In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns; the inverse of the wavelength is called the spatial frequency. Wavelength is designated by the Greek letter lambda; the term wavelength is sometimes applied to modulated waves, to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, lower frequencies have longer wavelengths. Wavelength depends on the medium. Examples of waves are sound waves, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary.

Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary; the range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components; the wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, where v is called the phase speed of the wave and f is the wave's frequency. In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3×108 m/s, thus the wavelength of a 100 MHz electromagnetic wave is about: 3×108 m/s divided by 108 Hz = 3 metres.

The wavelength of visible light ranges from deep red 700 nm, to violet 400 nm. For sound waves in air, the speed of sound is 343 m/s; the wavelengths of sound frequencies audible to the human ear are thus between 17 m and 17 mm, respectively. Somewhat higher frequencies are used by bats so they can resolve targets smaller than 17 mm. Wavelengths in audible sound are much longer than those in visible light. A standing wave is an undulatory motion. A sinusoidal standing wave includes stationary points of no motion, called nodes, the wavelength is twice the distance between nodes; the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed. For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall.

The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Wavelength and wave velocity are related just as for a traveling wave. For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. Traveling sinusoidal waves are represented mathematically in terms of their velocity v, frequency f and wavelength λ as: y = A cos ⁡ = A cos ⁡ where y is the value of the wave at any position x and time t, A is the amplitude of the wave, they are commonly expressed in terms of wavenumber k and angular frequency ω as: y = A cos ⁡ = A cos ⁡ in which wavelength and wavenumber are related to velocity and frequency as: k = 2 π λ = 2 π f v = ω v, or λ = 2 π k = 2 π v ω =

Matheus Sales

Matheus de Sales Cabral, known as Matheus Sales, is a Brazilian footballer who plays for Figueirense, on loan from Coritiba, as a defensive midfielder. Born in Guarulhos, São Paulo, Matheus Sales joined Palmeiras' youth setup in 2009, after being approved in a trial. In 2014, after being linked to Internacional, he signed a new four-year deal with the club. Matheus Sales made his first team – and Série A – debut on 25 October 2015, starting in a 0–2 home loss against Sport Recife. In the year's Copa do Brasil, he started in both legs of the final, earning plaudits for his performance on the second match; as of match played 20 January 2016 PalmeirasCopa do Brasil: 2015 Campeonato Brasileiro Série A: 2016Bahia Copa do Nordeste: 2017 Palmeiras official profile Matheus Sales at Soccerway

Kristin Feireiss

Kristin Feireiss is a German architectural and design curator and editor. Her career has included co-founding the Aedes Architecture Forum in Berlin, serving as director of the Netherlands Architecture Institute, participating as an international juror and commissioner at the Architecture Biennale in Venice. In 2013, Feireiss became a Pritzker Architecture Prize juror. Feireiss was born in Berlin, she embarked on a course in Art History at Johann Wolfgang Goethe University in Frankfurt in 1963, graduated from Freie Universität Berlin in 1967. In the late 1960s, Feireiss began working as a journalist for cultural magazines and radio programs, she worked for Internationales Design Zentrum Berlin between 1976 and 1980. In 1980, she co-founded Aedes in a forum for architecture, she has served in various capacities for a number of other organizations including Netherlands Architecture Institute, Venice Biennale of Architecture, Pritzker Architecture Prize, the European Cultural Parliament. Feireiss is the author or co-author of various works, including Architecture in times of need: Make It Right rebuilding New OrleansLower Ninth Ward, with Brad Pitt.

In 1995, Feireiss was awarded the Literature Prize of the DAI, on 23 March 2001 she was awarded the Federal Cross of Merit. Feireiss was honored as a Knight of the Order of the Netherlands Lion. On 26 October 2007, Kristin Feireiss received an honorary doctorate from the Carolo-Wilhelmina Technische Universität in Braunschweig. In awarding this degree, the TU Braunschweig paid tribute to Feireiss for her activities as a journalist and founder of the Aedes Architecture Forum, for serving for more than 25 years as a mediator between academic architectural research and an interdisciplinary, international public. In 2016 she was awarded the Honorary Fellowship by the Royal Institute of British Architects. Kristin Feireiss. Die Gestalten, Berlin 2008, ISBN 978-3-899-55211-9. Kristin Feireiss. Prestel, München 2009, ISBN 978-3-791-34276-4. Wie ein Haus aus Karten. Die Neckermanns – meine Familiengeschichte. Ullstein, Berlin 2012, ISBN 978-3-550-08899-5