6:1 mismatch through 75 meters of RG-8A coax would incur 10.8 dB of loss at 146 MHz. Thus, a better match of the antenna to the feed line, that is, a lower SWR, becomes increasingly important with increasing frequency, even if the transmitter is able to accommodate the impedance seen (or an antenna tuner is used between the transmitter and feed line).

Certain types of transmissions can suffer other negative effects from reflected waves on a transmission line. Analog TV can experience "ghosts" from delayed signals bouncing back and forth on a long line. FM stereo can also be affected and digital signals can experience delayed pulses leading to bit errors. Whenever the delay times for a signal going back down and then again up the line are comparable to the modulation time constants, effects occur. For this reason, these types of transmissions require a low SWR on the feedline, even if SWR induced loss might be acceptable and matching is done at the transmitter.

Methods of measuring standing wave ratio
Many different methods can be used to measure standing wave ratio. The most intuitive method uses a slotted line which is a section of transmission line with an open slot which allows a probe to detect the actual voltage at various points along the line. Thus the maximum and minimum values can be compared directly. This method is used at VHF and higher frequencies. At lower frequencies, such lines are impractically long.

Directional couplers can be used at HF through microwave frequencies. Some are a quarter wave or more long, which restricts their use to the higher frequencies. Other types of directional couplers sample the current and voltage at a single point in the transmission path and mathematically combine them in such a way as to represent the power flowing in one direction. The common type of SWR / power meter used in amateur operation may contain a dual directional coupler. Other types use a single coupler which can be rotated 180 degrees to sample power flowing in either direction. Unidirectional couplers of this type are available for many frequency ranges and  power levels and with appropriate coupling values for the analog meter used. The forward and reflected power measured by directional couplers can be used to calculate SWR. The computations can be done mathematically in analog or digital form or by using graphical methods built into the meter as an additional scale or by reading from the crossing point between two needles on the same meter. The above measuring instruments can be used "in line" that is, the full power of the transmitter can pass through the measuring device so as to allow continuous monitoring of SWR. Other instruments, such as network analyzers, low power directional couplers and antenna bridges use low power for the measurement and must be connected in place of the transmitter. Bridge circuits can be used to directly measure the real and imaginary parts of a load impedance and to use those values to derive SWR. These methods can provide more information than just SWR or forward and reflected power. Stand alone antenna analyzers use various measuring methods and can display SWR and other parameters plotted against frequency. By using directional couplers and a bridge in combination, it is possible to make an in line instrument that reads directly in complex impedance or in SWR. Stand alone antenna analyzers also are available that measure multiple parameters.

Power standing wave ratio
The term power standing wave ratio (PSWR) is sometimes referred to, and defined as, the square of the voltage standing wave ratio. The term is widely cited as "misleading". "The expression "power standing-wave ratio", which may sometimes be encountered, is even more misleading, for the power distribution along a loss-free line is constant. ..."

- J.H. Gridley (2014)

However it does correspond to one type of measurement of SWR using what was formerly a standard measuring instrument at microwave frequencies, the slotted line. The slotted line is a waveguide (or air-filled coaxial line) in which a small sensing antenna which is part of a crystal detector or detector is placed in the electric field in the line. The voltage induced in the antenna is rectified by either a point contact diode (crystal rectifier) or a Schottky barrier diode that is incorporated in the detector. These detectors have a square law output for low levels of input. Readings therefore corresponded to the square of the electric field along the slot, E2(x), with maximum and minimum readings of E2max and E2min found  as the probe is moved along the slot. The ratio of these yields the square of the SWR, the so-called PSWR.

This technique of rationalization of terms is fraught with problems. The square law behavior of the detector diode is exhibited only when the voltage across the diode is below the knee of the diode. Once the detected voltage exceeds the knee, the response of the diode becomes nearly linear. In this mode the diode and its associated filtering capacitor produce a voltage that is proportional to the peak of the sampled voltage. The operator of such a detector would not have a ready indication as to the mode in which the detector diode is operating and therefore differentiating the results between SWR or so called PSWR is not practical. Perhaps even worse, is the common case where the minimum detected voltage is below the knee and the maximum voltage is above the knee. In this case, the computed results are largely meaningless. Thus the terms PSWR and Power Standing Wave Ratio are deprecated and should be considered only from a legacy measurement perspective.

Implications of SWR on medical applications
SWR can also have a detrimental impact upon the performance of microwave-based medical applications. In microwave electrosurgery an antenna that is placed directly into tissue may not always have an optimal match with the feedline resulting in an SWR. The presence of SWR can affect monitoring components used to measure power levels impacting the reliability of such measurements.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Standing wave ratio


text:
Star coupler

A star coupler is a device that takes in an input signal and splits it into several output signals.

In fiber optics, and especially in telecommunications, a star coupler is a passive optical device, used in network applications. An optical signal introduced into any input port is distributed to all output ports. Because of the way a passive star coupler is constructed, the number of ports is usually a power of 2; i.e., two input ports and two output ports (a "two-port" coupler, customarily called a directional coupler, or splitter ); four input ports and four output ports (a "four-port" coupler); eight input ports and eight output ports (an "eight-port" coupler), etc.

Digital Equipment Corporation (now part of Hewlett-Packard) of Maynard, Massachusetts sold a star coupler which interconnected links to computers via coaxial cable rather than optical fibres, but the function was essentially the same. The signal that was distributed was 70 Mbit/s computer interconnect (CI) data and the star coupler provided two redundant paths of either 8 or 16 ports each. Digital's star coupler was developed for use with the VAX- and later Alpha-based computers running Digital's OpenVMS operating system, to provide a passive, highly reliable interconnect for Digital's cluster technology.

title: Star coupler


text:
Start signal

In telecommunication, a start signal is a signal that prepares a device to receive data or to perform a function.

In asynchronous serial communication, start signals are used at the beginning of a character that prepares the receiving device for the reception of the code elements.

A start signal is limited to one signal element usually having the duration of a unit interval.

title: Start signal


text:
Statement

Statement or statements may refer to:

Common uses

 * Statement (computer science), the smallest standalone element of an imperative programming language
 * Statement (logic and semantics), declarative sentence that is either true or false
 * Statement, a declarative phrase in language (linguistics)
 * Statement, a North American paper size of 5 1⁄2 in × 8 in (140 mm × 203 mm), also known under various names such as half letter and memo
 * Financial statement, formal summary of the financial activities of a business, person, or other entity
 * Mathematical statement, a statement in logic and mathematics
 * Political statement, any act or nonverbal form of communication that is intended to influence a decision to be made for or by a group
 * Press statement, written or recorded communication directed at members of the news media
 * Statement of Special Educational Needs, outlining specific provision needed for a child in England
 * Witness statement (law), a signed document recording the evidence given by a person with testimony relevant to an incident
 * A written ministerial statement to Parliament in the United Kingdom

Music

 * Statements (album), a 1962 album by the jazz vibraphonist Milt Jackson
 * "Statement" (song), a 2008 song by the band Boris
 * "Statement", a song by NF from the album Therapy Session
 * "Statements" (song), a 2017 song by Loreen

title: Statement


text:
Step-index profile

For an optical fiber, a step-index profile is a refractive index profile characterized by a uniform refractive index within the core and a sharp decrease in refractive index at the core-cladding interface so that the cladding is of a lower refractive index. The step-index profile corresponds to a power-law index profile with the profile parameter approaching infinity. The step-index profile is used in most single-mode fibers and some multimode fibers.

A step-index fiber is characterized by the core and cladding refractive indices n1 and n2 and the core and cladding radii a and b. Examples of standard core and cladding diameters 2a/2b are 8/125, 50/125, 62.5/125, 85/125, or 100/140 (units of μm). The fractional refractive-index change $$\triangle \, = \frac{n_1 - n_2}{n_1} \ll \ 1$$. The value of n1 is typically between 1.44 and 1.46, and $$\triangle$$ is typically between 0.001 and 0.02.

Step-index optical fiber is generally made by doping high-purity fused silica glass (SiO2) with different concentrations of materials like titanium, germanium, or boron.

Modal dispersion in a step index optical fiber is given by

$$\text{pulse dispersion} = \frac{\triangle\ n_1\ \ell}{c}\,\!$$

where
 * $$\triangle\,\!$$ is the fractional index of refraction
 * $$n_1\,\!$$ is the refractive index of core
 * $$\ell\,\!$$ is the length of the optical fiber under observation
 * $$c$$ is the speed of light.

title: Step-index profile


text:
Stopband

A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on application, the required attenuation within the stopband may typically be a value between 20 and 120 dB higher than the nominal passband attenuation, which often is 0 dB.

The lower and upper limiting frequencies, also denoted lower and upper stopband corner frequencies, are the frequencies where the stopband and the transition bands meet in a filter specification. The stopband of a low-pass filter is the frequencies from the stopband corner frequency (which is slightly higher than the passband 3 dB cut-off frequency) up to the infinite frequency. The stopband of a high-pass filter consists of the frequencies from 0 hertz to a stopband corner frequency (slightly lower than the passband cut-off frequency).

A band-stop filter has one stopband, specified by two non-zero and non-infinite corner frequencies. The difference between the limits in the band-stop filter is the stopband bandwidth, which usually is expressed in hertz.

A bandpass filter typically has two stopbands. The shape factor of a bandpass filter is the relationship between the 3 dB bandwidth, and the difference between the stopband limits.

title: Stopband


text:
Stop signal

In telecommunication, a stop signal is a signal that marks the end of part of a transmission, for example:
 * 1) In asynchronous serial communication, a signal at the end of a character that prepares the receiving device for the reception of a subsequent character. A stop signal is usually limited to one signal element having any duration equal to or greater than a specified minimum value.
 * 2) A signal to a receiving mechanism to wait for the next signal.

title: Stop signal


text:
Stressed environment

In radio communications, a stressed environment is an environment that is under the influence of extrinsic factors that degrade communications integrity, such as when (a) the beginning communications medium is disturbed by natural or man-made events (such as an intentional nuclear burst), (b) the received signal is degraded by natural or man-made interference (such as jamming signals or co-channel interference), (c) an interfering signal can reconfigure the network, and/or (d) an adversary threatens successful communications, in which case radio signals may be encrypted in order to deny the adversary an intelligible message, traffic flow information, network information, or automatic link establishment (ALE) control information.

title: Stressed environment


text:
Substitution method

In optical fiber technology, the substitution method is a method of measuring the transmission loss of a fiber. It consists of:
 * 1) using a stable optical source, at the wavelength of interest, to drive a mode scrambler, the output of which overfills (drives) a 1 to 2 meter long reference fiber having physical and optical characteristics matching those of the fiber under test,
 * 2) measuring the power level at the output of the reference fiber,
 * 3) repeating the procedure, substituting the fiber under test for the reference fiber, and
 * 4) subtracting the power level obtained at the output of the fiber under test from the power level obtained at the output of the reference fiber, to get the transmission loss of the fiber under test.

The substitution method has certain shortcomings with regard to its accuracy, but its simplicity makes it a popular field test method. It is conservative, in that if it were used to measure the individual losses of several long fibers, and the long fibers were concatenated, the total loss obtained (excluding splice losses) would be expected to be lower than the sum of the individual fiber losses.

Some modern optical power meters have the capability to set to zero the reference level measured at the output of the reference fiber, so that the transmission loss of the fiber under test may be read out directly.

title: Substitution method


text:
Summation check

In telecommunication, the term summation check (sum check) has the following meanings:

 * A checksum based on the formation of the sum of the digits of a numeral.
 * Note: The sum of the individual digits is usually compared with a previously computed value.
 * A comparison of checksums on the same data on different occasions or on different representations of the data in order to verify data integrity.

title: Summation check


text:
Supervisory program

A supervisory program or supervisor is a computer program that is usually referred as an operating system. It controls the execution of other routines such as regulating work schedules, input/output operations, and error actions.

Historically, this term was essentially associated with IBM's line of mainframe operating systems starting with OS/360. In other operating systems, the supervisor is generally called the kernel.

title: Supervisory program


text:
Reduced-carrier transmission

Reduced-carrier transmission is an amplitude modulation (AM) transmission in which the carrier signal level is reduced to reduce wasted electrical power. Suppressed-carrier transmission is a special case in which the carrier level is reduced below that required for demodulation by a normal receiver.

Reduction of the carrier level permits higher power levels in the sidebands than would be possible with conventional AM transmission. Carrier power must be restored by the receiving station to permit demodulation, usually by means of a beat frequency oscillator (BFO). Failure of the BFO to match the original carrier frequency when receiving such a signal will cause a heterodyne.

Suppressed carriers are often used for single sideband (SSB) transmissions, such as for amateur radio on shortwave. That system is referred to in full as SSB suppressed carrier (SSBSC) or (SSB-SC). International broadcasters agreed in 1985 to also use SSBSC entirely by 2015, though IBOC and IBAC digital radio (namely Digital Radio Mondiale) seems likely to make this irrelevant.

FM stereo transmissions use a double-sideband suppressed carrier (DSBSC) signal from a stereo generator, together with a pilot tone of exactly half the original carrier frequency. This allows reconstitution of the original stereo carrier, and hence the stereo signal.

title: Reduced-carrier transmission


text:
Surface wave

In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface waves can travel along the surface of solids, such as Rayleigh or Love waves. Electromagnetic waves can also propagate as "surface waves" in that they can be guided along with a refractive index gradient or along an interface between two media having different dielectric constants. In radio transmission, a ground wave is a guided wave that propagates close to the surface of the Earth.

Mechanical waves
In seismology, several types of surface waves are encountered. Surface waves, in this mechanical sense, are commonly known as either Love waves (L waves) or Rayleigh waves. A seismic wave is a wave that travels through the Earth, often as the result of an earthquake or explosion. Love waves have transverse motion (movement is perpendicular to the direction of travel, like light waves), whereas Rayleigh waves have both longitudinal (movement parallel to the direction of travel, like sound waves) and transverse motion. Seismic waves are studied by seismologists and measured by a seismograph or seismometer. Surface waves span a wide frequency range, and the period of waves that are most damaging is usually 10 seconds or longer. Surface waves can travel around the globe many times from the largest earthquakes. Surface waves are caused when P waves and S waves come to the surface.

Examples are the waves at the surface of water and air (ocean surface waves). Another example is internal waves, which can be transmitted along the interface of two water masses of different densities.

In theory of hearing physiology, the traveling wave (TW) of Von Bekesy, resulted from an acoustic surface wave of the basilar membrane into the cochlear duct. His theory purported to explain every feature of the auditory sensation owing to these passive mechanical phenomena. Jozef Zwislocki, and later David Kemp, showed that that is unrealistic and that active feedback is necessary.

Electromagnetic waves
Ground waves are radio waves propagating parallel to and adjacent to the surface of the Earth, following the curvature of the Earth. This radiative ground wave is known as Norton surface wave, or more properly Norton ground wave, because ground waves in radio propagation are not confined to the surface.

Another type of surface wave is the non-radiative, bound-mode Zenneck surface wave or Zenneck–Sommerfeld surface wave. The earth has one refractive index and the atmosphere has another, thus constituting an interface that supports the guided Zenneck wave's transmission. Other types of surface wave are the trapped surface wave, the gliding wave and Dyakonov surface waves (DSW) propagating at the interface of transparent materials with different symmetry. Apart from these, various types of surface waves have been studied for optical wavelengths.

Microwave field theory
Within microwave field theory, the interface of a dielectric and conductor supports "surface wave transmission". Surface waves have been studied as part of transmission lines and some may be considered as single-wire transmission lines.

Characteristics and utilizations of the electrical surface wave phenomenon include:
 * The field components of the wave diminish with distance from the interface.
 * Electromagnetic energy is not converted from the surface wave field to another form of energy (except in leaky or lossy surface waves) such that the wave does not transmit power normal to the interface, i.e. it is evanescent along that dimension.
 * In coaxial cable in addition to the TEM mode there also exists a transverse-magnetic (TM) mode which propagates as a surface wave in the region around the central conductor. For coax of common impedance this mode is effectively suppressed but in high impedance coax and on a single central conductor without any outer shield, low attenuation and very broadband propagation is supported. Transmission line operation in this mode is called E-Line.

Surface plasmon polariton

The surface plasmon polariton (SPP) is an electromagnetic surface wave that can travel along an interface between two media with different dielectric constants. It exists under the condition that the permittivity of one of the materials forming the interface is negative, while the other one is positive, as is the case for the interface between air and a lossy conducting medium below the plasma frequency. The wave propagates parallel to the interface and decays exponentially vertical to it, a property called evanescence. Since the wave is on the boundary of a lossy conductor and a second medium, these oscillations can be sensitive to changes to the boundary, such as the adsorption of molecules by the conducting surface.

Sommerfeld–Zenneck surface wave
The Sommerfeld–Zenneck wave or Zenneck wave is a non-radiative guided electromagnetic wave that is supported by a planar or spherical interface between two homogeneous media having different dielectric constants. This surface wave propagates parallel to the interface and decays exponentially vertical to it, a property known as evanescence. It exists under the condition that the permittivity of one of the materials forming the interface is negative, while the other one is positive, as for example the interface between air and a lossy conducting medium such as the terrestrial transmission line, below the plasma frequency. Its electric field strength falls off at a rate of e-αd/√d in the direction of propagation along the interface due to two-dimensional geometrical field spreading at a rate of 1/√d, in combination with a frequency-dependent exponential attenuation (α), which is the terrestrial transmission line dissipation, where α depends on the medium’s conductivity. Arising from original analysis by Arnold Sommerfeld and Jonathan Zenneck of the problem of wave propagation over a lossy earth, it exists as an exact solution to Maxwell's equations. The Zenneck surface wave, which is a non-radiating guided-wave mode, can be derived by employing the Hankel transform of a radial ground current associated with a realistic terrestrial Zenneck surface wave source. Sommerfeld-Zenneck surface waves predict that the energy decays as R−1 because the energy distributes over the circumference of a circle and not the surface of a sphere. Evidence does not show that in radio space wave propagation, Sommerfeld-Zenneck surfaces waves are a mode of propagation as the path-loss exponent is generally between 20 dB/dec and 40 dB/dec.

Standards and doctrines

 * "Surface wave ". Telecom Glossary 2000, ATIS Committee T1A1, Performance and Signal Processing, T1.523–2001.
 * "Surface wave", Federal Standard 1037C.
 * "Surface wave", MIL-STD-188
 * "Multi-service tactics, techniques, and procedures for the High-Frequency Automatic Link Establishment (HF-ALE): FM 6-02.74; MCRP 3–40.3E; NTTP 6-02.6; AFTTP(I) 3-2.48; COMDTINST M2000.7" Sept., 2003.

Books

 * Barlow, H.M., and Brown, J., "Radio Surface Waves", Oxford University Press 1962.
 * Budden, K. G., "Radio waves in the ionosphere; the mathematical theory of the reflection of radio waves from stratified ionised layers". Cambridge, Eng., University Press, 1961. LCCN 61016040 /L/r85
 * Budden, K. G., "The wave-guide mode theory of wave propagation". London, Logos Press; Englewood Cliffs, N.J., Prentice-Hall, c1961. LCCN 62002870 /L
 * Budden, K. G., " The propagation of radio waves : the theory of radio waves of low power in the ionosphere and magnetosphere". Cambridge (Cambridgeshire); New York : Cambridge University Press, 1985. ISBN 0-521-25461-2 LCCN 84028498
 * Collin, R. E., "Field Theory of Guided Waves". New York: Wiley-IEEE Press, 1990.
 * Foti, S., Lai, C.G., Rix, G.J., and Strobbia, C., "“Surface Wave Methods for Near-Surface Site Characterization”", CRC Press, Boca Raton, Florida (USA), 487 pp., ISBN 9780415678766, 2014
 * Sommerfeld, A., "Partial Differential Equations in Physics" (English version), Academic Press Inc., New York 1949, chapter 6 – "Problems of Radio".
 * Polo Jr., J. A., Mackay, T. G., and Lakhtakia, A., "Electromagnetic Surface Waves: A Modern Perspective". Waltham, MA, USA: Elsevier, 2013 .
 * Rawer, K.,"Wave Propagation in the Ionosphere", Dordrecht, Kluwer Acad.Publ. 1993.
 * Sommerfeld, A., "Partial Differential Equations in Physics" (English version), Academic Press Inc., New York 1949, chapter 6 – "Problems of Radio".
 * Weiner, Melvin M., "Monopole antennas" New York, Marcel Dekker, 2003. ISBN 0-8247-0496-7
 * Wait, J. R., "Electromagnetic Wave Theory", New York, Harper and Row, 1985.
 * Wait, J. R., "The Waves in Stratified Media". New York: Pergamon, 1962.
 * Waldron, Richard Arthur, "Theory of guided electromagnetic waves". London, New York, Van Nostrand Reinhold, 1970. ISBN 0-442-09167-2 LCCN 69019848 //r86
 * Weiner, Melvin M., "Monopole antennas" New York, Marcel Dekker, 2003. ISBN 0-8247-0496-7

Journals and papers

 * Zenneck, Sommerfeld, Norton, and Goubau
 * J. Zenneck, (translators: P. Blanchin, G. Guérard, É. Picot), "Précis de télégraphie sans fil : complément de l'ouvrage : Les oscillations électromagnétiques et la télégraphie sans fil", Paris : Gauthier-Villars, 1911. viii, 385 p. : ill.; 26 cm. (Tr. "Precisions of wireless telegraphy:  complement of the work:  Electromagnetic oscillations and wireless telegraphy.")
 * J. Zenneck, "Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie", Annalen der Physik, vol. 23, pp. 846–866, Sept. 1907. (Tr. "About the propagation of electromagnetic plane waves along a conductor plane and their relationship to wireless telegraphy.")
 * J. Zenneck, "Elektromagnetische Schwingungen und drahtlose Telegraphie", gart, F. Enke, 1905. xxvii, 1019 p. : ill.; 24 cm. (Tr''. "Electromagnetic oscillations and wireless telegraphy.")
 * J. Zenneck, (translator: A.E. Seelig) "Wireless telegraphy,", New York [etc.] McGraw-Hill Book Company, inc., 1st ed. 1915. xx, 443 p. illus., diagrs. 24 cm. LCCN 15024534 (ed. "Bibliography and notes on theory" pp. 408–428.)
 * A. Sommerfeld, "Über die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes", Ann. der Physik und Chemie, vol. 67, pp. 233–290, Dec 1899. (Tr. "Propagation of electro-dynamic waves along a cylindric conductor.")
 * A. Sommerfeld, "Über die Ausbreitung der Wellen in der drahtlosen Telegraphie", Annalen der Physik, Vol. 28, pp. 665–736, March 1909.  (Tr. "About the Propagation of waves in wireless telegraphy.")
 * A. Sommerfeld, "Propagation of waves in wireless telegraphy," Ann. Phys., vol. 81, pp. 1367–1153, 1926.
 * K. A. Norton, "The propagation of radio waves over the surface of the earth and in the upper atmosphere," Proc. IRE, vol. 24, pp. 1367–1387, 1936.
 * K. A. Norton, "The calculations of ground wave field intensity over a finitely conducting spherical earth," Proc. IRE, vol. 29, pp. 623–639, 1941.
 * G. Goubau, "Surface waves and their application to transmission lines," J. Appl. Phys., vol. 21, pp. 1119–1128; November,1950.
 * G. Goubau, “Über die Zennecksche Bodenwelle,” (Tr."On the Zenneck Surface Wave."), Zeitschrift für Angewandte Physik, Vol. 3, 1951, Nrs. 3/4, pp. 103–107.

 * Wait
 * Wait, J. R., "Lateral Waves and the Pioneering Research of the Late Kenneth A Norton".
 * Wait, J. R., and D. A. Hill, "Excitation of the HF surface wave by vertical and horizontal apertures". Radio Science, 14, 1979, pp 767–780.
 * Wait, J. R., and D. A. Hill, "Excitation of the Zenneck Surface Wave by a Vertical Aperture", Radio Science, Vol. 13, No. 6, November–December, 1978, pp. 969–977.
 * Wait, J. R., "A note on surface waves and ground waves", IEEE Transactions on Antennas and Propagation, Nov 1965. Vol. 13, Issue 6, pp. 996–997
 * Wait, J. R., "The ancient and modern history of EM ground-wave propagation". IEEE Antennas Propagat. Mag., vol. 40, pp. 7–24, Oct. 1998.
 * Wait, J. R., "Appendix C: On the theory of ground wave propagation over a slightly roughned curved earth", Electromagnetic Probing in Geophysics. Boulder, CO., Golem, 1971, pp. 37–381.
 * Wait, J. R., "Electromagnetic surface waves", Advances in Radio Research, 1, New York, Academic Press, 1964, pp. 157–219.

 * Others
 * R. E. Collin, "Hertzian Dipole Radiating Over a Lossy Earth or Sea: Some Early and Late 20th-Century Controversies", Antennas and Propagation Magazine, 46, 2004, pp. 64–79.
 * F. J. Zucker, "Surface wave antennas and surface wave excited arrays", Antenna Engineering Handbook, 2nd ed., R. C. Johnson and H. Jasik, Eds. New York: McGraw-Hill, 1984.
 * Yu. V. Kistovich, "Possibility of Observing Zenneck Surface Waves in Radiation from a Source with a Small Vertical Aperture", Soviet Physics Technical Physics, Vol. 34, No.4, April, 1989, pp. 391–394.
 * V. I. Baĭbakov, V. N. Datsko, Yu. V. Kistovich, "Experimental discovery of Zenneck's surface electromagnetic waves", Sov Phys Uspekhi, 1989, 32 (4), 378–379.
 * Corum, K. L. and J. F. Corum, "The Zenneck Surface Wave", Nikola Tesla, Lightning Observations, and Stationary Waves, Appendix II. 1994.
 * M. J. King and J. C. Wiltse, "Surface-Wave Propagation on Coated or Uncoated Metal Wires at Millimeter Wavelengths". J. Appl. Phys., vol. 21, pp. 1119–1128; November,
 * M. J. King and J. C. Wiltse, "Surface-Wave Propagation on a Dielectric Rod of Electric Cross-Section." Electronic Communications, Inc., Tirnonium: kld. Sci. Rept.'No. 1, AFCKL Contract No. AF 19(601)-5475; August, 1960.
 * T. Kahan and G. Eckart, "On the Electromagnetic Surface Wave of Sommerfeld", Phys. Rev. 76, 406–410 (1949).

Other media

 * L.A. Ostrovsky (ed.), "Laboratory modeling and theoretical studies of surface wave modulation by a moving sphere", m, Oceanic and Atmospheric Research Laboratories, 2002.

title: Surface wave


text:
Survivability

Survivability is the ability to remain alive or continue to exist. The term has more specific meaning in certain contexts.

Ecological
Following disruptive forces such as flood, fire, disease, war, or climate change some species of flora, fauna, and local life forms  are likely to survive more successfully than others because of consequent changes to their surrounding biophysical conditions.

Engineering
In engineering, survivability is the quantified ability of a system, subsystem, equipment, process, or procedure to continue to function during and after a natural or man-made disturbance; for example a nuclear electromagnetic pulse from the detonation of a nuclear weapon.

For a given application, survivability must be qualified by specifying the range of conditions over which the entity will survive, the minimum acceptable level or post-disturbance functionality, and the maximum acceptable downtime.

Military
In the military environment, survivability can be defined as the ability to remain mission capable after a single engagement. Engineers working in survivability are often responsible for improving four main system elements:

 * Detectability - the inability to avoid being aurally and visually detected as well as detected by radar (by an observer).
 * Susceptibility - the inability to avoid being hit (by a weapon).
 * Vulnerability - the inability to withstand the hit.
 * Recoverability - longer-term post-hit effects, damage control, and firefighting, capability restoration, or (in extremis) escape and evacuation.

The European Survivability Workshop introduced the concept of "Mission Survivability" whilst retaining the three core areas above, either pertaining to the "survivability" of a platform through a complete mission, or the "survivability" of the mission itself (i.e. probability of mission success). Recent studies have also introduced the concept of "Force Survivability" which relates to the ability of a force rather than an individual platform to remain "mission capable".

There is no clear prioritisation of the three elements; this will depend on the characteristics and role of the platform. Some platform types, such as submarines and airplanes, minimise their susceptibility and may, to some extent, compromise in the other areas. Main Battle Tanks minimise vulnerability through the use of heavy armours. Present day surface warship designs tend to aim for a balanced combination of all three areas.

A popular term is the "survivability onion"; described as 5-8 layers: "Don't be there. If you are there, don’t be seen. If you are seen, don’t be targeted/acquired. If you are targeted/acquired, don’t be hit. If you are hit, don’t be penetrated. If you are penetrated, don’t be killed."

Naval
Survivability denotes the ability of a ship and its on-board systems to remain functional and continue designated mission in a man-made hostile environment. The naval vessels are designed to operate in a man-made hostile environment, and therefore the survivability is a vital feature required from them. The naval vessel's survivability is a complicated subject affecting the whole life cycle of the vessel, and should be considered from the initial design phase of every war ship.

The classical definition of naval survivability includes three main aspects, which are susceptibility, vulnerability, and recoverability; although, recoverability is often subsumed within vulnerability. Susceptibility consists of all the factors that expose the ship to the weapons effects in a combat environment. These factors in general are the operating conditions, the threat, and the features of the ship itself. The operating conditions, such as sea state, weather and atmospheric conditions, vary considerably, and their influence is difficult to address (hence they are often not accounted for in survivability assessment). The threat is dependent on the weapons directed against the ship and weapon's performance, such as the range. The features of the ship in this sense include platform signatures (radar, infrared, acoustic, magnetic), the defensive systems on board, such as surface-to-air missiles, EW and decoys, and also the tactics employed by the platform in countering the attack (aspects such as speed, maneuverability, chosen aspect presented to the threat). Vulnerability refers to the ability of the vessel to withstand the short-term effects of the threat weapon. Vulnerability is an attribute typical to the vessel and therefore heavily affected by the vessel's basic characteristics such as size, subdivision, armouring, and other hardening features, and also the design of the ship's systems, in particular the location of equipment, degrees of redundancy and separation, and the presence within a system of single point failures. Recoverability refers to vessel's ability to restore and maintain its functionality after sustaining damage. Thus, recoverability is dependent on the actions aimed to neutralize the effects of the damage. These actions include firefighting, limiting the extent of flooding, and dewatering. Besides the equipment, the crew also has a vital role in recoverability.

Combat vehicle crew
The crews of military combat vehicles face numerous lethal hazards which are both diverse and constantly evolving. Improvised Explosive Devices (IEDs), mines, and enemy fire are examples of such persistent and variable threats. Historically, measures taken to mitigate these hazards were concerned with protecting the vehicle itself, but due to this achieving only limited protection, the focus has now shifted to safeguarding the crew within from an ever-broadening range of threats, including Radio Controlled IEDs (RCIEDs), blast, fragmentation, heat stress, and dehydration.

The expressed goal of "crew survivability" is to ensure vehicle occupants are best protected. It goes beyond simply ensuring crew have the appropriate protective equipment and has expanded to include measuring the overpressure and blunt impact forces experienced by a vehicle from real blast incidents in order to develop medical treatment and improve overall crew survivability. Sustainable crew survivability is dependent on the effective integration of knowledge, training, and equipment.

Prevention and training
Threat intelligence identifying trends, emerging technologies, and attack tactics used by enemy forces enables crews to implement procedures that will reduce their exposure to unnecessary risks. Such intelligence also allows for more effective pre-deployment training programs where personnel can be taught the most up-to-date developments in IED concealment, for example, or undertake tailored training that will enable them to identify the likely attack strategy of enemy forces. In addition, with expert, current threat intelligence, the most effective equipment can be procured or rapidly developed in support of operations.

Definitions of network survivability
"The capability of a system to fulfill its mission, in a timely manner, in the presence of threats such as attacks or large-scale natural disasters. Survivability is a subset of resilience."

“The capability of a system to fulfill its mission, in a timely manner, in the presence of attacks, failures, or accidents.”

title: Survivability


text:
Switched loop

In telephony, a Switched loop is a circuit that automatically releases a connection from an attendant console or switchboard, once the connection has been made to the appropriate terminal.

Loop buttons or jacks are used to answer incoming listed directory number calls, dial "0" internal calls, transfer requests, and intercepted calls. The attendant can handle only one telephone call at a time. Synonym: released loop.

title: Switched loop


text:
Synchronism

Synchronism may refer to:

 * Synchronism (Davidovsky), compositions by Argentine-American composer Mario Davidovsky incorporating acoustic instruments and electroacoustic sounds
 * Chronological synchronism, an event that links two chronologies such as historical and datable astronomical events
 * Synchronization, the coordination of events to operate a system in unison

Film

 * Synchronized sound, film sound technologically coupled to image
 * Post-synchronization, the process of re-recording dialogue after the filming process

title: Synchronism


text:
Synchronous orbit

A synchronous orbit is an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body.

Simplified meaning
A synchronous orbit is an orbit in which the orbiting object (for example, an artificial satellite or a moon) takes the same amount of time to complete an orbit as it takes the object it is orbiting to rotate once.

Properties
A satellite in a synchronous orbit that is both equatorial and circular will appear to be suspended motionless above a point on the orbited planet's equator. For synchronous satellites orbiting Earth, this is also known as a geostationary orbit. However, a synchronous orbit need not be equatorial; nor circular. A body in a non-equatorial synchronous orbit will appear to oscillate north and south above a point on the planet's equator, whereas a body in an elliptical orbit will appear to oscillate eastward and westward. As seen from the orbited body the combination of these two motions produces a figure-8 pattern called an analemma.

Nomenclature
There are many specialized terms for synchronous orbits depending on the body orbited. The following are some of the more common ones. A synchronous orbit around Earth that is circular and lies in the equatorial plane is called a geostationary orbit. The more general case, when the orbit is inclined to Earth's equator or is non-circular is called a geosynchronous orbit. The corresponding terms for synchronous orbits around Mars are areostationary and areosynchronous orbits.

Formula
For a stationary synchronous orbit:

 * $$R_{syn} = \sqrt[3]$$
 * G = Gravitational constant
 * m2 = Mass of the celestial body
 * T = rotational period of the body
 * $$R_{syn}$$ = Radius of orbit

By this formula one can find the stationary orbit of an object in relation to a given body.

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius.

Examples
An astronomical example is Pluto's largest moon Charon. Much more commonly, synchronous orbits are employed by artificial satellites used for communication, such as geostationary satellites.

For natural satellites, which can attain a synchronous orbit only by tidally locking their parent body, it always goes in hand with synchronous rotation of the satellite. This is because the smaller body becomes tidally locked faster, and by the time a synchronous orbit is achieved, it has had a locked synchronous rotation for a long time already.

title: Synchronous orbit


text:
System integrity

In telecommunications, the term system integrity has the following meanings:

 * 1) That condition of a system wherein its mandated operational and technical parameters are within the prescribed limits.
 * 2) The quality of an AIS when it performs its intended function in an unimpaired manner, free from deliberate or inadvertent unauthorized manipulation of the system.
 * 3) The state that exists when there is complete assurance that under all conditions an IT system is based on the logical correctness and reliability of the operating system, the logical completeness of the hardware and software that implement the protection mechanisms, and data integrity.

title: System integrity


text:
Systems control

Systems control, in a communications system, is the control and implementation of a set of functions that:

 * 1) prevent or eliminate degradation of any part of the system,
 * 2) initiate immediate response to demands that are placed on the system,
 * 3) respond to changes in the system to meet long range requirements, and
 * 4) may include various subfunctions, such as
 * 5) * immediate circuit utilization actions,
 * 6) * continuous control of circuit quality,
 * 7) * continuous control of equipment performance,
 * 8) * development of procedures for immediate repair, restoration, or replacement of facilities and equipment,
 * 9) * continuous liaison with system users and with representatives of other systems, and
 * 10) * the provision of advice and assistance in system use.

title: Systems control


text:
Systems design

Systems design interfaces, and data for an electronic control system to satisfy specified requirements. Systems design could be seen as the application of systems theory to product development. There is some overlap with the disciplines of systems analysis, systems architecture and systems engineering.

Overview
If the broader topic of product development "blends the perspective of marketing, design, and manufacturing into a single approach to product development," then design is the act of taking the marketing information and creating the design of the product to be manufactured. Systems design is therefore the process of defining and developing systems to satisfy specified requirements of the user.

The basic study of system design is the understanding of component parts and their subsequent interaction with one another.

Physical design
The physical design relates to the actual input and output processes of the system. This is explained in terms of how data is input into a system, how it is verified/authenticated, how it is processed, and how it is displayed. In physical design, the following requirements about the system are decided.
 * 1) Input requirement,
 * 2) Output requirements,
 * 3) Storage requirements,
 * 4) Processing requirements,
 * 5) System control and backup or recovery.

Put another way, the physical portion of system design can generally be broken down into three sub-tasks:
 * 1) User Interface Design
 * 2) Data Design
 * 3) Process Design

Web System design
Online websites, such as Google, Twitter, Facebook, Amazon and Netflix are used by millions of users worldwide. A scalable, highly available system must be designed to accommodate an increasing number of users. Here are the things to consider in designing the system:
 * 1) Functional and non functional requirements
 * 2) Capacity estimation
 * 3) Database to use, Relational or NoSQL
 * 4) Vertical scaling, Horizontal scaling, Shard
 * 5) Load Balancing
 * 6) Primary-secondary Replication
 * 7) Cache and CDN
 * 8) Stateless and Stateful servers
 * 9) Datacenter georouting
 * 10) Message Queue, Publish-Subscribe Architecture
 * 11) Performance Metrics Monitoring and Logging
 * 12) Build, test, configure deploy automation
 * 13) Finding single point of failure
 * 14) API Rate Limiting
 * 15) Service Level Agreement

title: Systems design


text:
Tactical communications

Tactical communications are military communications in which information of any kind, especially orders and military intelligence, are conveyed from one command, person, or place to another upon a battlefield, particularly during the conduct of combat. It includes any kind of delivery of information, whether verbal, written, visual or auditory, and can be sent in a variety of ways. In modern times, this is usually done by electronic means. Tactical communications do not include communications provided to tactical forces by the Defense Communications System to non-tactical military commands, to tactical forces by civil organizations, nor does it include strategic communication.

Early means
The earliest way of communicating with others in a battle was by the commander's voice or by human messenger. A runner would carry reports or orders from one officer to another. Once the horse was domesticated messages could travel much faster. A very fast way to send information was to use either drums, trumpets or flags. Each sound or banner would have a pre-determined significance for the soldier who would respond accordingly. Auditory signals were only as effective, though, as the receiver's ability to hear them. The din of battle or long distances could make using noise less effective. They were also limited in the amount of information they could convey; the information must be simple, such as attack or retreat.

Visual cues, such as flags or smoke signals required the receiver to have a clear line of sight to the signal, and know when and where to look for them. Intricate warning systems have though always been used such as scouting towers with fires to signal incoming threats - this could occur at the tactical as well as the strategic level. The armies of the 19th century used two flags in combinations that replicated the alphabet. This allowed commanders the ability to send any order they wanted as they needed to, but still relied on line-of-sight. During the Siege of Paris (1870–71) the defending French effectively used carrier pigeons to relay information between tactical units.

The wireless revolution
Although visual communication flew at the speed of light, it relied on a direct line of sight between the sender and the receiver. Telegraphs helped theater commanders to move large armies about, but one certainly could not count on using immobile telegraph lines on a changing battlefield.

At the end of the 19th century the disparate units across any field were instantaneously joined to their commanders by the invention and mass production of the radio. At first the radio could only broadcast tones, so messages were sent via Morse code. The first field radios used by the United States Army saw action in the Spanish–American War (1898) and the Philippine Insurrection (1899–1902). At the same time as radios were deployed the field telephone was developed and made commercially viable. This caused a new signal occupation specialty to be developed: lineman.

During the Interwar period the German army invented Blitzkrieg in which air, armor, and infantry forces acted swiftly and precisely, with constant radio communication. They triumphed until their enemies equipped themselves to communicate and coordinate similarly.

The digital battlefield
Security was a problem. If you broadcast your plans over radio waves, anyone with a similar radio listening to the same frequency could hear your plans. Trench codes became the tactical part of World War I cryptography. Advances in electronics, particularly after World War II, allowed for electronic scrambling of voice radio. Operational and strategic messages during the war were by text were encrypted with ciphers too complex for humans to crack without the assistance of a similar, high-tech machine, such as the German Enigma machine. Once computer science advanced, tactical voice radio could be encrypted, and large amounts of data could be sent over the airwaves in quick bursts of signals with more complex encryption.

Communication between armies were of course much more difficult before the electronic age and could only be achieved with messengers on horseback or by foot and with time delays according to the distance the messenger needed to travel. Advances in long-range communications aided the commander on the battlefield, for then they could receive news of any outside force or factor that could impact the conduct of a battle.

title: Tactical communications


text:
Tape relay

A tape relay is a method of retransmitting teletypewriter traffic from one communication channel to another, in which messages arriving on an incoming channel are recorded in the form of perforated tape, this punched tape then being either fed directly and automatically into an outgoing channel, or manually transferred to an automatic transmitter for transmission on an outgoing channel. Tape relay, sometimes informally called "torn tape operation", was commonplace during much of the 20th century.

title: Tape relay