Mathematical Properties of Waves

Physical waves, or mechanical waves, form through the vibration of a medium, be it a string, the Earths crust, or particles of gases and fluids. Waves have mathematical properties that can be analyzed to understand the motion of the wave. This article introduces these general wave properties, rather than how to apply them in specific situations in physics. Transverse Longitudinal Waves There are two types of mechanical waves. A is such that the displacements of the medium are perpendicular (transverse) to the direction of travel of the wave along the medium. Vibrating a string in periodic motion, so the waves move along it, is a transverse wave, as are waves in the ocean. A longitudinal wave is such that the displacements of the medium are back and forth along the same direction as the wave itself. Sound waves, where the air particles are pushed along in the direction of travel, is an example of a longitudinal wave. Even though the waves discussed in this article will refer to travel in a medium, the mathematics introduced here can be used to analyze properties of non-mechanical waves. Electromagnetic radiation, for example, is able to travel through empty space, but still, has the same mathematical properties as other waves. For example, the Doppler effect for sound waves is well known, but there exists a similar Doppler effect for light waves, and they are based around the same mathematical principles. What Causes Waves? Waves can be viewed as a disturbance in the medium around an equilibrium state, which is generally at rest. The energy of this disturbance is what causes the wave motion. A pool of water is at equilibrium when there are no waves, but as soon as a stone is thrown in it, the equilibrium of the particles is disturbed and the wave motion begins.The disturbance of the wave travels, or propogates, with a definite speed, called the wave speed (v).Waves transport energy, but not matter. The medium itself doesnt travel; the individual particles undergo back-and-forth or up-and-down motion around the equilibrium position. The Wave Function To mathematically describe wave motion, we refer to the concept of a wave function, which describes the position of a particle in the medium at any time. The most basic of wave functions is the sine wave, or sinusoidal wave, which is a periodic wave (i.e. a wave with repetitive motion). It is important to note that the wave function doesnt depict the physical wave, but rather its a graph of the displacement about the equilibrium position. This can be a confusing concept, but the useful thing is that we can use a sinusoidal wave to depict most periodic motions, such as moving in a circle or swinging a pendulum, which dont necessarily look wave-like when you view the actual motion. Properties of the Wave Function wave speed (v) - the speed of the waves propagationamplitude (A) - the maximum magnitude of the displacement from equilibrium, in SI units of meters. In general, it is the distance from the equilibrium midpoint of the wave to its maximum displacement, or it is half the total displacement of the wave.period (T) - is the time for one wave cycle (two pulses, or from crest to crest or trough to trough), in SI units of seconds (though it may be referred to as seconds per cycle).frequency (f) - the number of cycles in a unit of time. The SI unit of frequency is the hertz (Hz) and1 Hz 1 cycle/s 1 s-1angular frequency (ω) - is 2Ï€ times the frequency, in SI units of radians per second.wavelength (ÃŽ ») - the distance between any two points at corresponding positions on successive repetitions in the wave, so (for example) from one crest or trough to the next, in SI units  of meters.  wave number (k) - also called the propagation constant, this useful quantity is defined as 2 Ï₠¬ divided by the wavelength, so the SI units are radians per meter.pulse - one half-wavelength, from equilibrium back Some useful equations in defining the above quantities are: v ÃŽ » / T ÃŽ » fω 2 Ï€ f 2 Ï€/TT 1 / f 2 Ï€/ωk 2Ï€/ωω vk The vertical position of a point on the wave, y, can be found as a function of the horizontal position, x, and the time, t, when we look at it. We thank the kind mathematicians for doing this work for us, and obtain the following useful equations to describe the wave motion: y(x, t) A sin ω(t - x/v) A sin 2Ï€ f(t - x/v)y(x, t) A sin 2Ï€(t/T - x/v)y(x, t) A sin (ω t - kx) The Wave Equation One final feature of the wave function is that applying calculus to take the second derivative yields the wave equation, which is an intriguing and sometimes useful product (which, once again, we will thank the mathematicians for and accept without proving it): d2y / dx2 (1 / v2) d2y / dt2 The second derivative of y with respect to x is equivalent to the second derivative of y with respect to t divided by the wave speed squared. The key usefulness of this equation is that whenever it occurs, we know that the function y acts as a wave with wave speed v and, therefore, the situation can be described using the wave function.

Solar Energy. Global Warming Is The Slow Increase Of The

Solar Energy Global Warming is the slow increase of the average temperature of the Earth’s atmosphere and oceans. Global Warming is a phenomenon caused by the buildup of greenhouse gasses in the atmosphere that trap heat from the sun in the atmosphere. Energy in the form of heat comes to the Earth as sunlight. The heat cause by sunlight would normally leave the atmosphere as a form of infrared radiation. Greenhouse gases however trap the radiation causing the heat to remain in the atmosphere. The gradual increase in heat due to the buildup of these gasses and the heat that these gasses trap is called the greenhouse effect. This â€Å"greenhouse effect† is what gives the Earth’s atmosphere a lot of its warmth. However, as the amount of†¦show more content†¦Solar energy is one of those solutions. Solar energy is the cleanest, most efficient, and cheapest form of renewable energy. The physics behind the harnessing of solar energy is the law of the conservation of energ y. Solar energy is defined as the energy that comes from the suns radiation. Solar energy can be harnessed and used through, the law of the conservation of energy. The law of conservation of energy states that the energy within a system is constant. The law also states that energy cannot be created or destroyed it can only change forms. Solar energy in the form of sunlight can be converted into electricity. The electricity created from sunlight is called solar power. In order to turn sunlight into electrical energy a solar panel is used. The solar panels are made up of photovoltaic cells. These cells convert sunlight into direct current electricity throughout the day. This direct current is then transformed into the usable alternating current electricity by the inverter. When more energy is produced than is needed, like on bright sunny days, the extra electricity is automatically while the rest is stored in a battery. The only setback of solar energy is that it isn’t always avai lable. However when the sun goes down or the weather blocks sunlight the energy that was previously stored will be used. This energy feeds directly into the breaker supplying electricity to the house or building. This electricity power the devices in a house like theShow MoreRelatedRenewable Sources of Energy: Soloar Energy Essay870 Words   |  4 Pageswould only increase and thus become more expensive. Solar power is energy efficient, what is meant by that is that solar power cannot ever run out as long as it is installed properly. Solar power cells is a source of electrical energy that converts a powerful source of energy such as the sun into electricity, using it’s energy to create electrical currents within the solar panel. Solar panels produce electricity using technology called â€Å"Solar Photovoltaic (PV)†. Diagram of how solar panels generallyRead MoreTaking a Look at Global Warming1483 Words   |  6 Pagespeople, global warming just means that the Earth is getting warmer. What they don’t realize is that global warming is so much more than that. No matter how you call it, â€Å"global warming† or â€Å"climate disruption†, its effects are all the same. Rising sea levels, wildfires, droughts, and storms are all results of these rising temperatures. And if humans keep pumping large amounts of carbon dioxide into the atmosphere, these natural disasters will be just the first of many. To better understand global warmingRead MoreEssay on The Threat of Global Warming1667 Words   |  7 PagesThe Threat of Global Warming Through the eyes of most scientists, global warming is seen as a very serious and severe threat. The actions taken by humans, such as industry and consumption of fossil fuels plus the increase in population and agriculture have played a big part in global warming. If something is not done soon the results could be very bad.   Ã‚  Ã‚  Ã‚  Ã‚  By the middle of the twenty first century, there is evidence that the Earth will be warmer than it has been at any time in human historyRead MoreAdvantages And Advantages Of Bioenergy And Solar Energy993 Words   |  4 PagesNowadays, global warming is causing terrible damages from climate change such as powerful typhoons, hurricanes, tsunami, super flood to human lives. It has become a big issue since the changes have happened more frequently. Therefore, many scientists are struggling with finding some alternative sources of energy to fossil fuel which release a great amount of carbon dioxide that have affected global warming. Governments also struggle with finding some possible solutions to deal with climate changeRead MoreGlobal Warming1677 Words   |  7 PagesThrough the eyes of most scientists, global warming is seen as a very serious and severe threat. The actions taken by humans, such as industry and consumption of fossil fuels plus the increase in popu lation and agriculture have played a big part in global warming. If something is not done soon the results could be very bad. By the middle of the twenty first century, there is evidence that the Earth will be warmer than it has been at any time in human history, and quite possibly since theRead MoreThe Effects Of Global Warming On The Earth s Natural State Of Being1554 Words   |  7 PagesGlobal warming has been a universal issue for many decades. It started back at the beginning of the Industrial Revolution, when people unknowingly released fumes from factories into the air. Although global warming has been an all-around topic, it has recently started to gain media attention due to the many catastrophic events that have occurred around the globe. Global warming can be defined as, â€Å"a gradual increase in the overall temperature of the earth s atmosphere generally attributed to theRead MoreThe Effects Of Global Warming On Our Environment1290 Words   |  6 PagesOne of the more troubling themes of over the past few years is global warming. Global warming is the result of human activity overloading our atmosphere with carbon dioxide and other toxic emissions. These emissions trap heat, drive up Earth’s temperature, and create significant and harmful impacts on our health, our environment, and our climate. In an effort to hinder global warming, advocates have made several efforts to decrease the amount of harmful emissions being released into the atmosphereRead MoreEssay on Global Warming585 Words   |  3 Pages3:32 PM. Global warming is affecting countries all around the world. Greenhouse gas is one of the major problems contributing to global. There are many mechanics of global warming the worst factors increasing warming is greenhouse gas. Which is the Earth keeping the heat from the sun then radiates it back to space, but CO2, methane, nitrous oxide and water vapor in the air slow down this radiation. C02 has increased by the burning of fossil fuels from our cars and biomass. The increase of greenhouseRead MoreGlobal Warming And The Warming1544 Words   |  7 PagesGlobal warming has become a well conversed topic among scientists and peoples in the world today. There are extremists who do everything possible to stop contributing to the warming, but the average person does little to alleviate the issue and in many cases refuses to acknowledge that there is a problem at all. Dating back to millions of years ago, even before humanity was born, the world has always experienced one form or another of warming; so the warming seen today is not as bizarre as many mayRead MoreGlobal Warming Forewords Global warming is the result of a large concentration of CO2 and1400 Words   |  6 PagesGlobal Warming Forewords Global warming is the result of a large concentration of CO2 and greenhouse gases (GHGs) in the atmosphere. Human activities such as burning fossil fuels, deforestation, and emissions are held responsible for this situation developing. The climate change is the result, and a factor of global warming. There are several factors impacting global warming, and these include ozone layer depletion, carbon cycle, pollution, human actions, and orbit of the earth. There is a debate

The other peace settlements at the end of the 1st World War Free Essays

To score two countries in a scale of 1 to 5 is not an easy thing. When you score something it mostly depends on which side you are. For example if you are a citizen of a defeated nation, you won’t agree with the treaty at all, because you don’t want your country to be smaller, you don’t want your country to loose power! But as you had no choice then to accept that cruel treaty, you’ll of course think it’s VERY UNFAIR! And if you are a citizen of a new created state or a state that gain benefits from the defeated nations, you’ll agree with the treaty, for example Czech citizen might be VERY happy of the treaties, because the Czechoslovakia were created. We will write a custom essay sample on The other peace settlements at the end of the 1st World War or any similar topic only for you Order Now If there weren’t any treaty, there’ll be no Czech! For me as a foreigner (China), I’m looking at an outside way. I don’t agree with the treaty! As your question asked, I can choose any two treaties of the four treaties, but it’s for nothing, because I think all four treaties are unfair! I’ll give 5 to all the treaties. The treaty took many territories from the defeated nations and some territories were very important for the country, because they are the main industry resource. In the treaty of Neuilly, they even took Bulgaria’s power from the access to the Mediterranean. This point is VERY unfair! I think everybody might have access to the sea! Perhaps you’ll think I’m very idealist, but I really think our world might be MORE fair! People might have more rights, the life of people might be more equal! They want to weak them as much as they can, that the defeated nations won’t be able to attack them again. They are thinking only about their self. They are SO SELFISH! In fact some points of the treaty actually helped to stop the conflict between states, for example the treaty of St Germain. In this treaty Austria was separated from Hungary and many territories of Austria were given away and created as new states, but actually before this treaty, the old Austrian Empire had already collapsed in 1918 and many new states had already been set up, so this treaty was only sorting out the conflict between states. This point of the treaty is really not bad, but then many millions in Eastern Europe were given self-determination and freedom to rule themselves. Most of its industry had gone to Czechoslovakia. Nobody cared about how does this country (Austria) feels, how they think about it. So after this treaty, Austria collapsed and also suffered severe economic problems. All the defeated nations had to disarm and pay reparations. This is really very MEAN! The countries that made this treaty thought only about the benefits for them and to squeeze the defeated nations as hard as they can and also of course be sure they won’t be able to attack them again. They’ve never thought about what will happen if they’ll be the defeated nation, if they’ll have to accept this kind of treaty. I’m sure if they are the one of the defeated nations, they won’t agree with the treaty! From all the points, which I’ve written down, I give every treaty 5 on the scale of fairness. How to cite The other peace settlements at the end of the 1st World War, Papers

Johannes Brahms Essay Example For Students

Johannes Brahms Essay Ein Deutsches Requiem, Op. 45April 24, 2003There are those moments in life where one is certain that the everydayminutiae that worries one so is as insubstantial as smoke. The hands weuse for mundane activities, the breath scarcely noticed as it enters andexits the body, the eye that is witness to countless imagesall theseinstruments lay idle until music animates them. Requiem, such a paradoxical body of music it is the ephemeral handof death yet vibrating with power, life and beauty. Like a perpetual tidalwave crashing on the shores of Paradise, it consumes the senses andintoxicates every fiber of the body until death seems altogether a dream. And yet, destruction hovers at the fringes of every phrase, rounding a tonehere and cutting another one; cleaving the uncertainty from those who woulddisbelieve until one almost feels compelled to follow those magnificentvoices down into the valley of death simply because one does not wish themto stop. The stage could barely contain the host that was required to performthis dirge. There came the Concert Choir followed by the Chamber Choir,then the University Chorus and finally, the NIU Philharmonic. The stagewas awash in black and white, faces turned upward, ready and expectant. Instruments guided by their players tuned their voices and preparedthemselves for the massive undertaking of one Johannes Brahms and his EinDeutsches Requiem, Op. 45.There is a proven relationship between objects that travel through airat great velocities and or magnitudes. They can be seen at slower speedsto actually bend air before them and push it outward in a cone. Just asthe stage could barely contain the performers, the concert hall couldbarely contain their music, both instrumental and vocal. When the firstpassage was begun, I have every confidence that could time have beenslowed, there would have been a visible wave that pushed the audience back;and thus was Brahms come to Northern Illinois University. The Universitys Philharmonic was truly a talented group ofindividuals, but in light of the material presented that evening, they weremerely the lines upon which the words had been written; the glory belongedto those magnificent voices. As the first selection began, I was comfortedby light sopranos and clear male tenors as they assured me that blessedare they that mourn; for they shall be comforted.These gentle assurances were chased doggedly by such power anddamnation that goose bumps ran slowly up my spine and gently pushed thehairs up at the base of my neck. For all flesh is as grass, and all theglory of man as the flower of grass. The grass withereth, and the flowerthereof falleth away. I was being cautioned by this flood of choruses;cautioned that my days were predetermined and that accomplishment was asfleeting as the life that had attained them. Momentary peace returned as they readied themselves for the nextselection; and then there was longing. Such a palpable longing, it hungthick as vapor in the air and left me feeling incomplete and not quite surewhy. They cried out for peace and hope, trying to draw it around themforcibly as they would a cloak, grasping at the material and finding itlacking to provide the warmth they sought. Suddenly, there was a womans voice. It was a full soprano, vibratingwith an offer of that previously sought peace. She was the voice of allmothers, the voice of the Virgin Mary, and as a mother would comfort asmall child, she gave comfort As one whom his mother comforteth, so willI comfort youAgain, peace descended on the stage and I waited expectantly for whatwas to follow. I promise you, the next two selections that were to followwould have made the most respected and accomplished man shrink into hisshoulders and become as unsure as the boy who had clung to his mothersknee. Then suddenly, the wave descended. There was such determination inthose voices, so much reckoning for an entire life compressed into theseshort, clipped phrases that not a body moved in that concert hall save theones sustaining that tide of perseverance as it rode the backs of powerfulchords and melodies; beating them before it like leaves before a storm. .u93698aa022f6462584f49613c2a006fb , .u93698aa022f6462584f49613c2a006fb .postImageUrl , .u93698aa022f6462584f49613c2a006fb .centered-text-area { min-height: 80px; position: relative; } .u93698aa022f6462584f49613c2a006fb , .u93698aa022f6462584f49613c2a006fb:hover , .u93698aa022f6462584f49613c2a006fb:visited , .u93698aa022f6462584f49613c2a006fb:active { border:0!important; } .u93698aa022f6462584f49613c2a006fb .clearfix:after { content: ""; display: table; clear: both; } .u93698aa022f6462584f49613c2a006fb { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u93698aa022f6462584f49613c2a006fb:active , .u93698aa022f6462584f49613c2a006fb:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u93698aa022f6462584f49613c2a006fb .centered-text-area { width: 100%; position: relative ; } .u93698aa022f6462584f49613c2a006fb .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u93698aa022f6462584f49613c2a006fb .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u93698aa022f6462584f49613c2a006fb .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u93698aa022f6462584f49613c2a006fb:hover .ctaButton { background-color: #34495E!important; } .u93698aa022f6462584f49613c2a006fb .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u93698aa022f6462584f49613c2a006fb .u93698aa022f6462584f49613c2a006fb-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u93698aa022f6462584f49613c2a006fb:after { content: ""; display: block; clear: both; } READ: Existential and Expressive Arts Therapy EssayA pause enveloped the stage and then, slowly and with muchdeliberation, we were all set free of this bond of frustration and sense oflonging. Soft and gentle voices, clear and almost melodic, lulled us allwith sweet assurances that all was well. They pushed firmly against us,pressing us into that final sleep; angelic sopranos and male tenors weavingtogether a pre-cognitive cocoon and sealing us into it with the mosthaunting of phrases. Blessed are the dead.blessed are thedead.blessed are the dead.As a lover of Requiems, (my personal favorite happens to be Mozarts K626; the Kyrie) I would absolutely welcome the opportunity to see anotherwork by this body of performers. I was pleasantly surprised by the levelof professionalism as well as the level of talent possessed by these youngmen and women. NIU is, I would hope, extremely proud of her music andchoral departments as they add such a wonderful color and sense of beautyto the university as a whole. Formal Concert Paper #2School of Music -presents-Johannes BrahmsEin Deutsches Requiem, Op. 45April 24, 2003

Napoleon Bonaparte and Is Modern State free essay sample

Bonaparte instituted lasting reforms that mark the transition from absolute government to the modern state. One of Napoleons greatest contributions was the codification of French law and especially the great Civil Code that replaced the 360 local codes of the Ancient Regime. It was a combination of the egalitarianism of the Revolution and the authoritarianism of Napoleon. The code forbade privileges based on birth, allowed freedom of religion, and specified that government jobs go to the most qualified. It was, however, the first modern legal code to be adopted with a pan-European scope and it strongly influenced the law of many of the countries formed during and after the Napoleonic Wars. The Code was a major step in replacing the previous patchwork of feudal laws. The old paternal authority within the family was restored, for instance, while womens rights were strictly limited Napoleon once remarked that â€Å"women should stick to knitting. We will write a custom essay sample on Napoleon Bonaparte and Is Modern State or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page However, the achievements of the Revolution were continued with guarantees of equality, property rights and the rights of the citizen won in 1789. Published in a small compact edition in 1810, it became a model for legal rationalisation in many other states of Europe. One feature which was greatly to affect the future of France was the insistence on equal division of estates between sons. Napoleon also had to shape public opinion this was accomplished by crude forms of propaganda, but more importantly by the use of secret agents, arbitrary arrests, and executions. Like all dictators we think of Mussolini, Hitler and Stalin Napoleon relied on public opinion to prevent hostile criticism. In other words, dissent was nearly impossible. Printers and booksellers swore oaths of allegiance and all newspapers fell under state control. So, by repressing liberty, subverting republicanism and restoring absolutism, Napoleon reversed some of the liberal gains of the Revolution. He favored equality before the law and careers open to talent BUT he believed that political liberty threatened the efficiency of the state with anarchy.He would govern in the interests of the people as an enlightened but absolute ruler. In addition Napoleon favored a state system of public education. The curriculum would be secular and schools would be managed under the direction of the state and not the Church. For Napoleon, education would serve a dual role. State funded education would provide him with capable officials necessary to administer his laws and trained officers to man his army.The young would also be indoctrinated to obedience and authority. Napoleon established the University of France a giant board of education that placed education under state control. To this day, little has changed education is strictly centralized with curriculum and academic standards set for the entire nation. Women, of course, were excluded. Marriage is their whole destination, Napoleon once wrote. Women did not need education, all they needed was religion.I will conclude by saying that his drive, will, military genius and charisma made him a great man, a world historical figure, a man who made history. Machiavelli would have found Napoleon to be his perfect prince ; And , by spreading revolutionary ideals and institutions, Napoleon made it impossible for the restoration of the ancient regime. After Napoleon there was no turning back: feudalism was dead, society was secularized, the modern nation state replaced the dynastic state, and the bourgeoisie became the new class of privilege and status.

The Malayan Emergency Counter Insurgency Success

Warrants Essay Example

Warrants Essay Example Warrants Essay Warrants Essay Warrants Name: Course: Instructor: Institution: Date: Warrants Research on warrants Warrants are issued by a judge on behalf of the state. These warrants authorize a criminal’s arrest and detention. It also authorizes searches and seizure of a person’s property. A criminal warrant is a legal document ordering the law enforcement officers to carry out some of the activities in line with a criminal case. These warrants may be issue without the accused person’s knowledge. The criminal may not be aware of being accused of a crime when this warrant is issued. However, it may also be issued after the accused has been ordered to appear in court. The judge issues the criminal warrant in order to obtain evidence or ensure belief that the accused has actually committed the criminal act. Included in the warrant is written information about the case, the criminal’s name and the crime he is accused of. The warrant also included the name of the judge who issued it and the issue date. These warrants entail the actions the officers should undertake. How ever, the warrant’s format and details differ depending on the court’s location. At times, the arrest warrants contain realistic mistakes. These mistakes may include misspelling the suspect’s name or stating a wrong crime. In such situations, the suspect should be shown the warrant by the police. After this, if the suspect is able to prove himself not to be the real criminal, then the orders specified in the warrant will not apply to the suspect. However, in most cases the police do not show the warrant to the suspect. Mistakes such as wrong identity are usually resolved later. Errors such as clerical are never considered enough proof to terminate the warrant. These criminal arrest warrants are provided after a complaint has been filed. This complaint is based on a judicial finding. This finding ensures a probable cause. However, the probable cause warrants is just one the examples of the criminal arrest warrants (Cole Smith, 2010). When they began and why The European arrest warrants were introduced in 2004 to enable direct issuance of the warrants by a judge. This enabled the direct enforcement of the warrant of arrest presented by the judicial authority by one member state to another member state. This enables the issuance of the arrest warrant for any offence punishable by imprisonment for a maximum sentence of at least one year. When the accused person has already been sentenced, this crime should provide a four months imprisonment. The warrants were introduced to reduce the great time that was taken before extraditing a person from one of the European states to another. This also enabled the criminals to find it difficult to evade justice. It also equalized the freedom of movement within the European Union countries and increase safety. Since then, this has proved to be effective. This has also enabled the fugitives to face justice. The introduction of the warrants enables the tracing and arresting of the criminals. Thereafter, they are brought before the magistrate’s court where the magistrate fixes the hearing date that is usually within twenty-one days of arrest. The accused are informed on the contents of the warrants by the court. This enables them to agree to the accusations leveled up against them or disagree with them. The person then remains in custody or is bailed. The arrest warrants enabled all these acts to be possible. Therefore, this is the reason why it was important for them to be implemented (Schmalleger, 2012). What are they used for There are many kinds of warrants. Arrest warrants are documents issued by the court to authorize the arrest of criminals. The police take these suspected criminals in to custody and hold them until trial. The person arrested is always listed on the warrant. In some cases, the judge can state the amount of bail in the warrant. The warrant should also state that there is a probable cause for believing that the accused committed the crime. Another type of warrant is a search warrant. This is usually issued to enable the law enforcement officers to investigate a crime. This warrant enables the officers to carry out a search on a criminal and to carry out a search on a person’s property. This search is done to find out if the accused has any relations to the crime he is being accused of committing. In case the law enforcement officers find evidence, they can seize it as part of the investigation. Example, a search warrant can enable the officers to search the house of a person accu sed of murder. In case the officers find weapons such as guns or a knife stained with blood, the officers may seize the weapon to act as evidence in court. Another warrant is a bench warrant. The judge issues this warrant in a criminal case. In case the accused fails to fulfill the court’s requirements, a warrant is issued to take the accused person to custody. A case of absenteeism in court by the accused makes the judge to serve a bench warrant to the police in order for them to bring the accused to court. In addition, this warrant is issued on failure to pay fine or on lack of community service performance as ordered by the court. However, before issuing these warrants, the judge must ensure that the person had a court notice on when to show up in court or that the person had an order by the court to pay the fine on a particular date or perform the community service on specific days. This warrant is only issued with sufficient cause unlike other warrants that are issued with probable cause. This is because the judge only requires sufficient evidence in order to issue the warrant. In addition, the bench warrants are the only wa rrants applicable in the civil cases (Stoddart, 2006). When and how the warrants are served To obtain a warrant, the police present a written sworn statement to the judge or the magistrate. The sworn statement that is usually given under oath must give sufficient and accurate information to ensure a probable cause under arrest warrants and sufficient cause under bench warrants. This is to ensure that the crime was committed or the accused failed to satisfy the court’s requirements. There should be certainty that the name contained in the warrant belongs to the person who committed the crime. A broad description of the person accused of the crime does not apply in the issuing of the warrants. Example, a judge will not issue a warrant based on an affidavit that Smith was robbed by a tall black man and Steve matches the description. This is a vague description and it would apply to many people since there are countless tall black men everywhere. Therefore, this description does not establish a probable cause that Steve robbed Smith. Therefore, the probable cause to arr est Steve would be sufficient if the affidavit included accurate information on Steve. This sufficient information may include at least more than one witness and a photo of Steve. The officers obtain the arrest warrant when they need to arrest a criminal. This is usually after a case is leveled up against the criminal. The judge issues the arrest warrant in order for the criminal to face trial. A search warrant is issued when the officers need to conduct an investigation and obtain evidence that can be used in court. In most cases, people do not allow the police officers to search their premises or work place for evidence without search warrants. Therefore, the judge issues search warrants in order to enable the police to have an easy work obtaining evidence. In cases of absenteeism in court by the accused, the officers obtain a bench warrant The judge issues this warrant in order to enable the police to find the suspect and bring him to court for him to face his trial. In addition, it is also issued when the accused fails to pay his fine or when he fails to perform hi s community service as required (Schmalleger, 2012). State’s rules on warrants Different states have different rules on warrants. The Canadian police officers obtain the arrest warrants from the judge or the peace justice. The judge issues these warrants as per the Canadian criminal code. This code requires that upon the issue of the warrant, the officer arresting the accused should give a notice to the accused. This notice is on the order to arrest the accused and the basis for its issue. The officer then presents the warrant upon request. In the United Kingdom, the arrest warrant is also issued by the justice of peace. This is under the 1980 court rule. In this state, information laid before the justice of peace in writing concerning a criminal offence is only approved for persons over the age of eighteen. These arrest warrants are only issued for a person over eighteen. The offence the person is being accused of should be one punishable by imprisonment. On the other hand, the magistrates issue the warrants in Northern Ireland. The court issues the warrants in the United States. However, the United States congress or the legislatures can also issue them. In this state, the warrant should be supported by a sworn statement. Therefore, this satisfies the probable cause. In addition, the officer making the arrest should present the criminal before the magistrate as fast as possible. The officer making an arrest in accordance with a warrant that is presented upon complaint should follow some basic rules. The person should be presented before the magistrate without unnecessary delays. The government attorney should move to the district where the warrant was issued to terminate the complaint. The defendant cannot be arrested without a warrant since the probable cause rule will not have been satisfied. However, upon the absence of the magistrate or judge, the accused appears before the state or the local judicial officer (Cole Smith, 2010). References Cole, G. F., Smith, C. E. (2010). The American system of criminal justice. Belmont, CA: Wadsworth Cengage Learning. Schmalleger, F. (2012). Criminal justice: A brief introduction. Boston: Prentice Hall. Stoddart, C. N. (2006). Criminal warrants. Edinburgh: Butterworths.