In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring by sexual reproduction. Other ways of defining species include their karyotype, DNA sequence, behaviour or ecological niche. In addition, paleontologists use the concept of the chronospecies since fossil reproduction cannot be examined. While these definitions may seem adequate, when looked at more they represent problematic species concepts. For example, the boundaries between related species become unclear with hybridisation, in a species complex of hundreds of similar microspecies, in a ring species. Among organisms that reproduce only asexually, the concept of a reproductive species breaks down, each clone is a microspecies. All species are given a two-part name, a "binomial"; the first part of a binomial is the genus.
The second part is called the specific epithet. For example, Boa constrictor is one of four species of the genus Boa. None of these is satisfactory definitions, but scientists and conservationists need a species definition which allows them to work, regardless of the theoretical difficulties. If species were fixed and distinct from one another, there would be no problem, but evolutionary processes cause species to change continually, to grade into one another. Species were seen from the time of Aristotle until the 18th century as fixed kinds that could be arranged in a hierarchy, the great chain of being. In the 19th century, biologists grasped. Charles Darwin's 1859 book The Origin of Species explained how species could arise by natural selection; that understanding was extended in the 20th century through genetics and population ecology. Genetic variability arises from mutations and recombination, while organisms themselves are mobile, leading to geographical isolation and genetic drift with varying selection pressures.
Genes can sometimes be exchanged between species by horizontal gene transfer. Viruses are a special case, driven by a balance of mutation and selection, can be treated as quasispecies. Biologists and taxonomists have made many attempts to define species, beginning from morphology and moving towards genetics. Early taxonomists such as Linnaeus had no option but to describe what they saw: this was formalised as the typological or morphological species concept. Ernst Mayr emphasised reproductive isolation, but this, like other species concepts, is hard or impossible to test. Biologists have tried to refine Mayr's definition with the recognition and cohesion concepts, among others. Many of the concepts are quite similar or overlap, so they are not easy to count: the biologist R. L. Mayden recorded about 24 concepts, the philosopher of science John Wilkins counted 26. Wilkins further grouped the species concepts into seven basic kinds of concepts: agamospecies for asexual organisms biospecies for reproductively isolated sexual organisms ecospecies based on ecological niches evolutionary species based on lineage genetic species based on gene pool morphospecies based on form or phenotype and taxonomic species, a species as determined by a taxonomist.
A typological species is a group of organisms in which individuals conform to certain fixed properties, so that pre-literate people recognise the same taxon as do modern taxonomists. The clusters of variations or phenotypes within specimens would differentiate the species; this method was used as a "classical" method of determining species, such as with Linnaeus early in evolutionary theory. However, different phenotypes are not different species. Species named in this manner are called morphospecies. In the 1970s, Robert R. Sokal, Theodore J. Crovello and Peter Sneath proposed a variation on this, a phenetic species, defined as a set of organisms with a similar phenotype to each other, but a different phenotype from other sets of organisms, it differs from the morphological species concept in including a numerical measure of distance or similarity to cluster entities based on multivariate comparisons of a reasonably large number of phenotypic traits. A mate-recognition species is a group of sexually reproducing organisms that recognize one another as potential mates.
Expanding on this to allow for post-mating isolation, a cohesion species is the most inclusive population of individuals having the potential for phenotypic cohesion through intrinsic cohesion mechanisms. A further development of the recognition concept is provided by the biosemiotic concept of species. In microbiology, genes can move even between distantly related bacteria extending to the whole bacterial domain; as a rule of thumb, microbiologists have assumed that kinds of Bacteria or Archaea with 16S ribosomal RNA gene sequences more similar than 97% to each other need to be checked by DNA-DNA hybridisation to decide if they belong to the same species or not. This concept was narrowed in 2006 to a similarity of 98.7%. DNA-DNA hybri
Genetically modified crops
Genetically modified crops are plants used in agriculture, the DNA of, modified using genetic engineering methods. In most cases, the aim is to introduce a new trait to the plant which does not occur in the species. Examples in food crops include resistance to certain pests, environmental conditions, reduction of spoilage, resistance to chemical treatments, or improving the nutrient profile of the crop. Examples in non-food crops include production of pharmaceutical agents and other industrially useful goods, as well as for bioremediation. Farmers have adopted GM technology. Acreage increased from 1.7 million hectares in 1996 to 185.1 million hectares in 2016, some 12% of global cropland. As of 2016, major crop traits consist of both. In 2015, 53.6 million ha of GM maize were under cultivation. GM maize outperformed its predecessors: yield was 5.6 to 24.5% higher with less mycotoxins and thricotecens. Non-target organisms were unaffected, except for Braconidae, represented by a parasitoid of European corn borer, the target of Lepidoptera active Bt maize.
Biogeochemical parameters such as lignin content did not vary, while biomass decomposition was higher. A 2014 meta-analysis concluded that GM technology adoption had reduced chemical pesticide use by 37%, increased crop yields by 22%, increased farmer profits by 68%; this reduction in pesticide use has been ecologically beneficial, but benefits may be reduced by overuse. Yield gains and pesticide reductions are larger for insect-resistant crops than for herbicide-tolerant crops. Yield and profit gains are higher in developing countries than in developed countries. There is a scientific consensus that available food derived from GM crops poses no greater risk to human health than conventional food, but that each GM food needs to be tested on a case-by-case basis before introduction. Nonetheless, members of the public are much less than scientists to perceive GM foods as safe; the legal and regulatory status of GM foods varies by country, with some nations banning or restricting them, others permitting them with differing degrees of regulation.
However, opponents have objected to GM crops on grounds including environmental impacts, food safety, whether GM crops are needed to address food needs, whether they are sufficiently accessible to farmers in developing countries and concerns over subjecting crops to intellectual property law. Safety concerns led 38 countries, including 19 in Europe, to prohibit their cultivation. Multiple natural mechanisms allow gene flow from one species to another; these occur in nature on a large scale – for example, it is one mechanism for the development of antibiotic resistance in bacteria. This is facilitated by transposons, retroviruses and other mobile genetic elements that translocate DNA to new loci in a genome. Movement occurs over an evolutionary time scale. Traditional crop breeders have long introduced foreign germplasm into crops by creating novel crosses. A hybrid cereal grain was created by crossing wheat and rye. Since traits including dwarfing genes and rust resistance have been introduced in that manner.
Plant tissue culture and deliberate mutations have enabled humans to alter the makeup of plant genomes. The term genetic engineering is applied to genetic modifications made using biotechnology; the first plant produced in that way came in an antibiotic-resistant tobacco plant. The first field trials occurred in France and the USA in 1986, using tobacco plants engineered for herbicide resistance. In 1987, Plant Genetic Systems, founded by Marc Van Montagu and Jeff Schell, was the first company to genetically engineer insect-resistant plants by incorporating genes that produced insecticidal proteins from Bacillus thuringiensis; the People's Republic of China was the first country to allow commercialized transgenic plants, introducing a virus-resistant tobacco in 1992, withdrawn in 1997. The first genetically modified crop approved for sale in the U. S. in 1994, was the FlavrSavr tomato. It had a longer shelf life. In 1994, the European Union approved tobacco engineered to tolerate the herbicide bromoxynil, making it the first commercially genetically engineered crop marketed in Europe.
In 1995, Bt Potato was approved by the US Environmental Protection Agency, making it the country's first-pesticide producing crop. In 1995 canola with modified oil composition, Bt maize, bromoxynil-tolerant cotton, Bt cotton, glyphosate-tolerant soybeans, virus-tolerant squash, additional delayed ripening tomatoes were approved; as of mid-1996, 35 approvals had been granted to commercially grow 8 transgenic crops and one flower crop, with 8 different traits in 6 countries plus the EU. In 2000, Vitamin A-enriched golden rice was developed, though as of 2016 it was not yet in commercial production. In 2013 the leaders of the three research teams that first applied genetic engineering to crops, Robert Fraley, Marc Van Montagu and Mary-Dell Chilton, were awarded the World Food Prize for improving the "quality, quantity or availability" of food in the world. In the US, by 2014, 94% of the planted area of soybeans, 96% of cotton and 93% of corn were genetically modified varieties. In developing countries, about 18 million farmers planted 54% of GM crops worldwide by 2013.
Genetically engineered crops
Crop wild relative
A crop wild relative is a wild plant related to a domesticated plant, whose geographic origins can be traced to regions known as Vavilov Centers. It may be a wild ancestor of the domesticated plant, or another related taxon; the wild relatives of crop plants constitute an important resource for improving agricultural production and for maintaining sustainable agro-ecosystems. With the advent of anthropogenic climate change and greater ecosystem instability CWRs are to prove a critical resource in ensuring food security for the new millennium, it was Nikolai Vavilov, the Russian botanist who first realized the importance of crop wild relatives in the early 20th century. Genetic material from CWRs has been utilized by humans for thousands of years to improve the quality and yield of crops. Farmers have used traditional breeding methods for millennia, wild maize is grown alongside maize to promote natural crossing and improve yields. More plant breeders have utilised CWR genes to improve a wide range of crops like rice and grain legumes.
CWRs have contributed many useful genes to crop plants, modern varieties of most major crops now contain genes from their wild relatives. Therefore, CWRs are wild plants related to socio-economically important species including food and forage crops, medicinal plants, condiments and forestry species, as well as plants used for industrial purposes, such as oils and fibres, to which they can contribute beneficial traits. A CWR can be defined as "... a wild plant taxon that has an indirect use derived from its close genetic relationship to a crop...” CWRs are essential components of natural and agricultural ecosystems and hence are indispensable for maintaining ecosystem health. Their conservation and sustainable use is important for improving agricultural production, increasing food security, maintaining a healthy environment; the natural populations of many CWRs are at risk. They are threatened by habitat loss through the destruction and degradation of natural environment or their conversion to other uses.
Deforestation is leading to the loss of many populations of important wild relatives of fruit and industrial crops. Populations of wild relatives of cereal crops that occur in arid or semi-arid lands are being reduced by over grazing and resulting desertification; the growing industrialization of agriculture is drastically reducing the occurrence of CWRs within the traditional agro-ecosystems. The wise conservation and use of CWRs are essential elements for increasing food security, eliminating poverty, maintaining the environment. Conservation strategies for CWRs consider both in situ and ex situ conservation; these are complementary approaches to CWR conservation, since each has its own advantages and disadvantages. For example, whilst ex situ conservation protects CWR from threats in the wild, it can limit evolution and adaptation to new environmental challenges. In 2016, 29% of wild relative plant species were missing from the world’s genebanks, with a further 24% represented by fewer than 10 samples.
Over 70% of all crop wild relative species worldwide were in urgent need of further collecting to improve their representation in genebanks, over 95% were insufficiently represented with regard to the full range of geographic and ecological variation in their native distributions. While the most critical priorities for further collecting were found in the Mediterranean and Near East and Southern Europe and East Asia, South America, crop wild relatives insufficiently represented in genebanks are distributed across all countries worldwide. Oats – Avena byzantina Quinoa – Chenopodium berlandieri Finger Millet – Eleusine africana Barley – Hordeum arizonicum Rice – Oryza rufipogon African Rice – Oryza barthii Pearl Millet – Pennisetum purpureum Rye – Secale cereale subsp. Dighoricum Sorghum – Sorghum halepense Broom millet – Panicum fauriei Wheat – Einkorn wheat Maize – Zea diploperennis Note: Many different vegetables share one common ancestor in the Brassica family and plants. Many vegetables are hybrids of different species, again this is true of Brassicas.
Asparagus – Asparagus dauricus Beet – Beta vulgaris subsp. Maritima Black Mustard – Wild mustard Cabbage - Brassica elongata Carrot – Daucus gracilis Garlic – Allium atroviolaceum Leek – Welsh onion Lettuce – Prickly lettuce Mustard – Brassica carinata Onion – Allium galanthum Rape – Common dogmustard Spinach – Spinacia turkestanica Squash – Cucurbita okeechobeensis Turnip – Brassica rapa Almond – Chinese plum Apple – Malus sieversii, but with some cultivars belonging to Malus sylvestris or being a hybrid of the two. Apricot – Prunus brigantina Avocado – Persea schiedeana Banana – Musa acuminata and Musa balbisiana Breadfruit (Artocarp
Drosophila melanogaster is a species of fly in the family Drosophilidae. The species is known as the common fruit fly or vinegar fly. Starting with Charles W. Woodworth's proposal of the use of this species as a model organism, D. melanogaster continues to be used for biological research in genetics, microbial pathogenesis, life history evolution. As of 2017, eight Nobel prizes had been awarded for research using Drosophila. D. Melanogaster is used in research because it can be reared in the laboratory, has only four pairs of chromosomes and lays many eggs, its geographic range includes all continents, including islands. D. melanogaster is a common pest in homes and other places where food is served. Flies belonging to the family Tephritidae are called "fruit flies"; this can cause confusion in the Mediterranean and South Africa, where the Mediterranean fruit fly Ceratitis capitata is an economic pest. Wildtype fruit flies are yellow-brown, with brick-red eyes and transverse black rings across the abdomen.
They exhibit sexual dimorphism. Males are distinguished from females based on colour differences, with a distinct black patch at the abdomen, less noticeable in emerged flies, the sexcombs. Furthermore, males have a cluster of spiky hairs surrounding the reproducing parts used to attach to the female during mating. Extensive images are found at FlyBase. Under optimal growth conditions at 25 °C, the D. melanogaster lifespan is about 50 days from egg to death. The developmental period for D. melanogaster varies with temperature, as with many ectothermic species. The shortest development time, 7 days, is achieved at 28 °C. Development times increase at higher temperatures due to heat stress. Under ideal conditions, the development time at 25 °C is 8.5 days, at 18 °C it takes 19 days and at 12 °C it takes over 50 days. Under crowded conditions, development time increases. Females lay some 400 eggs, about five at a time, into rotting fruit or other suitable material such as decaying mushrooms and sap fluxes.
The eggs, which are about 0.5 mm long, hatch after 12–15 hours. The resulting larvae grow for about 4 days while molting twice, at about 48 h after hatching. During this time, they feed on the microorganisms that decompose the fruit, as well as on the sugar of the fruit itself; the mother puts feces on the egg sacs to establish the same microbial composition in the larvae's guts that has worked positively for herself. The larvae encapsulate in the puparium and undergo a 4-day-long metamorphosis, after which the adults eclose; the female fruit fly prefers a shorter duration. Males, prefer it to last longer. Males perform a sequence of five behavioral patterns to court females. First, males orient themselves while playing a courtship song by horizontally extending and vibrating their wings. Soon after, the male positions himself at the rear of the female's abdomen in a low posture to tap and lick the female genitalia; the male curls his abdomen and attempts copulation. Females can reject males by moving away and extruding their ovipositor.
Copulation lasts around 15–20 minutes, during which males transfer a few hundred long sperm cells in seminal fluid to the female. Females store the sperm in two mushroom-shaped spermathecae. A last male precedence is believed to exist; this precedence was found to occur through both incapacitation. The displacement is attributed to sperm handling by the female fly as multiple matings are conducted and is most significant during the first 1–2 days after copulation. Displacement from the seminal receptacle is more significant than displacement from the spermathecae. Incapacitation of first male sperm by second male sperm becomes significant 2–7 days after copulation; the seminal fluid of the second male is believed to be responsible for this incapacitation mechanism which takes effect before fertilization occurs. The delay in effectiveness of the incapacitation mechanism is believed to be a protective mechanism that prevents a male fly from incapacitating his own sperm should he mate with the same female fly repetitively.
Sensory neurons in the uterus of female D. melanogaster respond to a male protein, sex peptide, found in sperm. This protein makes the female reluctant to copulate for about 10 days after insemination; the signal pathway leading to this change in behavior has been determined. The signal is sent to a brain region, a homolog of the hypothalamus and the hypothalamus controls sexual behavior and desire. Gonadotropic hormones in Drosophila maintain homeostasis and govern reproductive output via a cyclic interrelationship, not unlike the mammalian estrous cycle. Sex Peptide perturbs this homeostasis and shifts the endocrine state of the female by inciting juvenile hormone synthesis in the corpus allatum. D. Melanogaster is used for life extension studies, such as to identify genes purported to increase lifespan when mutated. Females become receptive to courting males about 8–12 hours after emergence. Specific neuron groups in females have been found to affect copulation behavior a
The phenotype of an organism is the composite of the organism's observable characteristics or traits, including its morphology or physical form and structure. An organism's phenotype results from two basic factors: the expression of an organism's genetic code, or its genotype, the influence of environmental factors, which may interact, further affecting phenotype; when two or more different phenotypes exist in the same population of a species, the species is called polymorphic. A well-documented polymorphism is Labrador Retriever coloring. Richard Dawkins in 1978 and again in his 1982 book The Extended Phenotype suggested that bird nests and other built structures such as caddis fly larvae cases and beaver dams can be considered as "extended phenotypes"; the genotype-phenotype distinction was proposed by Wilhelm Johannsen in 1911 to make clear the difference between an organism's heredity and what that heredity produces. The distinction is similar to that proposed by August Weismann, who distinguished between germ plasm and somatic cells.
The genotype-phenotype distinction should not be confused with Francis Crick's central dogma of molecular biology, a statement about the directionality of molecular sequential information flowing from DNA to protein, not the reverse. The term "phenotype" has sometimes been incorrectly used as a shorthand for phenotypic difference from wild type, bringing the absurd statement that a mutation has no phenotype. Despite its straightforward definition, the concept of the phenotype has hidden subtleties, it may seem that anything dependent on the genotype is a phenotype, including molecules such as RNA and proteins. Most molecules and structures coded by the genetic material are not visible in the appearance of an organism, yet they are observable and are thus part of the phenotype, it may seem that this goes beyond the original intentions of the concept with its focus on the organism in itself. Either way, the term phenotype includes inherent traits or characteristics that are observable or traits that can be made visible by some technical procedure.
A notable extension to this idea is the presence of "organic molecules" or metabolites that are generated by organisms from chemical reactions of enzymes. Another extension adds behavior to the phenotype. Behavioral phenotypes include cognitive and behavioral patterns; some behavioral phenotypes may characterize psychiatric syndromes. Phenotypic variation is a fundamental prerequisite for evolution by natural selection, it is the living organism as a whole that contributes to the next generation, so natural selection affects the genetic structure of a population indirectly via the contribution of phenotypes. Without phenotypic variation, there would be no evolution by natural selection; the interaction between genotype and phenotype has been conceptualized by the following relationship: genotype + environment → phenotype A more nuanced version of the relationship is: genotype + environment + genotype & environment interactions → phenotype Genotypes have much flexibility in the modification and expression of phenotypes.
The plant Hieracium umbellatum is found growing in two different habitats in Sweden. One habitat is rocky, sea-side cliffs, where the plants are bushy with broad leaves and expanded inflorescences; these habitats alternate along the coast of Sweden and the habitat that the seeds of Hieracium umbellatum land in, determine the phenotype that grows. An example of random variation in Drosophila flies is the number of ommatidia, which may vary between left and right eyes in a single individual as much as they do between different genotypes overall, or between clones raised in different environments; the concept of phenotype can be extended to variations below the level of the gene that affect an organism's fitness. For example, silent mutations that do not change the corresponding amino acid sequence of a gene may change the frequency of guanine-cytosine base pairs; these base pairs have a higher thermal stability than adenine-thymine, a property that might convey, among organisms living in high-temperature environments, a selective advantage on variants enriched in GC content.
Richard Dawkins described a phenotype that included all effects that a gene has on its surroundings, including other organisms, as an extended phenotype, arguing that "An animal's behavior tends to maximize the survival of the genes'for' that behavior, whether or not those genes happen to be in the body of the particular animal performing it." For instance, an organism such as a beaver modifies its environment by building a beaver dam. When a bird feeds a brood parasite such as a cuckoo, it is unwittingly extending its phenotype.
In biology, a mutation is the permanent alteration of the nucleotide sequence of the genome of an organism, virus, or extrachromosomal DNA or other genetic elements. Mutations result from errors during DNA replication or other types of damage to DNA, which may undergo error-prone repair, or cause an error during other forms of repair, or else may cause an error during replication. Mutations may result from insertion or deletion of segments of DNA due to mobile genetic elements. Mutations may or may not produce discernible changes in the observable characteristics of an organism. Mutations play a part in both normal and abnormal biological processes including: evolution and the development of the immune system, including junctional diversity; the genomes of RNA viruses are based on RNA rather than DNA. The RNA viral genome can be double single stranded. In some of these viruses replication occurs and there are no mechanisms to check the genome for accuracy; this error-prone process results in mutations.
Mutation can result in many different types of change in sequences. Mutations in genes can either have no effect, alter the product of a gene, or prevent the gene from functioning properly or completely. Mutations can occur in nongenic regions. One study on genetic variations between different species of Drosophila suggests that, if a mutation changes a protein produced by a gene, the result is to be harmful, with an estimated 70 percent of amino acid polymorphisms that have damaging effects, the remainder being either neutral or marginally beneficial. Due to the damaging effects that mutations can have on genes, organisms have mechanisms such as DNA repair to prevent or correct mutations by reverting the mutated sequence back to its original state. Mutations can involve the duplication of large sections of DNA through genetic recombination; these duplications are a major source of raw material for evolving new genes, with tens to hundreds of genes duplicated in animal genomes every million years.
Most genes belong to larger gene families of shared ancestry. Novel genes are produced by several methods through the duplication and mutation of an ancestral gene, or by recombining parts of different genes to form new combinations with new functions. Here, protein domains act as modules, each with a particular and independent function, that can be mixed together to produce genes encoding new proteins with novel properties. For example, the human eye uses four genes to make structures that sense light: three for cone cell or color vision and one for rod cell or night vision. Another advantage of duplicating a gene is. Other types of mutation create new genes from noncoding DNA. Changes in chromosome number may involve larger mutations, where segments of the DNA within chromosomes break and rearrange. For example, in the Homininae, two chromosomes fused to produce human chromosome 2. In evolution, the most important role of such chromosomal rearrangements may be to accelerate the divergence of a population into new species by making populations less to interbreed, thereby preserving genetic differences between these populations.
Sequences of DNA that can move about the genome, such as transposons, make up a major fraction of the genetic material of plants and animals, may have been important in the evolution of genomes. For example, more than a million copies of the Alu sequence are present in the human genome, these sequences have now been recruited to perform functions such as regulating gene expression. Another effect of these mobile DNA sequences is that when they move within a genome, they can mutate or delete existing genes and thereby produce genetic diversity. Nonlethal mutations increase the amount of genetic variation; the abundance of some genetic changes within the gene pool can be reduced by natural selection, while other "more favorable" mutations may accumulate and result in adaptive changes. For example, a butterfly may produce offspring with new mutations; the majority of these mutations will have no effect. If this color change is advantageous, the chances of this butterfly's surviving and producing its own offspring are a little better, over time the number of butterflies with this mutation may form a larger percentage of the population.
Neutral mutations are defined as mutations whose effects do not influence the fitness of an individual. These can increase in frequency over time due to genetic drift, it is believed that the overwhelming majority of mutations have no significant effect on an organism's fitness. DNA repair mechanisms are able to mend most changes before they become permanent mutations, many organisms have mechanisms for eliminating otherwise-permanently mutated somatic cells. Beneficial mutations can improve reproductive success. Mutationism is one of several alternatives to evolution by natural selection that have existed both before and after the publication of Charles Darwin's 1859 book, On the Origin of Species. In the theory, mutation was the source of novelty
Frequency is the number of occurrences of a repeating event per unit of time. It is referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency; the period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals, radio waves, light. For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics and radio, frequency is denoted by a Latin letter f or by the Greek letter ν or ν; the relation between the frequency and the period T of a repeating event or oscillation is given by f = 1 T.
The SI derived unit of frequency is the hertz, named after the German physicist Heinrich Hertz. One hertz means. If a TV has a refresh rate of 1 hertz the TV's screen will change its picture once a second. A previous name for this unit was cycles per second; the SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz. As a matter of convenience and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are described by their frequency instead of period; these used conversions are listed below: Angular frequency denoted by the Greek letter ω, is defined as the rate of change of angular displacement, θ, or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument to the sine function: y = sin = sin = sin d θ d t = ω = 2 π f Angular frequency is measured in radians per second but, for discrete-time signals, can be expressed as radians per sampling interval, a dimensionless quantity.
Angular frequency is larger than regular frequency by a factor of 2π. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.: y = sin = sin d θ d x = k Wavenumber, k, is the spatial frequency analogue of angular temporal frequency and is measured in radians per meter. In the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has an inverse relationship to the wavelength, λ. In dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: f = v λ. In the special case of electromagnetic waves moving through a vacuum v = c, where c is the speed of light in a vacuum, this expression becomes: f = c λ; when waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change. Measurement of frequency can done in the following ways, Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period dividing the count by the length of the time period.
For example, if 71 events occur within 15 seconds the frequency is: f = 71 15 s ≈ 4.73 Hz If the number of counts is not large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a random error into the count of between zero and one count, so on average half a count; this is called gating error and causes an average error in the calculated frequency of Δ f = 1 2 T