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80-548: Friedrich Clemens Gerke Tower is a 230 metre tall telecommunication tower of reinforced concrete in Cuxhaven in Germany . Friedrich Clemens Gerke Tower, which is named after Friedrich Clemens Gerke , was completed in 1991 and is not accessible for tourists. In spite of its size, it is only used as receiving point for cable TV , as a radio relay station and as a mobile phone transmitter , but not for broadcasting. The tower

160-569: A kite can serve as a temporary support. It can carry an antenna or a wire (for VLF, LW or MW) up to an appropriate height. Such an arrangement is used occasionally by military agencies or radio amateurs. The American broadcasters TV Martí broadcast a television program to Cuba by means of such a balloon. In 2013, interest began in using unmanned aerial vehicles (drones) for telecom purposes. For two VLF transmitters wire antennas spun across deep valleys are used. The wires are supported by small masts or towers or rock anchors. The same technique

240-411: A local wavelength . An example is shown in the figure. In general, the envelope of the wave packet moves at a speed different from the constituent waves. Using Fourier analysis , wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths. Louis de Broglie postulated that all particles with a specific value of momentum p have

320-469: A capacitive top-load. In a second paper the same year he showed that the amount of power radiated horizontally in ground waves reached a maximum at a mast height of ⁠ 5  / 8 ⁠ wavelength . By 1930 the expense of the T-antenna led broadcasters to adopt the mast radiator antenna, in which the metal structure of the mast itself functions as the antenna. One of the first types used

400-455: A circular aperture, the diffraction-limited image spot is known as an Airy disk ; the distance x in the single-slit diffraction formula is replaced by radial distance r and the sine is replaced by 2 J 1 , where J 1 is a first order Bessel function . The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion , the radius to

480-459: 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

560-478: A fraction of the weight (70% less ) which has allowed monopoles and towers to be built in locations that were too expensive or difficult to access with the heavy lifting equipment that is needed for a steel structure. Overall a carbon fiber structure is 40 - 50% faster to be erected compared to traditional building materials. As of 2022 , wood, previously an uncommon material for telecommunications tower construction, has started to become increasingly common. In 2022,

640-647: A guyed radio mast is installed. One example is the Gerbrandy Tower in Lopik , Netherlands. Further towers of this building method can be found near Smilde , Netherlands and the Fernsehturm in Waldenburg , Germany. Radio, television and cell towers have been documented to pose a hazard to birds. Reports have been issued documenting known bird fatalities and calling for research to find ways to minimize

720-468: A linear system the sinusoid is the unique shape that propagates with no shape change – just a phase change and potentially an amplitude change. The wavelength (or alternatively wavenumber or wave vector ) is a characterization of the wave in space, that is functionally related to its frequency, as constrained by the physics of the system. Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition . In

800-426: A regular lattice. This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure. Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to

880-432: A result, the change in direction upon entering a different medium changes with the wavelength of the wave. For electromagnetic waves the speed in a medium is governed by its refractive index according to where c is the speed of light in vacuum and n ( λ 0 ) is the refractive index of the medium at wavelength λ 0 , where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in

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960-411: A sinusoidal waveform traveling at constant speed v {\displaystyle v} is given by where v {\displaystyle v} is called the phase speed (magnitude of the phase velocity ) of the wave and f {\displaystyle f} is the wave's frequency . In a dispersive medium , the phase speed itself depends upon the frequency of the wave, making

1040-403: A tower doubling as a flagpole attracted controversy in 2004 in relation to the U.S. presidential campaign of that year , and highlighted the sentiment that such disguises serve more to allow the installation of such towers in subterfuge, away from public scrutiny, rather than to serve towards the beautification of the landscape. A mast radiator or mast antenna is a radio tower or mast in which

1120-585: A tower, the structure may be parallel-sided or taper over part or all of its height. When constructed of several sections which taper exponentially with height, in the manner of the Eiffel Tower , the tower is said to be an Eiffelized one. The Crystal Palace tower in London is an example. Guyed masts are sometimes also constructed out of steel tubes. This construction type has the advantage that cables and other components can be protected from weather inside

1200-404: 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 often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as: where y is the value of the wave at any position x and time t , and A is the amplitude of

1280-531: A wavelength λ = h / p , where h is the Planck constant . This hypothesis was at the basis of quantum mechanics . Nowadays, this wavelength is called the de Broglie wavelength . For example, the electrons in a CRT display have a De Broglie wavelength of about 10  m . To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space. The spatial spread of

1360-488: A wood telecommunications tower – the first of its kind in Italy – replaced a previously-existing steel structure to blend in with its wooded surroundings. One of the most commonly cited reasons telecom companies opt for wood is because it is the only material in the industry that is climate positive . For this reason, some utility pole distributors started to offer wood towers to meet the growing demands of 5G infrastructure. In

1440-424: Is also responsible for the familiar phenomenon in which light is separated into component colours by a prism . Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength

1520-415: Is also sometimes applied to modulated waves, and 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 the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. Wavelength depends on

1600-464: Is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes , and 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 (an example of boundary conditions ), thus determining the allowed wavelengths. For example, for an electromagnetic wave, if

1680-403: Is called diffraction . Two types of diffraction are distinguished, depending upon the separation between the source and the screen: Fraunhofer diffraction or far-field diffraction at large separations and Fresnel diffraction or near-field diffraction at close separations. In the analysis of the single slit, the non-zero width of the slit is taken into account, and each point in the aperture

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1760-458: Is currently the tallest guyed tubular mast in the world after the Belmont transmitting station was reduced in height in 2010. Reinforced concrete towers are relatively expensive to build but provide a high degree of mechanical rigidity in strong winds. This can be important when antennas with narrow beamwidths are used, such as those used for microwave point-to-point links, and when the structure

1840-495: Is described by the Jacobi elliptic function of m th order, usually denoted as cn ( x ; m ) . Large-amplitude ocean waves with certain shapes can propagate unchanged, because of properties of the nonlinear surface-wave medium. If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave . Such waves are sometimes regarded as having a wavelength even though they are not sinusoidal. As shown in

1920-413: Is known as a dispersion relation . Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with

2000-427: Is large compared to the slit separation d ) then the paths are nearly parallel, and the path difference is simply d sin θ . Accordingly, the condition for constructive interference is: where m is an integer, and for destructive interference is: Thus, if the wavelength of the light is known, the slit separation can be determined from the interference pattern or fringes , and vice versa . For multiple slits,

2080-578: Is not an essential feature. A special form of the radio tower is the telescopic mast . These can be erected very quickly. Telescopic masts are used predominantly in setting up temporary radio links for reporting on major news events, and for temporary communications in emergencies. They are also used in tactical military networks. They can save money by needing to withstand high winds only when raised, and as such are widely used in amateur radio . Telescopic masts consist of two or more concentric sections and come in two principal types: A tethered balloon or

2160-585: Is one in which the metal mast or tower itself is energized and functions as the transmitting antenna. The terms "mast" and "tower" are often used interchangeably. However, in structural engineering terms, a tower is a self-supporting or cantilevered structure, while a mast is held up by stays or guy-wires . There are a few borderline designs that are partly free-standing and partly guyed, called additionally guyed towers . Examples: The first experiments in radio communication were conducted by Guglielmo Marconi beginning in 1894. In 1895–1896 he invented

2240-488: Is related to position x via a squared sinc function : where L is the slit width, R is the distance of the pattern (on the screen) from the slit, and λ is the wavelength of light used. The function S has zeros where u is a non-zero integer, where are at x values at a separation proportion to wavelength. Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes ) and microscopes . For

2320-619: Is still in use. Disguised cell sites sometimes can be introduced into environments that require a low-impact visual outcome, by being made to look like trees, chimneys or other common structures. Many people view bare cellphone towers as ugly and an intrusion into their neighbourhoods. Even though people increasingly depend upon cellular communications, they are opposed to the bare towers spoiling otherwise scenic views. Many companies offer to 'hide' cellphone towers in, or as, trees, church towers, flag poles, water tanks and other features. There are many providers that offer these services as part of

2400-458: Is taken as the source of one contribution to the beam of light ( Huygens' wavelets ). On the screen, the light arriving from each position within the slit has a different path length, albeit possibly a very small difference. Consequently, interference occurs. In the Fraunhofer diffraction pattern sufficiently far from a single slit, within a small-angle approximation , the intensity spread S

2480-494: Is the danger of wind-induced oscillations. This is particularly a concern with steel tube construction. One can reduce this by building cylindrical shock-mounts into the construction. One finds such shock-mounts, which look like cylinders thicker than the mast, for example, at the radio masts of DHO38 in Saterland . There are also constructions, which consist of a free-standing tower, usually from reinforced concrete , onto which

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2560-483: Is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings . Wavelength 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 commonly designated by the Greek letter lambda ( λ ). The term "wavelength"

2640-412: Is the most widespread form of construction. It provides great strength, low weight and wind resistance, and economy in the use of materials. Lattices of triangular cross-section are most common, and square lattices are also widely used. Guyed masts are often used; the supporting guy lines carry lateral forces such as wind loads, allowing the mast to be very narrow and simply constructed. When built as

2720-511: Is to be occupied by people. In the 1950s, AT&T built numerous concrete towers, more resembling silos than towers, for its first transcontinental microwave route. In Germany and the Netherlands most towers constructed for point-to-point microwave links are built of reinforced concrete , while in the UK most are lattice towers . Concrete towers can form prestigious landmarks, such as

2800-417: Is used in the interferometer . A simple example is an experiment due to Young where light is passed through two slits . As shown in the figure, light is passed through two slits and shines on a screen. The path of the light to a position on the screen is different for the two slits, and depends upon the angle θ the path makes with the screen. If we suppose the screen is far enough from the slits (that is, s

2880-539: The CN Tower in Toronto , Canada. In addition to accommodating technical staff, these buildings may have public areas such as observation decks or restaurants. The Katanga TV tower near Jabalpur , Madhya Pradesh, in central India hosts a high-power transmitter for the public broadcasters Doordarshan and Prasar Bharati . The Stuttgart TV tower was the first tower in the world to be built in reinforced concrete. It

2960-422: The cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in a medium is less than in vacuum , which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum, as shown in

3040-532: 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 × 10  m/s . Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3 × 10  m/s divided by 10  Hz = 3 m. The wavelength of visible light ranges from deep red , roughly 700  nm , to violet , roughly 400 nm (for other examples, see electromagnetic spectrum ). For sound waves in air,

3120-435: The shortwave range, there is little to be gained by raising the antenna more than a half to three quarters of a wavelength above ground level, and at lower frequencies and longer wavelengths, the height becomes infeasibly great (greater than 85 metres (279 ft)). Shortwave transmitters rarely use masts taller than about 100 metres. Because masts, towers and the antennas mounted on them require maintenance, access to

3200-443: The speed of sound is 343 m/s (at room temperature and atmospheric pressure ). The wavelengths of sound frequencies audible to the human ear (20  Hz –20 kHz) are thus between approximately 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

3280-494: The vertical monopole or Marconi antenna , which was initially a wire suspended from a tall wooden pole. He found that the higher the antenna was suspended, the further he could transmit, the first recognition of the need for height in antennas. Radio began to be used commercially for radiotelegraphic communication around 1900. The first 20 years of commercial radio were dominated by radiotelegraph stations, transmitting over long distances by using very long wavelengths in

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3360-445: The very low frequency band – such long waves that they are nearly unused at present. Because the extreme wavelengths were one to several kilometers long, even the tallest feasible antennas by comparison were still too short, electrically , and consequently had inherently very low radiation resistance (only 5~25 Ohms). In any antenna, low radiation resistance leads to excessive power losses in its surrounding ground system , since

3440-596: The visual horizon . The only way to cover larger areas is to raise the antenna high enough so it has a line-of-sight path to them. Until 8 August 1991, the Warsaw radio mast was the world's tallest supported structure on land; its collapse left the KVLY / KTHI-TV mast as the tallest. There are over 50 radio structures in the United States that are 600 m ( 1 968.5 ft ) or taller. The steel lattice

3520-425: The whole structure is an antenna. Mast antennas are the transmitting antennas typical for long or medium wave broadcasting. Structurally, the only difference is that some mast radiators require the mast base to be insulated from the ground. In the case of an insulated tower, there will usually be one insulator supporting each leg. Some mast antenna designs do not require insulation, however, so base insulation

3600-548: The 1930s it was found that the diamond shape of the Blaw-Knox tower had an unfavorable current distribution which increased the power emitted at high angles, causing multipath fading in the listening area. By the 1940s the AM broadcast industry had abandoned the Blaw-Knox design for the narrow, uniform cross section lattice mast used today, which had a better radiation pattern. The rise of FM radio and television broadcasting in

3680-531: The 1940s–1950s created a need for even taller masts. The earlier AM broadcasting used LF and MF bands, where radio waves propagate as ground waves which follow the contour of the Earth. The ground-hugging waves allowed the signals to travel beyond the horizon, out to hundreds of kilometers. However the newer FM and TV transmitters used the VHF band, in which radio waves travel by line-of-sight , so they are limited by

3760-638: The 1960s. In Germany the Bielstein transmitter collapsed in 1985. Tubular masts were not built in all countries. In Germany, France, UK, Czech Republic, Slovakia, Japan and the Soviet Union, many tubular guyed masts were built, while there are nearly none in Poland or North America. Several tubular guyed masts were built in cities in Russia and Ukraine. These masts featured horizontal crossbars running from

3840-418: The United States, for example, wood utility pole distributor Bell Lumber & Pole began developing products for the telecommunications industry . Shorter masts may consist of a self-supporting or guyed wooden pole, similar to a telegraph pole. Sometimes self-supporting tubular galvanized steel poles are used: these may be termed monopoles. In some cases, it is possible to install transmitting antennas on

3920-399: The box has ideal conductive walls, the condition for nodes at the walls results because the conductive 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. Consequently, wavelength, period, and wave velocity are related just as for

4000-574: The buildings collapsed, several local TV and radio stations were knocked off the air until backup transmitters could be put into service. Such facilities also exist in Europe , particularly for portable radio services and low-power FM radio stations. In London , the BBC erected in 1936 a mast for broadcasting early television on one of the towers of a Victorian building, the Alexandra Palace . It

4080-524: The central mast structure to the guys and were built in the 1960s. The crossbars of these masts are equipped with a gangway that holds smaller antennas, though their main purpose is oscillation damping. The design designation of these masts is 30107 KM and they are exclusively used for FM and TV and are between 150–200-metre (490–660 ft) tall with one exception. The exception being the mast in Vinnytsia which has height of 354 m (1161 ft) and

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4160-569: The direction and wavenumber of a plane wave in 3-space , parameterized by position vector r . In that case, the wavenumber k , the magnitude of k , is still in the same relationship with wavelength as shown above, with v being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction. Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave . The typical convention of using

4240-407: The figure at right. This change in speed upon entering a medium causes refraction , or a change in direction of waves that encounter the interface between media at an angle. For electromagnetic waves , this change in the angle of propagation is governed by Snell's law . The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As

4320-400: The figure, wavelength is measured between consecutive corresponding points on the waveform. Localized wave packets , "bursts" of wave action where each wave packet travels as a unit, find application in many fields of physics. A wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called

4400-423: The first he derived the radiation resistance of a vertical conductor over a ground plane . He found that the radiation resistance increased to a maximum at a length of ⁠ 1  / 2 ⁠ wavelength , so a mast around that length had an input resistance that was much higher than the ground resistance, reducing the fraction of transmitter power that was lost in the ground system without assistance from

4480-471: The first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture : where the numerical aperture is defined as N A = n sin ⁡ θ {\displaystyle \mathrm {NA} =n\sin \theta \;} for θ being the half-angle of the cone of rays accepted by the microscope objective . The angular size of

4560-406: The hazard that communications towers can pose to birds. There have also been instances of rare birds nesting in cell towers and thereby preventing repair work due to legislation intended to protect them. Wavelength In physics and mathematics , wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it

4640-405: The light is not altered, just where it shows up. The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen. The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen. This distribution of wave energy

4720-411: The local water depth. Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an inhomogeneous medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response,

4800-445: The low-resistance antenna cannot effectively compete for power with the high-resistance earth. To partially compensate, radiotelegraph stations used huge capacitively top-loaded flattop antennas consisting of horizontal wires strung between multiple 100–300 meters (330–980 ft) steel towers to increase efficiency. AM radio broadcasting began around 1920. The allocation of the medium wave frequencies for broadcasting raised

4880-416: The medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are sound waves , light , 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

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4960-407: The medium is When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium. The variation in speed of light with wavelength is known as dispersion , and

5040-593: The normal tower installation and maintenance service. These are generally called "stealth towers" or "stealth installations", or simply concealed cell sites . The level of detail and realism achieved by disguised cellphone towers is remarkably high; for example, such towers disguised as trees are nearly indistinguishable from the real thing. Such towers can be placed unobtrusively in national parks and other such protected places, such as towers disguised as cacti in United States' Coronado National Forest . Even when disguised, however, such towers can create controversy;

5120-529: The past, ruggedized and under-run filament lamps were used to maximize the bulb life. Alternatively, neon lamps were used. Nowadays such lamps tend to use LED arrays. Height requirements vary across states and countries, and may include additional rules such as requiring a white flashing strobe in the daytime and pulsating red fixtures at night. Structures over a certain height may also be required to be painted with contrasting color schemes such as white and orange or white and red to make them more visible against

5200-413: The pattern is where q is the number of slits, and g is the grating constant. The first factor, I 1 , is the single-slit result, which modulates the more rapidly varying second factor that depends upon the number of slits and their spacing. In the figure I 1 has been set to unity, a very rough approximation. The effect of interference is to redistribute the light, so the energy contained in

5280-410: The possibility of using single vertical masts without top loading. The antenna used for broadcasting through the 1920s was the T-antenna , which consisted of two masts with loading wires on top, strung between them, requiring twice the construction costs and land area of a single mast. In 1924 Stuart Ballantine published two historic papers which led to the development of the single mast antenna. In

5360-541: The roofs of tall buildings. In North America , for instance, there are transmitting antennas on the Empire State Building , the Willis Tower , Prudential Tower , 4 Times Square , and One World Trade Center . The North Tower of the original World Trade Center also had a 110-metre (360 ft) telecommunications antenna atop its roof, constructed in 1978–1979, and began transmission in 1980. When

5440-537: The short wavelength is associated with a high loss and the wave dies out. The analysis of differential equations of such systems is often done approximately, using the WKB method (also known as the Liouville–Green method ). The method integrates phase through space using a local wavenumber , which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space. This method treats

5520-494: The sky. In some countries where light pollution is a concern, tower heights may be restricted so as to reduce or eliminate the need for aircraft warning lights. For example, in the United States the 1996 Telecommunications Act allows local jurisdictions to set maximum heights for towers, such as limiting tower height to below 200 feet (61 m) and therefore not requiring aircraft illumination under US Federal Communications Commission (FCC) rules. One problem with radio masts

5600-420: The special case of dispersion-free and uniform media, waves other than sinusoids propagate with unchanging shape and constant velocity. In certain circumstances, waves of unchanging shape also can occur in nonlinear media; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave , a traveling wave so named because it

5680-529: The system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave. Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in

5760-554: The tube and consequently the structure may look cleaner. These masts are mainly used for FM-/TV-broadcasting, but sometimes also as mast radiator. The big mast of Mühlacker transmitting station is a good example of this. A disadvantage of this mast type is that it is much more affected by winds than masts with open bodies. Several tubular guyed masts have collapsed. In the UK, the Emley Moor and Waltham TV stations masts collapsed in

5840-427: The wave packet, and the spread of the wavenumbers of sinusoids that make up the packet, correspond to the uncertainties in the particle's position and momentum, the product of which is bounded by Heisenberg uncertainty principle . When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon their relative phase. This phenomenon

5920-456: The wave vectors confined to the Brillouin zone . This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations . It is mathematically equivalent to the aliasing of a signal that is sampled at discrete intervals. The concept of wavelength is most often applied to sinusoidal, or nearly sinusoidal, waves, because in

6000-426: The wave. They are also commonly expressed in terms of wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the frequency) as: in which wavelength and wavenumber are related to velocity and frequency as: or In the second form given above, the phase ( kx − ωt ) is often generalized to ( k ⋅ r − ωt ) , by replacing the wavenumber k with a wave vector that specifies

6080-404: The whole of the structure is necessary. Small structures are typically accessed with a ladder . Larger structures, which tend to require more frequent maintenance, may have stairs and sometimes a lift, also called a service elevator. Tall structures in excess of certain legislated heights are often equipped with aircraft warning lamps , usually red, to warn pilots of the structure's existence. In

6160-425: Was also used at Criggion radio station . For ELF transmitters ground dipole antennas are used. Such structures require no tall masts. They consist of two electrodes buried deep in the ground at least a few dozen kilometres apart. From the transmitter building to the electrodes, overhead feeder lines run. These lines look like power lines of the 10 kV level, and are installed on similar pylons. For transmissions in

6240-453: Was designed by architects Gerhard Kreisel, Dipl. Ing. and Günter H. Müller Dipl. Ing., Kiel . 53°51′26″N 8°40′40″E  /  53.85722°N 8.67778°E  / 53.85722; 8.67778 This article about a mast or transmitter tower in Europe is a stub . You can help Misplaced Pages by expanding it . Telecommunication tower A mast radiator or radiating tower

6320-405: Was designed in 1956 by the local civil engineer Fritz Leonhardt . Fiberglass poles are occasionally used for low-power non-directional beacons or medium-wave broadcast transmitters. Carbon fibre monopoles and towers have traditionally been too expensive but recent developments in the way the carbon fibre tow is spun have resulted in solutions that offer strengths exceeding steel (10 times) for

6400-504: Was the diamond cantilever or Blaw-Knox tower . This had a diamond ( rhombohedral ) shape which made it rigid, so only one set of guy lines was needed, at its wide waist. The pointed lower end of the antenna ended in a large ceramic insulator in the form of a ball-and-socket joint on a concrete base, relieving bending moments on the structure. The first, a 665 foot (203 m) half-wave mast was installed at radio station WABC 's 50  kW transmitter at Wayne, New Jersey in 1931. During

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