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Electronics/Charge

Two atoms are walking down the street. The first atom says to the second atom "I think I lost an electron!" The second says "Are you sure?" To which the first states "I'm positive!"

Balance of Charge
Atoms, the smallest particles of matter, are made of protons, electrons, and neutrons. Protons have a positive charge, Electrons have a negative charge that cancels the proton's positive charge. Neutrons are particles that are similar to a proton but have a neutral charge. There are no differences between positive and negative charges except that particles with the same charge repel each other and particles with opposite charge attract each other. If a solitary positive proton and negative electron are placed near each other they will come together to form a hydrogen atom. This repulsion and attraction (force between stationary charged particles) is known as Electrostatic Force and extends theoretically to infinity, but is diluted with distance.

Both atoms and the universe have a neutral charge overall and come with the same number of protons and electrons. When an atom has one or more missing electrons it is left with a positive charge, and when an atom has at least one extra electron it has a negative charge. Having a positive or a negative charge makes an atom an ion. Atoms only gain and lose protons and neutrons through fusion, fission, and being radioactive. Although atoms are made of many particles and objects are made of many atoms, they behave similar to charged particles in terms of how they repel and attract.

In an atom the protons and neutrons combine to form a tightly bound nucleus. This nucleus is surrounded by a vast cloud of electrons circling it at great distance held near the protons by electromagnetic attraction. The cloud exists as a series of overlapping shells / bands in which the inner valence bands are filled with electrons and are tightly bound to the atom. The outer conduction bands contain no electrons except those that have accelerated to the conduction bands by gaining energy. With enough energy an electron will escape an atom. When an electron in the conduction band decelerates and falls to another conduction band or the valence band emitting an photon, is known as the photoelectric effect.

 * laser: When electrons travel back and forth between conduction bands emitting synchronized photons.

 * 1) When the conduction and valence bands overlap, the atom is a conductor and allows for the free movement of electrons. Conductors are metals and can be thought of as a bunch of atomic nuclei surrounded by a churning "sea of electrons".
 * 2) When there is a large gap between the conduction and valence bands, the atom is an insulator and trap electrons. Insulators are non-metals and are good at stopping the flow of electrons.
 * 3) When there is a small gap between the conduction and valence bands, the atom is a semiconductor. Semiconductors behave like conductors and insulators, and work using the conduction and valence bands. The electrons in the outer valence band are known as holes. They behave like positive charges because of how they flow. In semiconductors electrons collide with the material and their progress is halted. This makes the electrons have an effective mass that is less than their normal mass. In some semiconductors holes have a larger effective mass than the conduction electrons.

Electronic devices are based on the idea of exploiting the differences between conductors, insulators, and semiconductors.

Conductors
In a conductor the electrons of an object are free to move. Due to their repulsive nature the valence electrons leave the center of the object and spread out evenly across its surface in order to be as far apart as possible. This cavity of empty space is known as a Faraday Cage and stops radiation, such as charge, radio waves, and EMPs (Electro-Magnetic Pulses) from entering and leaving the object. If there are holes in the Faraday Cage than radiation can pass.

One of the interesting things to do with conductors is the transfer of charge between metal spheres. At the start the spheres are neutral. The first step involves putting sphere 1 next to but not touching sphere 2. This causes all the electrons in sphere 2 to travel away from sphere 1 to the far end of sphere 2. So sphere 2 now has a negative end filled with electrons and a positive end lacking electrons. Next sphere 2 is grounded by contact with a conductor connected with the earth and the earth takes its electrons leaving sphere 2 with a positive charge. The positive charge (absence of electrons) spreads evenly across the surface due to its lack of electrons.

Insulators
In an insulator the electrons of an object are stuck. This allows charge to build up on the surface of the object by way of the triboelectric effect. The triboelectric effect (rubbing electricity effect) involves the exchange of electrons when two different insulators such as glass, hard rubber, amber, or even the seat of one's pants, come into contact. The polarity and strength of the charges produced differ according to the material composition and its surface smoothness. For example, glass rubbed with silk will build up a charge, as will hard rubber rubbed with fur. The effect is greatly enhanced by rubbing materials together.

 * Van de Graaff Generator: A charge pump (pump for electrons) that generates static electricity. In a Van de Graaff generator, a conveyor belt uses rubbing to pick up electrons, which are then deposited on metal brushes. The end result is a charge difference.

Because the material being rubbed is now charged, contact with an uncharged object or an object with the opposite charge may cause a discharge of the built-up static electricity by way of a spark. A person simply walking across a carpet may build up enough charge to cause a spark to travel over a centimeter. The spark is powerful enough to attract dust particles to cloth, destroy electrical equipment, ignite gas fumes, and create lightning. In extreme cases the spark can destroy factories that deal with gunpowder and explosives. The best way to remove static electricity is by discharging it through grounding. Humid air will also slowly discharge static electricity. This is one reason why cells and capacitors lose charge over time.

Quantity of Charge
Protons and electrons have opposite but equal charge. Because in almost all cases, the charge on protons or electrons is the smallest amount of charge commonly discussed, the quantity of charge of one proton is considered one positive elementary charge and the charge of one electron is one negative elementary charge. Because atoms and such particles are so small, and charge in amounts of multi-trillions of elementary charges are usually discussed, a much larger unit of charge is typically used. The Coulomb is a unit of charge, which can be expressed as a positive or negative number, which is equal to approximately 6.2415×1018 elementary charges. Accordingly, an elementary charge is equal to approximately 1.602 ×10-19 coulombs. The commonly used abbreviation for the Coulomb is a capital C. The SI definition of a Coulomb is the quantity of charge which passes a point over a period of 1 second ( s ) when a current of 1 Ampere ( A ) flows past that point, i. e., C = A s or  A = C/s. An ampere is one of the fundamental units in physics from which various other units are defined, such as the coulomb.

title: Electronics/Charge


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Electronics/Frequency Spectrum

This page covers the spectrum of electromagnetic waves.

Properties of Waves

 * A wave is an oscillation, if represented in the plane using a Cartesian coordinate system looks like a sine wave, being the x axis time and the y axis amplitude. Amplitude is the variation of the wave across a given period being the peak the highest point of a wave. The difference between two peaks is a wavelength. Period is the time it takes a wavelength to pass by a point in space. Frequency is the number of waves that pass by in a second.
 * Black bodies - A cavity that absorbs all radiation and emits radiation at a specific frequency.
 * Resonant cavities - A cavity that allows standing waves of a specific frequency.

Sound
Sound is heard when there are two that things collide with each other. Sound wave is a longitude wave. Sound waves are affected by temperature and atmosphere's pressure

In water sound waves travel faster due to particles being more compressed. In Air, Sound wave pressure creates rare-fraction and rare-compression columns of air

dB scale
DB Scale is used to measured the pressure of a Sound

 * 0 dB means normal no sound
 * 20 dB means normal no amplification of sound
 * 40 dB means normal double amplification of sound

Infrasound: < 20 Hz
Sounds of frequency below 20 Hz is called InfraSound can not be heard by human's ears

sound travels the earth so it can be used to detect nuclear blasts and allows whales to communicate for 10,000 miles (sound channel).

can be greater than >120 dB is intensity but not heard by people. associated with avalanches, earthquakes, volcanoes, meteors, the earth groaning, rock concerts, and pipe organs. Intensifies emotions.

Infrasound has some really warped effects on society.

sound that travels the earth

often >120 dB is intensity.

If heard would be a large rumble as loud as a jet engine or gunfire.

At rock concerts they play infrasound. This intensifies emotions. This is one possible reason why people play loud music.

Attraction of pipe organs.

In addition the earth groans. Anyone know the mythological significance of the cry of the earth?

used by whales to communicate as the waves can travel 10,000 miles.

Infrasound appears to heighten emotions and make people nervous and thus has an association with the supernatural such as haunted houses. Since people are emotionally attached to the deceased and go to where they died, when you combine it with infrasound which is associated with chills, is this an explanation for ghosts?

One of the stranger uses of infrasound involves combining an ancient chamber that resonates infrasound with mind altering drugs to induce visions and out of body experiences.

Audible Sound: 20-20,000 Hz
Audible Sound are sound that can be perceived by human's ears. Audible Sounds are sounds in the range of frequencies 20-20,000 Hz

Human's Voice
 * Human's Voice (20-100)-20,000 Hz
 * Older human hearing 20-15,000 Hz

Computer Sound formats
 * MP3 up to 16 kHz
 * Ogg, AAC up to 20 kHz

Animal Sound
 * sonar 50 kHz, 192-200 kHz
 * dolphins 1-164 kHz
 * bats 20 - 115 kHz
 * whale 30-8000 Hz

Music
 * music 20 Hz - 20000 Hz

Telephone
 * phone 200-2000 Hz

Ultrasound: > 20 kHz
Sounds above 20 kHz are called Ultra Sound. Unable to be heard by people, but can be heard by dogs and dolphins.

Light
photons are emitted by a black body. Talk about energy of photons and how far they penetrate.

regulated by ITU In the US, the allocation of these bands is managed by the FCC Federal Standard 1037C and MIL-STD-188.

The VLA telescope array can resolve a &lambda of 8,xxx Hz

Candela
Unit of intensity

(ELF) Extremely low frequency: < 300 Hz

 * ELF is used by the US Navy to communicate with submerged submarines. The extremely high electrical conductivity of seawater shields submarines from most electromagnetic communications. Signals in the ELF frequency range, however, can penetrate much more deeply. The low transmission rate of most ELF communications limits their use as communications channels; generally an ELF signal serves to request that a submarine surface and initiate some other form of contact.

 * One of the difficulties posed when broadcasting in the ELF frequency range is antenna size. In order to transmit internationally using ELF frequencies, an extremely large antenna is required. The US maintains two sites, in Wisconsin and Michigan. Both sites use long power lines as antennae, in multiple strands ranging from 14 to 28 miles long. Considerable amounts of power are generated and emitted by ELF, and there have been some concerns over the possible ecological impact of such signals.

 * See also: TACAMO, HAARP, List of initialisms,

 * Starting at 7.8 Hz there is the Schumann resonance, which is due to the space between the surface of the Earth and the ionosphere. It acts as a resonant cavity fueled by energy from lightning strikes.  Serial Experiments Lain had the idea that the Schumann resonance could be a carrier for a collective consciousness.

(VF) Voice frequency: 300-3000 Hz

 * Voice band. Used to transmit speech. Allocated for telephone. Voice frequency varies from 300-3400 Hz. 4 kHz allocated for for a single voice-frequency including guard bands.

(VLF) Very Low Frequency: 3-30 kHz

 * Very Low Frequency or VLF refers to Radio Frequencies (RF) in the range of 3 - 30 kHz. Since there is not much space in this band of the spectrum, only the very simplest signals are used, such as for radionavigation. Many natural radio emissions, such as whistlers, can be heard in this band.

 * Because VLF can penetrate water to a depth of 20 meters, they are used to communicate with submarines.

 * Lightning generates low frequency radio waves called whistlers. Whistlers have been received from Jupiter showing the presence of lightning there.

 * The dawn chorus is an unexplained electromagnetic phenomenon that occurs most often at sunrise or shortly after, that (with the proper radio equipment) resembles the sound of a massive flock of birds. It is thought to be caused by high-energy electrons that get caught in the Van Allen radiation belts of the Earth's magnetosphere and fall to the Earth's surface in the form of audible radio waves. Dawn choruses occur more frequently during magnetic storms.

 * This phenomenon also occurs during aurorae, when it is termed an auroral chorus.

(LF) Low Frequency: 30-300 kHz

 * Low Frequency or LF (sometimes called longwave) refers to Radio Frequencies (RF) in the range of 30-300 kHz. In Europe, part of the LF spectrum is used for AM broadcast service. In the western hemisphere, its main use is for aircraft beacon, navigation, information, and weather systems.

 * pass through ionosphere
 * can penetrate oceans to 200 meters

 * Long wave is 144 - 351 kHz in Europe, Africa, and Asia. In the Americas, this band is reserved for aeronautical navigation.

 * Longwave radio frequencies are those below 500 kHz, which correspond to wavelengths longer than 600 meters. They have the property of following the curvature of the earth, making them ideal for continuous, continental communications. Unlike shortwave radio, longwave signals do not reflect nor refract using the ionosphere, so there are fewer phase-caused fadeouts.

 * In Europe, North Africa and Asia, longwave radio frequencies between 153 and 281 kHz are used for domestic and international broadcasting. In the Americas, frequencies between 200 and 430 kHz are used for non-directional radio beacons.

 * The frequency of 60 kHz is used by several nations, such as the United States, Germany, England, and Japan, for extremely accurate time and precision frequency signals. Many commercial appliances sold since approximately 2000 have a VLF receiver capable of receiving these signals, which penetrate indoors more effectively than mediumwave or shortwave signals.

 * Radio signals below 50 kHz are capable of penetrating ocean depths to approximately 200 meters. The United States, Russian, British, Swedish, and Indian navies communicate with submarines on these frequencies.

 * Longwave transmitting antennas take up large amounts of space, and have been the cause of controversy in the United States and Europe due to fears over proximity to high-power radio waves.

(MF) Medium Frequency: 300-3000 kHz

 * (AM) Amplitude Modulation radio is from 530 - 1,700 kHz. Also known as medium wave.  Was big from 1900's-1960's

 * AM radio technology is simpler than other types of radio, such as FM radio and DAB. An AM receiver detects the power of the radio wave, and amplifies changes in the power measurement to drive a speaker or earphones. The earliest crystal radio receivers used this principle.

 * AM radio was used for small scale voice and music broadcasts before World War I. The great increase in the use of AM radio came the following decade. The first commercial radio services began on AM in the 1920s. Radio programming boomed during the "Golden Age of Radio." Dramas, comedy and all other forms of entertainment were produced, as well as broadcasts of news and music.

 * Medium wave is by far the most used for commercial radio broadcasting; this is the "AM radio" that most people are familiar with.

 * For the long and medium wave bands, the wavelength is long enough that the wave diffracts around the curve of the Earth by ground wave propagation, giving AM radio, in particular long wave and medium wave at night, a long range.

 * Short wave is used by radio services intended to be heard great distances away from the transmitting station; the far range of short wave broadcasts comes at the expense of lower audio fidelity. The mode of propagation for short wave is different, see High frequency. AM is used mostly for broadcast uses - other shortwave users may use a modified version of AM such as SSB or an AM-compatible version of SSB such as SSB with carrier reinserted.

 * Frequencies between the broadcast bands are used for other forms of radio communication, such as baby monitors, walkie talkies, cordless telephones, radio control, amateur radio etc.

(HF) High Frequency: 3-30 MHz

 * High frequency (HF) radio frequencies are between 3 and 30 MHz. This range is often called shortwave.

 * Short wave is 1,700 - 30,000 kHz, divided into 14/15 "broadcast bands".

 * Since the ionosphere often reflects HF radio waves quite well, this range is extensively used for medium and long range terrestrial radio communication. However, suitability of this portion of the spectrum for such communication varies greatly with a complex combination of factors:

* Sunlight/darkness at site of transmission and reception * Transmitter/receiver proximity to terminator * Season * Sunspot cycle * Solar activity * Polar aurora * Maximum usable frequency * Lowest usable frequency * Frequency of operation within the HF range

 * HF is often used for continuous wave morse code transmissions.

 * See also: VHF, AM radio, Radio propagation

 * Shortwave radio operates between the frequencies of 3000 kHz and 30 MHz (30,000 kHz) and came to be referred to as such in the early days of radio because the wavelengths associated with this frequency range were shorter than those commonly in use at that time. An alternate name is HF, or high frequency.

 * Short wavelengths are associated with high frequencies because there is an inverse relationship between frequency and wavelength.

 * Shortwave frequencies are capable of reaching the other side of the planet by bouncing a signal off the ionosphere. The selection of a frequency to use to reach a target area depends on several factors:

* The distance from the transmitter to the target receiver * Time of day. During the day, higher shortwave frequencies (> 10 MHz) can travel longer distances than lower; at night, this : property is reversed. * Season of the year. * Solar conditions, including the number of sunspots, solar flares, and overall solar activity. Solar flares can prevent the : ionosphere from reflecting or refracting radio waves.

 * Some major users of the shortwave radio band include:

* Domestic broadcasting in countries with a widely dispersed population with few longwave, mediumwave or FM stations serving them * International broadcasting to foreign audiences * Utility stations transmitting messages not intended for a general public, such as aircraft flying between continents, encoded or ciphered diplomatic messages, weather reporting, or ships at sea * Amateur radio operators * Time signal stations

 * The Asia-Pacific Telecommunity estimates that there are approximately 600,000,000 shortwave radio receivers in use in 2002.

 * The World Radiocommunication Conference (WRC), organized under the auspices of the International Telecommunications Union, allocates bands for various services in conferences every few years. The next WRC is scheduled to take place in 2007. At the World Administrative Radio Conference (WARC) in 1997, the following bands were allocated to international broadcasters:

5,900-5,950 kHz 7,300-7,350 kHz (7,100-7,350 kHz outside of the Americas) 9,400-9,500 kHz 11,600-11,650 kHz 12,050-12,100 kHz 13,570-13,600 kHz 13,800-13,870 kHz 15,600-15,800 kHz 17,480-17,550 kHz 18,900-19,020 kHz

 * Shortwave broadcasting channels are allocated with a 5 kHz separation. International broadcasters, however, may operate outside the normal WARC-allocated bands or use off-channel frequencies to attract attention in crowded bands.

 * The power used by shortwave transmitters ranges from less than one watt for some experimental transmissions to 500 kilowatts and higher for intercontinental broadcasters. Shortwave transmitting centers often use specialized antenna designs to concentrate radio energy on a bearing aimed at the target area.

Table of contents [showhide] 1 International broadcasting 2 Amateur radio 3 Shortwave listening 4 Numbers Stations

5 Shortwave radio: the future 1 Shortwave Broadcasts and Music

International broadcasting

See International broadcasting for details on the history and practice of broadcasting to foreign audiences.

Amateur radio

The privilege of operating shortwave radio transmitters for non-commercial purposes is open to licensed amateurs. In the US, they are licensed by the Federal Communications Commission (FCC). U.S. citizens do not need licenses to own or operate shortwave receivers. Recently the FCC has added an amateur radio license which requires no knowledge of Morse code, making it easier for beginners to get involved; however, a working knowledge of Morse code is required to operate on shortwave bands.

Amateur radio operators have made numerous technical advancements in the field of radio and make themselves available to transmit emergency communications when normal communications channels fail. Some amateurs practice operating off the power grid so as to be prepared for power loss.

Shortwave listening

Many hobbyists listen to shortwave broadcasters without operating transmitters. In many cases, the goal is to obtain as many stations from as many countries as possible (DXing); others listen to specialized shortwave utility, or "ute", transmissions such as maritime, naval, aviation, or military signals. Others focus on intelligence signals.

Shortwave listeners, or SWLs, can obtain "QSL" cards from broadcasters or utility stations as trophies of the hobby.

Numbers Stations

Numbers stations are shortwave radio stations of uncertain origin that broadcast streams of numbers, words, or phonetic sounds. Although officially there is no indication of their origin, radio hobbyists have determined that many of them are used by intelligence services as one-way communication to agents in other countries.

Shortwave radio: the future

The development of direct broadcasts from satellites has reduced the demand for shortwave receivers, but there are still a great number of shortwave broadcasters. A new digital radio technology, Digital Radio Mondiale, is expected to improve the quality of shortwave audio from very poor to standards comparable to the FM broadcast band. The future of shortwave radio is threatened by the uprise of power line communication (PLC), where a data stream is transmitted over unshielded power lines. As the frequencies used overlap with the shortwave bands severe distortions make listening to shortwave radio near power lines difficult or impossible.

Shortwave Broadcasts and Music

Some musicians have been attracted to the unique aural qualities of shortwave radio. John Cage employed shortwave radios as live instruments in a number of pieces, and other musicians have sampled broadcasts, used tape loops of broadcasts, or drawn inspiration from the unusual sounds on some frequencies. Karlheinz Stockhausen used shortwave radio in works including Telemusik (1966), Hymnen (1966–67) and Spiral (1968), and Holger Czukay, Pat Metheny, Aphex Twin, Meat Beat Manifesto, and Wilco have also used broadcasts.

(VHF) Very High Frequency: 30-300 MHz/10-1 m

 * Common uses for VHF are FM radio broadcast at 88-108 MHz and television broadcast (together with UHF). VHF is also commonly used for terrestrial navigation systems (VOR in particular) and aircraft communications.

 * UHF and VHF are the most common frequency bands for television.

 * VHF frequencies' propagation characteristics are ideal for short-distance terrestrial communication. Unlike HF frequencies, the ionosphere does not usually reflect VHF radio and thus transmissions are restricted to the local area (and can't interfere with transmissions thousands of kilometres away) It is also less affected by atmospheric noise and interference from electrical equipment than low frequencies. Whilst it is more easily blocked by land features than HF and lower frequencies, it is less bothered by buildings and other less substantial objects than higher frequencies. It was also easier to construct efficient transmitters, receivers, and antennas for it in the earlier days of radio. In most countries, the VHF spectrum is used for broadcast audio and television, as well as commercial two-way radios (such as that operated by taxis and police), marine two-way audio communications, and aircraft radios.

 * The large slice of technically and commercially valuable slice of the VHF spectrum taken up by television transmission has attracted the attention of many companies and governments recently, with the development of more efficient digital television broadcasting standards. In some countries much of this spectrum will likely become available (probably for sale) in the next decade or so (currently scheduled for 2008 in the United States).

 * In the United Kingdom, the authorities chose to develop colour television exclusively on UHF, beginning in the late 1960s. The last British VHF TV transmitters closed down in 1986. VHF band III is now used in the UK for digital audio broadcasting.

FM been around since 1940

42-50 MHz Pre WWII allocation of FM 1940 88-106 MHz Post WWII allocation of FM 1945

FM stereo technology

 * New technology was added to FM radio in the early 1960s to allow FM stereo transmissions, where the frequency modulated radio signal is used to carry stereophonic sound, using the pilot-tone multiplex system.

 * This multiplexes the left and right audio signal channels in a manner that is compatible with mono sound, using a sum-and-difference technique to produce a single "mono-compatible" signal, which has a baseband part that is equal to the sum of the left and right channels (L+R), and a higher-frequency part that is the difference of the left and right channels (L-R) amplitude modulated on a 38 kHz subcarrier. A 19 kHz pilot tone is then added, to allow allow receivers to detect the presence of a stereo-encoded signal.

 * This signal can then be passed through the FM modulation and demodulation process as if it was a monophonic signal, and the stereo signals extracted from the demodulated FM signal by reversing the multiplexing process.

 * Simple mono FM receivers will not extract the left and right signals, but simply reproduce the baseband part of the "mono-compatible" signal. (This relies on the fact that the subcarrier-modulated part of the mono-compatible signal is in a part of the audio spectrum that is inaudible to people, and the pilot tone is a low-intensity tone in a part of the audio spectrum that is inaudible to most people).

 * This backwards compatibility was important, as when the FM stereo system was introduced in the U.S. in the 1960s, mono FM transmissions had been in service since the 1940s, and there was a large installed base of mono receivers that needed to be able to receive stereo broadcasts without any modification.

 * Stereo receivers could automatically switch between "mono" and "stereo" modes based on the presence of the pilot tone. They were also equipped with a notch filter to remove the pilot tone. In poor signal conditions, stereo receivers could also fall back to mono mode, even on a stereo signal, allowing improved signal-to-noise performance in these conditions.

 * The stereo multiplexing system has been further extended to add an extra, even higher frequency, 57 kHz subcarrier, which is used to carry low-bandwidth digital Radio Data System information, allowing digitally controlled radios to provide extra features.

 * FM radio channel assignments in the US

 * In the United States, frequency-modulated broadcasting stations operate in a frequency band extending from 87.8 MHz to 108.0 MHz, for a total of 20.2 MHz. It is divided into 100 channels, each 0.2 MHz wide, designated "channel 200" through "channel 300."

 * To receive a station, an FM receiver is tuned to the center frequency of the station's channel. The lowest channel, channel 200, extends from 87.8 MHz to 88.0 MHz; thus its center frequency is 87.9 MHz. Channel 201 has a center frequency of 88.1 MHz, and so on, up to channel 300, which extends from 107.8 to 108.0 MHz and has a center frequency of 107.9 MHz.

 * Because each channel is 0.2 MHz wide, the center frequencies of adjacent channels differ by 0.2 MHz. Because the lowest channel is centered on 87.9 MHz the tenths digit of the center frequency of any FM station in the United States is always an odd number. FM audio for television channel 6 is broadcast at a carrier frequency of 87.75 MHz, and many radios can tune down this low; a few low-power television stations licensed for channel 6 are operated solely for their right to use this frequency and broadcast only nominal video programming. For the same reason, assignment restrictions between TV stations on channel 6 and nearby FM stations are stringent: there are only two stations in the United States (KSFH and translator K200AA) licensed to operate on 87.9 MHz.

 * FM stations in a market are generally spaced four channels (800 kHz) apart. This spacing was developed in response to problems perceived on the original FM band, mostly due to deficiencies in receiver technology of the time. With modern equipment, this is widely understood to be unnecessary, and in many countries shorter spacings are used. Other spacing restrictions relate to mixing products with nearby television, air-traffic control, and two-way radio systems as well as other FM broadcast stations. The most significant such taboo restricts the allocation of stations 10.6 and 10.8 MHz apart, to protect against mixing products which will interfere with an FM receiver's standard 10.7 MHz intermediate frequency stage.

 * Commercial broadcasting is licensed only on channels 221 through 300, with 200 through 220 being reserved for noncommercial educational broadcasting. In some markets close to the Canadian or Mexican border, such as Detroit, Michigan and San Diego, California, commercial stations operating from those countries target U.S. audiences on "reserved band" channels, as neither Canada nor Mexico has such a reservation.

Mazer = microwave

(UHF) Ultra High Frequency: 300-3000 MHz/100-10 cm
UHF and VHF are the most common frequency bands for television.

UHF frequencies have higher attenuation from atmospheric moisture and benefit less from 'bounce', or the reflection of signals off the ionosphere back to earth, when compared to VHF frequencies. The frequencies of 300-3000 MHz are always at least an order of magnitude above the MUF (Maximum Usable Frequency). The MUF for most of the earth is generally between 25-35 MHz. Higher frequencies also benefit less from ground mode transmission. However, the short wavelengths of UHF frequencies allow compact receiving antennas with narrow elements; many people consider them less ugly than VHF-receiving models

In the United States, UHF stations (broadcast channels above 13) originally gained a reputation for being more locally owned, less polished, less professional, less popular, and for having a weaker signal than their VHF counterparts (channels 2-13). The movie UHF, starring Weird Al Yankovic, parodies this phenomenon. Recently, with the emergence of eight major broadcast television networks, that notion has changed as bigger and bigger media companies seek a bigger slice of the television pie. Many Fox, UPN, WB, and Pax network affiliates broadcast in the UHF band.

As cable television, digital television, and DSS have penetrated the television market, the distinction between VHF and UHF stations has dissipated.

In Australia, UHF was first anticipated in the mid 1970s with channels 28 to 69. The first UHF TV broadcasts in Australia were operated by Special Broadcasting Service (SBS) on channel 28 in Sydney and Melbourne starting in 1980, and translator stations for the Australian Broadcasting Corporation (ABC). The UHF band is now used extensively as ABC, SBS, commercial and community (public access) television services have expanded particularly through regional areas.

Ultra High Frequency A band reserved for television.

(SHF) Super High Frequency: 3-30 GHz/10-1 cm
Microwave

Note: above 300 GHz, the absorption of electromagnetic radiation by Earth's atmosphere is so great that the atmosphere is effectively opaque to higher frequencies of electromagnetic radiation, until the atmosphere becomes transparent again in the so-called infrared and optical window frequency ranges.

Uses

A microwave oven uses a magnetron microwave generator to produce microwaves at a frequency of approximately 2.4 GHz for the purpose of cooking food. Microwaves cook food by causing molecules of water and other compounds to vibrate. The vibration creates heat which warms the food. Since organic matter is made up primarily of water, food is easily cooked by this method.

A maser is a device similar to a laser, except that it works at microwave frequencies. Microwaves are also used in satellite transmissions because this frequency passes easily through the Earth's atmosphere with less interference than higher wavelengths.

Radar also uses microwave radiation to detect the range, speed, and other characteristics of remote objects.

Wireless LAN communication protocols such as IEEE 802.11 and bluetooth also use microwaves in the 2.4 GHz ISM band, although some variants use a 5 GHz band for communication.

Cable TV and Internet access on coax cable as well as broadcast television use some of the lower microwave frequencies.

Microwaves can be used to transmit power over long distances, create a solar array to beam power to earth.

The microwave spectrum is defined as electromagnetic energy ranging from approximately 300 MHz to 1000 GHz in frequency. Most common applications are within the 1 to 40 GHz range.

Microwave Frequency Bands are defined in the table below:

L Band	1 to 2 GHz S Band	2 to 4 GHz C Band	4 to 8 GHz X Band	8 to 12 GHz Ku Band	12 to 18 GHz K Band	18 to 26 GHz Ka Band	26 to 40 GHz Q Band	30 to 50 GHz U Band	40 to 60 GHz V Band	46 to 56 GHz W Band	56 to 100 GHz

For some of the history in the development of electromagnetic theory applicable to modern microwave applications see the following figures:

* Michael Faraday. * James Clerk Maxwell. * Heinrich Hertz. * Nikola Tesla. * Guglielmo Marconi. * Samuel Morse. * Sir William Thomson, later Lord Kelvin. * Oliver Heaviside. * Lord Rayleigh. * Oliver Lodge.

Specific significant areas of research and work developing microwaves and their applications:

Specific work on microwaves Work carried out by	Area of work Barkhausen and Kurz	Positive grid oscillators Hull	Smooth bore magnetron Varian Brothers	Velocity modulated electron beam → klystron tube Randall and Boot	Cavity magnetron

See also: * Home appliances. * Microwave auditory effect. * Radio. * Optics.

The Cosmic Microwave Background Radiation is a form of electromagnetic radiation that fills the whole of the universe. It has the characteristics of black-body radiation at a temperature of 2.726 kelvins. It has a frequency in the microwave range.

CMR and the Big Bang

This radiation is regarded as the best available evidence of the Big Bang (BB) theory and its discovery in the mid-1960s marked the end of general interest for alternatives such as the steady state theory. The CMR gives a snapshot of the Universe when, according to standard cosmology, the temperature dropped enough to allow electrons and protons to form hydrogen atoms, thus making the universe transparent to radiation. When it originated some 300,000 years after the Big Bang—this point in time is generally known as the "last scattering surface"—the temperature of the Universe was about 6000 K. Since then it has dropped because of the expansion of the Universe, which cools radiation inversely proportional to the fourth power of the Universe's scale length.

Features

One of the microwave background's most salient features is a high degree of isotropy. There are some anisotropies, the most pronounced of which is the dipole anisotropy at a level of about 10-4 at a scale of 180 degrees of arc. It is due to the motion of the observer against the CBR, which is some 700 km/s for the Earth.

Variations due to external physics also exist; the Sunyaev-Zel'dovich Effect is one of the major factors here, in which an cloud of high energy electrons scatters the radiation transferring some energy to the CMB photons.

Even more interesting are anisotropies at a level of roughly 1/100000 and on a scale of a few arc minutes. Those very small variations correspond to the density fluctuations at the last scattering surface and give valuable information about the seeds for the large scale structures we observe now. These density fluctations arise because different parts of the universe are not in contact with each other.

In addition, the Sachs-Wolfe effect causes photons from the Cosmic microwave background to be gravitationally redshifted. These small-scale variations give observational constraints on the properties of universe, and are therefore one important test for cosmological models.

Detection, Prediction and Discovery

The CBR was predicted by George Gamow, Ralph Alpher, and Robert Hermann in the 1940s and was accidentally discovered in 1964 by Penzias and Wilson, who received a Nobel Prize for this discovery. The CBR had, however, been detected and its temperature deduced in 1941, seven years before Gamow's prediction. Based on the study of narrow absorption line features in the spectra of stars, the astronomer Andrew McKellar wrote: "It can be calculated that the 'rotational' temperature of interstellar space is 2 K."

Because water absorbs microwave radiation, a fact that is used to build microwave ovens, it is rather difficult to observe the CMB with ground-based instruments. CMB research therefore makes increasing use of air and space-borne experiments.

Experiments

Of these experiments, the Cosmic Background Explorer (COBE) satellite that was flown in 1989-1996 is probably the most famous and which made the first detection of the large scale anisotropies (other than the dipole). In June 2001, NASA launched a second CBR space mission, WMAP, to make detailed measurements of the anisotropies over the full sky. Results from this mission provide a detailed measurement of the angular power spectrum down to degree scales, giving detailed constraints on various cosmological parameters. The results are broadly consistent with those expected from cosmic inflation as well as various other competing theories, and are available in detail at NASA's data center for Cosmic Microwave Background (CMB) [ed. see links below],

A third space mission, Planck, is to be launched in 2007. Unlike the previous two space missions, Planck is a collaboration between NASA and ESA (the European Space Agency).

CBR and Non-Standard Cosmologies

During the mid-1990's, the lack of detection of anisotropies in the CBR led to some interest in nonstandard cosmologies (such as plasma cosmology) mostly as a backup in case detectors failed to find anisotropy in the CBR. The discovery of these anisotropies combined with a large amount of new data coming in has greatly reduced interest in these alternative theories.

Some supporters of non-standard cosmology argue that the primodorial background radiation is uniform (which is inconsistent with the big bang) and that the variations in the CBR are due to the Sunyaev-Zel'dovich effect mentioned above (among other effects).

(IR) Infared 1 mm-700 nm
Note: above 100 GHz, the absorption of electromagnetic radiation by Earth's atmosphere is so great that the atmosphere is effectively opaque to higher frequencies of electromagnetic radiation, until the atmosphere becomes transparent again in the so-called infrared and optical window frequency ranges.

Infra-red means below red, where red is the color with the longest wavelength.

(FIR) far-IR (30-1000 µm)

(MIR/IIR) mid-IR (5-30 µm) - Infrared radiation is often linked to heat, since objects at room temperature or above will emit radiation mostly concentrated in the mid-infrared band (see black body).

(NIR) near-IR (0.7-5 µm)

However, these terms are not precise, and are used differently in various studies.

Uses Infrared is used in night-vision equipment, when there is insufficient visible light to see an object. The radiation is detected and turned into an image on a screen, hotter objects showing up brighter, enabling the police and military to chase targets. "Night vision"

Smoke is more transparent to infrared than to visible light, so fire fighters use infrared imaging equipment when working in smoke-filled areas. Fire fighters also use this equipment in wood-frame buildings after a fire has been extinguished to look for hot spots behind the walls, where a fire can break out again.

A more common use of IR is in television remote controls. In this case it is used in preference to radio waves because it does not interfere with the television signal. IR data transmission is also employed in short-range communication among computer peripherals and personal digital assistants. These devices usually conform to standards published by IrDA, the Infrared Data Association. Remote controls and IrDA devices use infrared light-emitting diodes (LEDs) to emit infrared radiation which is focused by a plastic lens into a narrow beam. The beam is modulated, i.e. switched on and off, to encode the data. The receiver uses a silicon photodiode to convert the infrared radiation to an electric current. It responds only to the rapidly pulsing signal created by the transmitter, and filters out slowly changing infrared radiation from sunlight, people and other warm objects.

The light used in fiber optic communication is typically infrared.

heat based

not really. EM waves are constantly being emitted by objects, black-body radiation, but the frequency depends on temperature. for room temperature objects and humans, it is mostly below light in the infrared, but for things like fires and red hot iron, it is in the light spectrum more, and for colder and hotter objects it is at different frequencies.

how about this, anything that has at least as much energy as infared will warm things up. Anything that has less will not warm atoms up.

Global Warming Carbon Dioxide absorbs certain wavlengths of infrared light. This is thought to cause global warming.

Visible
1 PetaHz 1015 Hz

Visible light exists on the tip end of infared and just below it is UV. Basically you can almost get a sunburn from visible light.

The optical spectrum (visible light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. The optical spectrum is a composite, or mixture, of the various colors.

There are no exact bounds to the optical spectrum ; a light-adapted eye typically has a maximum sensitivity of ~555 nm (in the green). Commonly the response of the eye is considered to cover 380 nm to 780 nm although a range of 400 nm to 700 nm range is more common. The eye may, however, have some visual response at even wider wavelength ranges.

Wavelengths in the range visible to the eye occupy most of the "optical window", a range of wavelengths that are easily transmitted through the Earth's atmosphere.

Note: Ultraviolet and Infrared are often considered to be "light" but are generally not visible to the human eye.

Visible Light

Visible light is electromagnetic radiation that is made of colors of light that the eye can see. This light has wavelengths that are generally expressed in nanometers.

See Rydberg formula.

Vision Rods and cones

People see red, yellow, green, blue and purple

People don't notice the difference because red and purple both have a low intensity.

purple is cut off because the atmosphere absorbs it.

light bulbs

(UV) UltraViolet
Ultra-Violet means beyond violet, where violet is the color with the shortest wavelength.

It is colloquially called black light, as it is invisible to the human eye.

The sun emits ultraviolet light in the UV-A, UV-B, and UV-C bands

Ordinary glass is transparent to UV-A but is opaque to shorter wavelengths. This is why people don't get sunburns in cars. During the first nuclear blast, Feynman was the only person who saw it because he looked through a window. Quartz glass, depending on quality, can be transparent even to vacuum UV wavelengths.

Table of contents [showhide] 1 Health effects 2 Astronomy 3 Uses 3.1 Fluorescent lamps 3.2 Disinfecting drinking water 3.3 Analyzing minerals 3.4 Sterilization 3.5 Resolution 3.6 Spectroscopy 3.7 Photolithography 3.8 Other 4 References

Health effects

In general, UV-A is the least harmful, but can contribute to the aging of skin, DNA damage and possibly skin cancer. It penetrates deeply and does not cause sun burn. Because it does not cause reddenning of the skin (erythema) it can not be measured in the SPF testing. There is no good clinical measurement of the blocking of UVA radiation, but it is important that your sunscreen block both UVA and UVB.

High intensities of UV-B light are hazardous to the eyes, and exposure can cause welder's flash (photokeratitis or arc eye).

UVA, UV-B and UV-C all can damage collagen fibers and thereby accelerate aging of the skin.

Tungsten-Halogen lamps have bulbs made of quartz, not of ordinary glass. Tungsten-Halogen lamps that are not filtered by an additional layer of ordinary glass are a common, useful, and possibly dangerous, source of UV-B light.

UV-A light is known as "dark-light" and, because of its longer wavelength, can penetrate most windows. It also penetrates deeper into the skin than UV-B light and is thought to be a prime cause of wrinkles.

UV-B light in particular has been linked to skin cancers such as melanoma. The radiation ionizes DNA molecules in skin cells, causing covalent bonds to form between adjacent thymine bases, producing thymidine dimers. Thymidine dimers do not base pair normally, which can cause distortion of the DNA helix, stalled replication, gaps, and misincorporation. These can lead to mutations, which can result in cancerous growths. The mutagenicity of UV radiation can be easily observed in bacteria cultures.

This cancer connection is the reason for concern about ozone depletion and the ozone hole.

UV-C rays are the strongest, most dangerous type of ultraviolet light. Little attention has been given to UV-C rays in the past since they are normally filtered out by the ozone layer and do not reach the Earth. Thinning of the ozone layer and holes in the ozone layer are causing increased concern about the potential for UVC light exposure, however.

As a defense against UV light, the body tans when exposed to moderate (depending on skin type) levels of radiation by releasing the brown pigment melanin. This helps to block UV penetration and prevent damage to the vulnerable skin tissues deeper down. Suntan lotion that partly blocks UV is widely available (often referred to as "sun block" or "sunscreen"). Most of these products contain an "SPF rating" that describes the amount of protection given. This protection applies only to UV-B light. In any case, most dermatologists recommend against prolonged sunbathing.

A positive effect of UV light is that it induces the production of vitamin D in the skin. Grant (2002) claims tens of thousands of premature deaths occur in the U.S. annually from cancer due to insufficient UV-B exposures (apparently via vitamin D deficiency).

Astronomy

In astronomy, very hot objects preferentially emit UV light (see Wien's law). However, the same ozone layer that protects us causes difficulties for astronomers observing from the earth, so most UV observations are made from space. (See UV astronomy, space observatory).

Uses UV light has many various uses:

Fluorescent lamps Fluorescent lamps produce UV light by the emission of low-pressure mercury gas. A phosphorescent coating on the inside of the tubes absorbs the UV and turns it into visible light.

The main mercury emission wavelength is in the UV-C range. Unshielded exposure of the skin or eyes to mercury arc lamps that do not have a conversion phosphor is quite dangerous.

The light from a mercury lamp is predominantly at discrete wavelengths. Other practical UV light sources with more continuous emission spectra include xenon arc lamps (commonly used as sunlight simulators), deuterium arc lamps, mercury-xenon arc lamps, metal-halide arc lamps, and tungsten-halogen incandescent lamps.

Disinfecting drinking water Ultraviolet light is increasingly being used to disinfect drinking water and in waste water treatment plants. Dr. James R. Bolton discovered that ultraviolet light could treat Cryptosporidium, previously unknown. The findings resulted in two US patents and the use of UV light as a viable method to treat drinking water.

Analyzing minerals Ultraviolet lamps are also used in analyzing minerals, gems, and in other detective work including authentication of various collectibles. Materials may look the same under visible light, but fluoresce to different degrees under ultraviolet light; or may fluoresce differently under short wave ultraviolet versus long wave ultra violet. UV fluorescent dyes are used in many applications (for example, biochemistry and forensics). The fluorescent protein Green Fluorescent Protein (GFP) is often used in genetics as a marker. Many substances, proteins for instance, have significant light absorption bands in the ultraviolet that are of use and interest in biochemistry and related fields. UV-capable spectrophotometers are common in such laboratories.

Sterilization Ultraviolet lamps are used to sterilize workspaces and tools used in biology laboratories and medical facilities. Since microorganisms can be shielded from ultraviolet light in small cracks and other shaded areas, however, these lamps are used only as a supplement to other sterilization techniques.

Resolution Ultraviolet light is used for very fine resolution photolithography, as required for manufacture of semiconductors.

Spectroscopy UV light is often used in UV-visible spectroscopy

Photolithography UV light is used extensively in the electronics industry in a procedure known as photolithography, where a chemical known as a photoresist is exposed to UV light which has passed through a mask. The light allows chemical reactions to take place in the photoresist, and after development (a step that either removes the exposed or unexposed photoresist), a geometric pattern which is determined by the mask remains on the sample. Further steps may then be taken to "etch" away parts of the sample with no photoresist remaining.

It is photolithography which is primarily used to create integrated circuit components and printed circuit boards.

Other The onset of vacuum UV, 200 nm, is defined by the fact that ordinary air is opaque below this wavelength. This opacity is due to the strong absorption of light of these wavelengths by oxygen in the air. Pure nitrogen (less than about 10 ppm oxygen) is transparent to wavelengths in the range of about 150-200 nm. This has wide practical significance now that semiconductor manufacturing processes are using wavelengths shorter than 200 nm. By working in oxygen-free gas, the equipment does not have to be built to withstand the pressure differences required to work in a vacuum. Some other scientific instruments, such as Circular Dichroism spectrometers, are also commonly nitrogen purged and operate in this spectral region.

It is advisable to use protective eyewear when working with ultraviolet light, especially short wave ultraviolet. Ordinary eyeglasses give some protection. Most plastic lenses give more protection than glass lenses. Some plastic lens materials, such as polycarbonate, block most UV. There are protective treatments available for eyeglass lenses that need it to give better protection. The most important reason that ordinary eyeglasses only give limited protection, however, is that light can reach the eye without going through the lens. Full coverage is important if the risk from exposure is high. Full coverage eye protection is usually recommended for high altitude mountaineering, for instance. Mountaineers are exposed to higher than ordinary levels of UV light, both because there is less atmospheric filtering and because of reflection from snow and ice.

Some insects, such as bees, can see into the near ultraviolet, and flowers often have markings visible to such pollinators.

UV catastrophe

at wavelengths just below visible is where people get sunburns.

sun burn rating UV-A UV-B UV-C

UV bulbs

X-Ray: 30 PetaHz - 60 ExaHz/10 nanometer - 5 picometer
(German: Röntgenstrahlen)

Soft X-ray: (10-0.1 nm)

Hard X-ray: (100-5 pm)Low energy gamma rays

X-rays are generated by electron collisions.

X-rays are primarily used for diagnostic medical imaging and crystallography.

Physicist Johann Hittorf observed tubes with energy rays extending from a negative electrode. These rays produced a fluorescence when they hit the glass walls of the tubes. In 1876 the effect was named "cathode rays" by Eugene Goldstein. Later, English physicist William Crookes investigated the effects of energy discharges on rare gases. He constructed what is called the Crookes tube. It is a glass vacuum cylinder, containing electrodes for discharges of a high voltage electric current. He found, when he placed unexposed photographic plates near the tube, that some of them were flawed by shadows, though he did not investigate this effect. In 1892, Heinrich Hertz began experimenting and demonstrated that cathode rays could penetrate very thin metal foil (such as aluminum). Philip Lenard, a student of Heinrich Hertz, further researched this effect. He developed a version of the cathode tube and studied the penetration of X-rays through various materials. Philip Lenard, though, did not realize that he was producing X-rays.

In April 1887, Nikola Tesla began to investigate X-rays using his own devices as well as Crookes tubes. Tesla did this by experimenting with high voltages and vacuum tubes. From Nikola Tesla's technical publications, it is indicated that he invented and developed a special single-electrode X-ray tube. Tesla's tubes differ from other X-ray tubes in that they have no target electrode. He stated these facts in his 1897 X-ray lecture before the New York Academy of Sciences. The modern term for this process is the bremsstrahlung process, in which a high-energy secondary X-ray emission is produced when charged particles (such as electrons) pass through matter. By 1892, Tesla performed several such experiments; however, he did not categorize the emissions as what was later called X-rays (generalizing the phenonomena as radiant energy). Tesla did not publicly declare his findings nor did he make them widely known. His subsequent X-ray experimentation by vacuum high field emissions led him to alert the scientific community to the biological hazards associated with X-ray exposure.

Hermann von Helmholtz formulated mathematical equations for X-rays. He postulated a dispersion theory before Roentgen made his discovery and announcement. It was formed on the basis of the electromagnetic theory of light (Wiedmann's Annalen, Vol. XLVIII); however, he did not work with actual X-rays.

On November 8, 1895, Wilhelm Röntgen, a German scientist, began observing and further documenting X-rays while experimenting with vacuum tubes. Röntgen, on December 28, 1895, wrote a preliminary report "On a new kind of ray: A preliminary communication". He submitted it to the Würzburg's Physical-Medical Society journal. This was the first formal and public recognition of the categorization of X-rays. Röntgen referred to the radiation as "X", to indicate that it was an unknown type of radiation. The name stuck, although (over Röntgen's great objections), many of his colleagues suggested calling them Röntgen rays. They are still referred to as Röntgen rays in some countries. Roentgen received the first Nobel Prize in Physics for his discovery.

In 1895, Thomas Edison investigated materials' ability to fluoresce when exposed to X-rays. He found that calcium tungstate was the most effective substance. Around March 1896, the fluoroscope he developed became the standard for medical X-ray examinations. Nevertheless, Edison dropped x-ray research around 1903 after the death of Clarence Madison Dally, one of his glassblowers. Dally had a habit of testing X-ray tubes on his hands, and acquired a cancer in them so tenacious that both arms were amputated in a futile attempt to save his life.[1]

In 1906, physicist Charles Barkla discovered that X-rays could be scattered by gases, and that each element had a characteristic X-ray. He won the 1917 Nobel prize for this discovery.

The use of X-rays for medical purposes was pioneered by Major John Hall-Edwards in Birmingham, England. In 1908, he had to have his left arm amputated owing to the spread of X-ray dermatitis.

Detectors

The detection of X-rays is based on various methods. Most commonly known is the photographic plate as we know them from hospitals. Initially, most common detection was based on the ionisation of gasses. One of the most simple examples is the Geiger counter. Since the 1990-ies, new detectors were developed based on semiconductors. In the semiconductor, the X-ray photon was converted to electron-hole pairs which were collected to detect the X-ray

See also

* X-ray crystallography * X-ray Astronomy * X-ray machine * Geiger counter

Used to take photographs.

Gamma: Above 60 exahertz/Below 5 picometers
Gamma rays (often denoted by the Greek letter gamma, γ) are an energetic form of electromagnetic radiation (see Electromagnetic spectrum) produced by radioactivity or other nuclear or subatomic processes such as electron-positron annihilation. Gamma rays are more penetrating than either alpha or beta radiation, but less ionizing. Gamma rays are distinguished from X rays by their origin. Gamma rays are produced by nuclear transitions while X-rays are produced by energy transitions due to accelerating electrons. Because it is possible for some electron transitions to be of higher energy than nuclear transition, there is an overlap between low energy gamma rays and high energy X-rays.

Nuclear processes Radioactive decay processes

* Alpha decay * Beta decay * Electron capture * Gamma radiation * Neutron emission * Positron emission * Proton emission * Spontaneous fission

Nucleosynthesis

* Neutron Capture o The R-process o The S-process * Proton capture: o The P-process

Shielding for γ rays requires large amounts of mass. Shields that reduce gamma ray intensity by 50% include 1 cm (0.4 inches) of lead, 6 cm (2.4 inches) of concrete or 9 cm (3.6 inches) of packed dirt.

Gamma rays from nuclear fallout would probably cause the largest number of casualties in the event of the use of nuclear weapons in a nuclear war. An effective fallout shelter reduces human exposure at least 1000 times.

Gamma rays are less ionising than either alpha or beta rays. However, reducing human danger requires thicker shielding. They produce damage similar to that caused by X-rays such as burns, cancer, and genetic mutations.

In terms of ionization, gamma radiation interacts with matter via three main processes: the photoelectric effect, Compton scattering, and pair production.

Photoelectric Effect: This describes the case in which a gamma photon interacts with and transfers all of its energy to an orbital electron, ejecting that electron from the atom. The kinetic energy of the resulting photoelectron is equal to the energy of the incident gamma photon minus the binding energy of the electron. The photoelectric effect is thought to be the dominant energy transfer mechanism for x-ray and gamma ray photons with energies below 50 keV (thousand electronvolts), but it is much less important at higher energies.

Compton Scattering: This is an interaction in which an incident gamma photon loses enough energy to an orbital electron to cause its ejection, with the remainder of the original photon's energy being emitted as a new, lower energy gamma photon with an emission direction different from that of the incident gamma photon. The probability of Compton scatter decreases with increasing photon energy. Compton scattering is thought to be the principal absorption mechanism for gamma rays in the intermediate energy range 100 keV to 10 MeV (million electronvolts), an energy spectrum which includes most gamma radiation present in a nuclear explosion. Compton scattering is relatively independent of the atomic number of the absorbing material.

Pair Production: By interaction in the vicinity of the coulomb force of the nucleus, the energy of the incident photon is spontaneously converted into the mass of an electron-positron pair. A positron is a positively charged electron. Energy in excess of the equivalent rest mass of the two particles (1.02 MeV) appears as the kinetic energy of the pair and the recoil nucleus. The electron of the pair, frequently referred to as the secondary electron, is densely ionizing. The positron has a very short lifetime. It combines within 10−8 second with a free electron. The entire mass of these two particles is then converted into two gamma photons of 0.51 MeV energy each.

Gamma rays are often produced alongside other forms of radiation such as alpha or beta. When a nucleus emits an α or β particle, the daughter nucleus is sometimes left in an excited state. It can then jump down to a lower level by emitting a gamma ray in much the same way that an atomic electron can jump to a lower level by emitting ultraviolet radiation.

Gamma rays, x-rays, visible light, and UV rays are all forms of electromagnetic radiation. The only difference is the frequency and hence the energy of the photons. Gamma rays are the most energetic. An example of gamma ray production follows.

First cobalt-60 decays to excited nickel-60 by beta decay:

Then the nickel-60 drops down to the ground state (see nuclear shell model) by emitting a gamma ray:

Uses:

The powerful nature of gamma-rays have made them useful in the sterilising of medical equipment by killing bacteria. They are also used to kill bacteria in foodstuffs to keep them fresher for longer.

In spite of their cancer-causing properties, gamma rays are also used to treat some types of cancer. In the procedure called gamma-knife surgery, multiple concentrated beams of gamma rays are directed on the growth in order to kill the cancerous cells. The beams are aimed from different angles to focus the radiation on the growth while minimising damage to the surrounding tissues.

See also: physics, gamma-ray astronomy, gamma ray bursters, radiation therapy.

anything above

Highly energetic photons associated with black holes and galaxies also emitted by nuclear blasts

causes cellular death

Black holes are known to emit gamma ray bursts through their poles.

A large enough gamma ray burst could sterilize all life on earth.

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

title: Electronics/Frequency Spectrum


text:
User talk:Harry~enwikibooks

Yes, I am an administrator. Perl 01:01, 2 Apr 2004 (UTC)

Glad to know you finally got it. Take care. Harry 01:13, 2 Apr 2004 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Harry. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Harry~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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Renamed
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title: User talk:Harry~enwikibooks


text:
User talk:Wanderer~enwikibooks

Welcome! Nice to have you working with us at wikibooks. Im a system operator here so if you need anything deleted or any vandal blocked, just ask me. Perl 01:23, 2 Apr 2004 (UTC)

Some people will say that a piece of literature is never finished. This would especially be true for a wiki since people can always improve upon a module, I guess. If you want a hard copy, just click the printable version button. To download the whole wikibooks database, see Database download. By the way, you accidently posted your comment on my user page instead of my talk page. Don't worry, I've made the same mistake before. (I accidently posted a comment on Harry's user page instead of his talk page just yesterday, in fact.) Happy editing! Perl 12:35, 2 Apr 2004 (UTC)

????

I see you've started working with the practical inductor circuits and the like! Nice going so far, keep up the good work yes!

Welcome Wanderer, your work on the Electronics book looks great! --Karl Wick

As I said on the electronics talk page:

Sound, Brief History of the Universe, The Solar System, Evolution of the Earth's Atmosphere, Earthquakes and natural disasters, and Global Warming?

As sections in the chapter Analog Circuits?

Stick to the topic, please!

Saying "the earth behaves like a conductor", "the ionosphere behaves like a conductor and can reflect radio waves" is plenty. There is no need at allllll to go into the details like this. That should be in a radio book anyway, not a basic electronics book. This is supposed to be a book about electronic circuits for beginners, not about life, the universe, and everything.

I think you are doing most of this. What do you think?

- Omegatron 21:14, 20 Apr 2004 (UTC)

As I replied in the talk section.

Ok, I will admit that my writing does suffer a bit from feature creep. I like to be through, and there are certain subjects that are not taught in school. I have moved the offending sections to the Expanded Edition. If you see anything else that seems excessive I will move it to the Expanded Edition.

Wanderer

I can't agree more with Omegatron. I think me being a student and him being an engineer, see things a bit differently as a 'student of everything'. The thing I really wanted to do was cover a lot of electronics design and ultimately CONDENSE things. I wish to have a book on electronics that can go from 0-60 in about an hour or two. Explain series, parallel circuits, voltage dividers, op-amps and other analog electronics. What I personally don't care about is the science of these things. For that people are better off visiting sites like 4hv.org or something.

I love to read about all the details behind how things work, too. BUT... This is an electronics book, and should focus on electronics. Wikipedia is for providing details of everything about everything. If wikipedia and wikibooks both cover the same material, then why bother? Why is a book on electronics different from Wikipedia articles about electronics? Because it is focused. It should teach enough theory and physics that you understand the basics of what you are manipulating (charge and electron flow), because these are really necessary knowledge to understand what you are building. And it should move from easier topics to more complicated topics in an orderly way. But otherwise we should leave a lot of that stuff out and simply allow people to look it up on their own (band gaps, quantum mechanics, tunneling diodes, heavy electromagnetics, history of the universe, etc.) - Omegatron 14:44, 30 Apr 2004 (UTC)

logoff
Did you check the button that says "keep me logged in"? If you did, it should keep you logged in until the wikipedia cookie in your cookie folder gets deleted. Perl 20:54, 28 Apr 2004 (UTC)

Thank you for your comments! I wanted to make it a section in the Electronics book, but I see that the power section deals with DSP. The document I am working on deals mainly with applications in the home, so it can probably become an applications section in one of the latter chapters of the Electronics book when it is done. Norman Weiner

Copyright images
Your resistor square at http://en.wikibooks.org/wiki/Image:Electronics_R_cube.PNG needs a copyright statement to prevent it being deleted. --kwhitefoot 10:47, 7 January 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Wanderer. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Wanderer~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:51, 17 March 2015 (UTC)

Renamed
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text:
Electronics/Superconductors

In a superconductor, resistance drops to zero and current flows as a short without attenuating.

Until recently most superconductors operated at very low temperatures close to absolute zero. Recently there have been higher temperature superconductors.

Superconductors all for floating magnets.

Superconductors have a great promise for reducing electricity bills.

title: Electronics/Superconductors


text:
Electronics/Motors

Most electrical motors are induction based.

They work either through the flow of electricity or turing a magnet.

Waterfalls and windmills work by turning a magnet. Waterfalls tend to have even power, but windmills have odd erratic power based on the wind.

The driving force that turns the rotor containing the magnets is called the "Prime Mover"

Generators work by supplying current that drives a turbine.

Induction based motors work on AC and spinning magnets.

One of the problems of induction based motors is most of their power is reactive (caught in a magnetic field). Capacitors are required to make the power real. It is common in induction based generators to have a bank of variable capacitors to try to keep the power as real as possible.

title: Electronics/Motors


text:
Cookbook:Hummus

Hummus, also hoummus, hommus, hommous, is a blend of sesame seed paste and either chickpea paste or fava bean paste. This cookbook has three different recipes for Hummus:

 * Hummus of Palestine
 * Greek-style hummus

Książka kucharska/Hummus Hummus
 * Leaven free Hummus

title: Cookbook:Hummus


text:
Cookbook:Sesame Seed

Sesame seeds are small oily seeds, off-white or black colored, and a few mm across at most. They are a common food allergen. They taste vaguely like peanuts and cashews.

Sesame seeds can be added to salads for an extra 'nutty' texture. Sesame seeds are commonly sprinkled over rice in Japanese cooking. Sesame seeds can be added to almost any bread recipe by sprinkling or rolling the dough in the seeds before baking it, much as one might do for poppy seeds.

Ground sesame seeds are called tahini.

Sesame seeds may be "toasted" (fried actually) to bring out more flavor.

The flavor of sesame seeds can be had via the use of sesame oil, commonly available as a dark liquid.

Recipes featuring sesame seeds include

 * Tahini
 * Broccoli Stir Fry
 * Egg Roll
 * Wonton Soup
 * Pandora's Feast
 * Tahini Goddess Dressing

title: Cookbook:Sesame Seed


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Electronics/DC Voltage and Current

Ohm's Law
Ohm's law describes the relationship between voltage, current, and resistance.Voltage and current are proportional to the potential difference and inversely proportional to the resistance of the circuit

V = I \cdot R $$

 * Voltage (V) is measured in volts (V); Current (I) in amperes (A); and resistance (R) in ohms (Ω).

In this example, the current going through any point in the circuit, I, will be equal to the voltage V divided by the resistance R.

In this example, the voltage across the resistor, V, will be equal to the supplied current, I, times the resistance R.

If two of the values (V, I, or R) are known, the other can be calculated using this formula.

Any more complicated circuit has an equivalent resistance that will allow us to calculate the current draw from the voltage source. Equivalent resistance is worked out using the fact that all resistors are either in parallel or series. Similarly, if the circuit only has a current source, the equivalent resistance can be used to calculate the voltage dropped across the current source.

Kirchoff's Voltage Law
Kirchoff's Voltage Law (KVL):
 * The sum of voltage drops around any loop in the circuit that starts and ends at the same place must be zero.

Voltage as a Physical Quantity

 * 1) Voltage is the potential difference between two charged objects.
 * 2) Potentials can be added or subtracted  in series to make larger or smaller potentials as is commonly done in batteries.
 * 3) Positive charge flow from areas of high potential to lower potential.
 * 4) All the components of a circuit have resistance that acts as a potential drop.

Kirchoff's Current Law
Kirchoff's Current Law (KCL):
 * The sum of all current entering a node must equal the sum of all currents leaving the node.

KCL Example

-I1 + I2 + I3 = 0 ↔ I1 = I2 + I3

I1 - I2 - I3 - I4 = 0 ↔ I2 + I3 + I4 = I1

 * $$ I_1 = I_2 + I_3 + \cdots + I_n \,\! $$

Here is more about Kirchhoff's laws, which can be integrated here

Voltage Dividers
If two circuit elements are in series, there is a voltage drop across each element, but the current through both must be the same. The voltage at any point in the chain divides according to the resistances. A simple circuit with two (or more) resistors in series with a source is called a voltage divider.

 * [[Image:PotentialDivider.png|120px]]

Figure A: Voltage Divider circuit.

Consider the circuit in Figure A. According to KVL the voltage $$V_{in}$$ is dropped across resistors $$R_1$$ and $$R_2$$. If a current i flows through the two series resistors then by Ohm's Law.

 * $$i = \frac{V_{in}}{R_1+R_2}$$.

So
 * $$ V_{out}=iR_2 \,\!$$

Therefore
 * $$ V_{out}=\frac{V_{in}R_2}{R_1+R_2}$$

Similary if $$V_{R1}$$ is the voltage across $$R_1$$ then
 * $$ V_{R1}=\frac{V_{in}R_1}{R_1+R_2}$$

In general for n series resistors the voltage dropped across one of them say $$R_i$$ is
 * $$V_{Ri}=\frac{V_{in}R_i}{R_{eq}} $$

Where
 * $$R_{eq}=R_1+\cdots+R_n$$

Voltage Dividers as References
Clearly voltage dividers can be used as references. If you have a 9 volt battery and you want 4.5 volts, then connect two equal valued resistors in series and take the reference across the second and ground. There are clearly other concerns though, the first concern is current draw and the effect of the source impedance. Clearly connecting two 100 ohm resistors is a bad idea if the source impedance is, say, 50 ohms. Then the current draw would be 0.036 mA which is quite large if the battery is rated, say, 200 milliampere hours. The loading is more annoying with that source impedance too, the reference voltage with that source impedance is $$\frac {9(100)}{250}=3.6\mbox{ V}$$. So clearly, increasing the order of the resistor to at least 1 k$$\Omega$$ is the way to go to reduce the current draw and the effect of loading. The other problem with these voltage divider references is that the reference cannot be loaded if we put a 100 Ω resistor in parallel with a 10 kΩ resistor. When the voltage divider is made of two 10 kΩ resistors, then the resistance of the reference resistor becomes somewhere near 100 Ω. This clearly means a terrible reference. If a 10 MΩ resistor is used for the reference resistor will still be some where around 10 kΩ but still probably less. The effect of tolerances is also a problem; if the resistors are rated 5% then the resistance of 10 kΩ resistors can vary by ±500 Ω. This means more inaccuracy with this sort of reference.

Current Dividers
If two elements are in parallel, the voltage across them must be the same, but the current divides according to the resistances. A simple circuit with two (or more) resistors in parallel with a source is called a current divider.

Figure B: Parallel Resistors.

If a voltage V appears across the resistors in Figure B with only $$R_1$$ and $$R_2$$ for the moment then the current flowing in the circuit, before the division, i is according to Ohms Law.
 * $$i=\frac{V}{R_{eq}}$$

Using the equivalent resistance for a parallel combination of resistors is
 * $$i=\frac{V(R_1+R_2)}{R_1R_2}$$          (1)

The current through $$R_1$$ according to Ohms Law is
 * $$i_1=\frac{V}{R_1}$$           (2)

Dividing equation (2) by (1)
 * $$i_1=\frac{iR_2}{R_2+R_1}$$

Similarly
 * $$i_2=\frac{iR_1}{R_2+R_1}$$

In general with n Resistors the current $$i_x$$ is
 * $$i_x=\frac{iR_1R_2\cdots R_n}{ (R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}) R_x}$$

Or possibly more simply
 * $$\frac{i_x}{i}=\frac{R_{eq}}{R_x}$$

Where
 * $$R_{eq}=\frac{R_1\cdots R_n}{R_2\cdots R_n+\cdots+ R_1\cdots R_{n-1}}$$

title: Electronics/DC Voltage and Current


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Electronics/AC Voltage and Current

Resistor
In a resistor, the current is in phase with the voltage always. This means that the peaks and valleys of the two waveforms occur at the same times. Resistors can simply be defined as devices that perform the sole function of inhibiting the flow of current through an electrical circuit. Resistors are commercially available having various standard values, nevertheless variable resistors are also made called potentiometers, or pots for short. In theory electricity is a method used to harness myriad numbers including symbols to give the notion on how circuits function on a schematic drawing

Capacitor
The capacitor is different from the resistor in several ways. First, it consumes no real power. It does however, supply reactive power to the circuit. In a capacitor, as voltage is increasing the capacitor is charging. Thus a large initial current. As the voltage peaks the capacitor is saturated and the current falls to zero. Following the peak the circuit reverses and the charge leaves the capacitor. The next half of the cycle the circuit runs mirroring the first half.

The relationship between voltage and current in a capacitor is: $$i(t)=C{d(v(t)) \over dt}$$. This is valid not only in AC but for any function v(t). As a direct consequence we can state that in the real world, the voltage across a capacitor is always a continuous function of the time.

If we apply the above formula to a AC voltage (i.e. $$v(t)=V \cdot sin(\omega t + \Phi)$$), we get for the current a 90° phase shift: $$i(t)=V \cdot \omega \cdot cos(\omega t + \Phi)$$.

In an AC circuit, current leads voltage by a quarter phase or 90 degrees. Note that while in DC circuits after the initial charge or discharge no current can flow, in AC circuits a current flows all the time into and out of the capacitor, depending on the impedance in the circuit. This is similar to the resistance in DC circuits, except that the impedance has 2 parts; the resistance included in the circuit, and also the reactance of the capacitor, which depends not only on the size of the capacitor, but also on the frequency of the applied voltage. In a circuit that has DC applied plus a signal, a capacitor can be used to block the DC, while letting the signal continue.

Inductor
In inductors, current is the negative derivative of voltage, meaning that however the voltage changes the current tries to oppose that change. When the voltage is not changing there is no current and no magnetic field.

In an AC Circuit, voltage leads current by a quarter phase or 90 degrees.

Voltage Defined as the derivative of the flux linkage:

$$V(t)={d(Ni(t)) \over dt}$$

Resonance
A circuit containing resistors, capacitors, and inductors is said to be in resonance when the reactance of the inductor cancels that of the capacitor to leave the resulting total resistance of the circuit to be equal to the value of the component resistor. The resonance state is achieved by fine tuning the frequency of the circuit to a value where the resulting impedance of the capacitor cancels that of the inductor, resulting in a circuit that appears entirely resistive.

title: Electronics/AC Voltage and Current


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User talk:68.163.152.234

Please don't include material that could get us in trouble. Thanks, Silsor 06:16, 2 Apr 2004 (UTC)

title: User talk:68.163.152.234


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User:Silsor~enwikibooks

See my user page on Meta.

title: User:Silsor~enwikibooks


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Talk:Calculus/Power series

Help!
This page badly needs attention. I've tidied up some of it, but it still lacks content. Carl Turner 21:28, 26 May 2007 (UTC)

Problems
This page falsely implied all series have finite radii of convergence. Corrected and expanded. Also, series aren't always expanded around x=0, notably ln x. More work is needed, maybe including quote of full Taylor-Mclaurin expansion. - Robert 2/4/4

convergence
after find the convergence radius need to test the extremities.

eg: if the radius is 5 and the center is -3 the extremities is -8 and +2, so you need to test if the series converge with -8 and +2.

title: Talk:Calculus/Power series


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Engineering Mechanics

Engineering mechanics is the application of mechanics to solve problems involving common engineering elements.

The goal of this Engineering Mechanics course is to expose students to problems in mechanics as applied to plausibly real-world scenarios. Problems of particular types are explored in detail in the hopes that students will gain an inductive understanding of the underlying principles at work; students should then be able to recognize problems of this sort in real-world situations and respond accordingly.

Further, this text aims to support the learning of Engineering Mechanics with theoretical material, general key techniques, and a sufficient number of solved sample problems to satisfy the first objective as outlined above.

Distinction between branches of physics

As you see in the diagram mechanics is the first and most fundamental branch of physics, supporting Thermodynamics and Electricity, and including Statics, Dynamics (= Kinematics + kinetics); all of which are highly applicable in engineering. but the most important part of them is statics (study of body at rest) which is not only a base for all others, but also have the highest engineering application. Physics also involve optics, waves, quantum, and relativity theory, which have no fundamental engineering application yet.

Distinction between classic and modern physics
Classical physics generally includes the old theories in physics that are often used to describe the states of physical phenomena in the macroscopic scale e.g. laws governing the laws of motion of masses usually larger than atoms and molecules. Modern physics on the other hand deals with the more recent theories which govern physical phenomena. Two broad branches of modern physics include quantum physics and relativity. These modern theories surfaced as a result of probes into what happened to matter at much more microscopic and abstract states. Hence, classical theories of physics are often classified as theories dating before the 1900s, while modern physics include theories propounded in the 20th and 21st centuries.

Distinction between Physics and Engineering physics

 * Difference of pure and applied science

Prerequisites
This book assumes familiarity with high school physics and calculus, although the mathematics used is fairly elementary.

Statics
We describe the motion of bodies using Newton's second law of motion

\text{Force = Mass * Acceleration} \mathbf{f} = m~\mathbf{a} \, $$

Statics deals with the situation where the acceleration ($$\mathbf{a}\,$$) is zero - which happens when a body is at rest, or moving with constant velocity. That means that the total force on a body at rest or with constant velocity must be zero. In other words, the sum of the forces on the body must equal zero.

\text{Sum of Forces = 0} \qquad \text{or} \qquad \sum \mathbf{f} = \mathbf{0} $$

Free body diagram: a tool for understanding and solving
Engineers typically draw what is called a "free body diagram" to show all forces on a body at rest. These forces are then broken down into vectors consistent with a useful coordinate system and summed in sets (components parallel to each basis vector) which are then set to zero to meet the static constraint of no acceleration being present.

This typically results in sets of equations which can be solved using simple linear algebra techniques or even simple algebra and substitution.

Truss
Forces act along the members, and there are no shear forces or moments. A truss is therefore defined as a system composed entirely of two-force members, which only carry axial loads. The ends of a truss are pinned, so that they don't carry moments. The only reactions at the ends of a truss member are forces. External forces on trusses act only on the end points. Truss problems are solved by the method of sections, where an imaginary cut is made through the member(s) of interest, and global equilibrium of forces and moments are used to determine the forces in the members, or by the method of joints, in which a single joint is isolated and analyzed and the resulting forces (not necessarily with a numerical value) are transferred to adjacent joints, where the process is repeated. The resulting set of equations can then be solved by linear algebra, or substitution.

Chains and Cables
Chains and cables are attached at end points and have a continuous load on them due to their own weight (body forces) or external loads. Let a cable of length $$L\,$$ have a load of $$w\,$$ acting per unit distance between the supports. If the tension in the cable at any point is $$T(x)\,$$, then we have, for an infinitesimal length of the cable making an angle $$\theta(x)\,$$ with the horizontal,

\begin{align} \cfrac{d}{dx}[T~\cos\theta] = 0 \\ \cfrac{d}{dy}[T~\sin\theta] = w  \end{align} $$

Thus, we have,

\begin{align} T~\cos\theta = \text{constant} = K \\ T~\sin\theta = \int w~dx + C_1 \end{align} $$

or

\tan\theta = \cfrac{1}{K}~\left[\int w~dx + C_1 \right] $$

Now

\tan\theta = \cfrac{dy}{dx} ~. $$

So we have a differential equation for $$y\,$$ in terms of $$x\,$$:

\cfrac{dy}{dx} = \cfrac{1}{K}~\left[\int w~dx + C_1 \right] $$

Solving for $$y\,$$,

y = \cfrac{1}{K}~\left[\int \left(\int w~dx\right)~dx + C_1~x + C_2 \right] $$

If $$w\,$$ is a constant, then we have,

y = \cfrac{1}{K}~\left[\cfrac{w~x^2}{2} + C_1~x + C_2 \right] $$

which is the equation of a parabola.

For a rope where the loading is given in terms of the length of the rope (much more common), i.e., $$ T \equiv T(s) $$ and $$ \theta \equiv \theta(s) $$, we have,

\begin{align} \cfrac{d}{ds}[T~\cos\theta] & = 0 \\ \cfrac{d}{ds}[T~\sin\theta] & = w(s) \end{align} $$

where

ds = \sqrt{dx^2 + dy^2} $$

Dynamics
Simply said, dynamics means that an object is in motion with some speed when a force is applied on it. Eg: a car is moving on the road with some velocity.

While statics deal with the part of mechanics where all objects are stationary, dynamics deals with objects or structures with a non-zero acceleration.

Dynamics may be broken down into kinematics and kinetics. Kinematics deal with displacement, velocities and accelerations without concern for the forces involved. Kinetics deal with the forces and moments involved in making the body move along with the measurement of various parameters describing the motion.

Dynamics
Dynamics is a branch of mechanics that deals with the study of bodies in motion.

Branches of dynamics
Dynamics is divided into two branches called kinematics and kinetics.

Kinematics is a branch of mechanics that describes the movement of a particle or body that does not cause force.

Kinetics is a branch of mechanics that combines the force acting on the body with its mass and acceleration.

Symbols and Notations

 * s = distance
 * x = horizontal displacement
 * y = vertical displacement
 * v = velocity
 * vf = final velocity
 * vi = initial velocity
 * a = acceleration
 * g = acceleration due to gravity
 * t = time

title: Engineering Mechanics