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.

Article Review On The Constitution - 1067 Words

Furthermore, the constitution has a total of seven articles. Article I, creates the legislative branch, this article gives congress its powers and limits. Congress is the legislative branch of the government which means that they are responsible for making laws for the country. Article II, creates the executive branch, whom enforce the law created by congress. Article III, creates the judicial branch, this branch is the system of courts that look at the law and applies it to different cases. This includes the supreme court and courts created by congress. Article IV, this section talks about the states, it describes the responsibilities and duties of the states along with the responsibility of the federal government. Article V, describes how the constitution is flexible and how it can be changed by adding an amendment. Further, Article VI, states that is any federal laws that are made according to the constitution are supreme laws. State courts must follow federal law before state law . Finally, article VII states that ratifications were needed in order for the proposed constitution to take place. At least 9 states needed to ratify the constitution for it to be applied to all the states. Following these articles is a bill of rights which contain the first ten amendments of a total of 27, which give the citizens their freedoms and rights. More importantly, the constitution is built around six principles. Popular sovereignty, limited government, separation of powers, checks andShow MoreRelatedArticle Review On The Constitution1539 Words   |  7 PagesArticle XI Section 1. Proposal by legislature. Amendments to any part of the Constitution can be brought up by the approval of both the house and the senate. There must be an acceptance of this amendment between three fifths of members of each house. A review of the voting will be written into each houses journal. The house of representatives is comprised of four hundred thirty five American citizens. The senate is made up of one hundred American citizens, two from each state. The members for eachRead MoreArticle Review : Our Undemocratic Constitution1202 Words   |  5 PagesOur Undemocratic Constitution Essay Most Americans (including myself) consider the U.S. Constitution to be an exceptionally conservative entity. However, in Our Undemocratic Constitution, Levinson goes against the majority opinion and challenges the effectiveness of our constitution. He raises awareness towards some of the fundamental flaws within the American Constitution. Levinson emphasizes that the constitution is dysfunctional and undemocratic by drawing the reader’s attention to specific inadequaciesRead MorePower Of The State Organs Essay1739 Words   |  7 PagesPowers. 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Managing the Needs of Diverse Aboriginals Client Group Australia

Question: Discuss about the Managing the Needs of Diverse Client Group. Answer: Introduction The aboriginals of Australia are considered as the diverse population who are different from other population of Australia in culturally, linguistically also experimentally. The differences have affected their growth and they are considered a underprivileged group of the population of the country. They are deprived of the basic facilities offered by the government of the country. In the assignment, an attempt has been made to study the differences in receiving the basic facility by the Aborigine and Torres Strait Islander people of Australia with their counterparts like non-aborigine and Torres Strait Islander people of Australia in the context of health in particular and other facilities in general. At the level of health care facilities, it is very important to broaden the definition of health and it should include the physical, mental spiritual well-being of the whole communities. The health service is not related to the symptomatic treatment of the individual. The biomedical mo dels of health will focus on the diagnosis, treatment prevention so that the aboriginal Torres Strait Islander will get actual health benefits. Discrimination Discrimination in health between the aborigine and non-aborigine of Victoria has been identified by World Health Organisation. There have been great inequalities and discriminations between the aborigine and Torres Strait Islander people non-aborigine and Torres Strait Islander. This discrimination has been treated as the largest inequalities in the world (WHO, 2008). This has been studied that expectancy of the life of the aboriginal and Torres Strait Islander male population was estimated to be 10.6 years lower in comparison to the non-aboriginal and Torres Strait Islander and the life expectancy of the females of the aboriginal is also 9.5 years lower in comparison to the non-aboriginals. The aboriginals are suffering mostly from the non-communicable diseases such as cardiovascular disease, diabetes, mental disorder and the chronic respiratory diseases (AIHW, 2011). The aboriginal group of people suffered from massacres and infectious diseases since the colonisation of Australia and the number of the aboriginal and the Torres Strait Islander become very less gradually. These indigenous people became the most disadvantaged group. The poverty inequality experience their present state of life. The inequality in the status of the health has been identified and they are discriminated from the services (Landro, 2008). Impact of Racism In order to develop the social capital linkage of among the people of Australian Aborigine, racism has been a great barrier. The Aborigine people are considered as the victim of racism. The data conducted in the year 2011 about the experience of the impact of racism, this has been found that 70% of the Aborigine people suffer from racism issues for eight times in a year. This causes a high level of psychological disorder and distress. The impact of racism has been more on the people of Aborigine. It has been found that 30% of people avoid different situations in their everyday life (Hurley, et al., 2010). Racism has impacted a lot on the Aborigine. The people get victimised and that results in the degradation of the health in various ways. The Aborigine has mistrust on the heath services that leads to the reluctance in order to attend the mainstream of the health services provided to them. They do not immediately take the health care facility unless it a very grave medical problem (Vos, et al., 2007). Racism has also impacted in the discrimination in the employment market. The education system becomes unachievable for the Aborigine. The education system leads to a high rate of unemployment the possibility of attainment of educational level becomes lower. The psychological distress leads to the mental ill-health this also results in risk-taking behaviours of the health (Riezenman, 2008). The Aboriginal population of the country are deprived of the basic facilities. There is the prevalence of the poor health among this category of people in comparison to other counterparts like non-aborigine of the country. There is the difference between the cultural, linguistic and economic lifestyle of the people. The prejudice and racism and discrimination are considered as the most instrumental factors that obstruct the growth of the aborigine people of the country (Omachonu Einspruch, 2009). The aborigine of the Victoria is different from the non-origin of Victoria in the context of health facilities. There is the prevalence of depression anxiety more with the people of aboriginal in comparison to the non-origin of Victoria (Clark, 2008). The need of studying the causes of the depression among the people is one of the major concerns. Prejudice racism are considered as the two important determinants of the Aboriginal health in the country of Australia (Govindarajan, 2007). The se two are considered being associated with the high levels of the mental distress of the people of the Aboriginal in Australia Healthcare services and status of the Aboriginals The basic care and services level have not been extracted by the Aboriginal of the country. There are significant disparities between the two groups in the country and all the differences are based on the social determinants factors of the lifestyle risks. The differences found in between the two groups are that the Aboriginal people undergo the psychological distress, insecurity of food and financial stress (Grose, 2008). Due to the psychological distress the Aboriginal face negative impact of health. This has been found in different ways, both directly and indirectly. The depression, anxiety and the distress related to psychology become the factors of the poor health. There has been a witness of the unhealthy behaviour, coronary heart disease stroke among the non-Aborigine people of the country (Lehoux, et al., 2008). There is no food security and the nutritional intake of the population is very low. Due to the food insecurity, the group undergoes lots of problems both in socially and emotionally. There are social and emotional consequences. The distress, social exclusion, impaired learning also there is a loss of productivity found among the Aborigine in the country of Australia (Markwick A, 2011). Socio-economic status of the disadvantaged group The Aboriginal Victorian people are socio-economically disadvantaged in comparison to their counterparts. The Aborigine people have lower household income the employment rate of the people is very low. Due to the low income of the group it results in very less disposal earning to procure the food that is healthy. They are not able to engage themselves in the leisure activities. They can not make the social and physical activities. This leads to inadequate safety, housing and healthcare (Priest NC, 2011). There is also a low level of educational attainment of the people of the Aborigine. Due to lack of appropriate educational attainment, the Aborigine is at high risk of unemployment. The low level of income has limited the possibilities of getting a job for the disadvantaged group (Awofeso, 2011). The unemployment has put the job of the people at the risk and they do not get a living wage even. This contributes to the lower levels of the literacy on health. Disparities in socio capital There have been disparities in the context of socio capital between the advantages and disadvantages group of the country of Australia. With the Aboriginal Victorians, the levels of the socio-capital are very low. The study states that people with higher social capital get more advantage and it is associated with the higher and better health care. In that way, the Aboriginal Victorians get less scope to extract the facilities. The Aboriginal have been deprived of the social networks which offer them to get potential benefits of the education and economic that is well extracted from the white privileges and other non-Aborigine of the country (Varkey, et al., 2008). There are three types social capital. These three are the bonding, bridging linking. The bonding of the socio capital refers to the link or relationship of within the community of Aboriginal. The bridging socio-capital refers to the link between the advantage and disadvantage groups. The linking of the socio-capital refers to the relationships between the Aboriginal communities and with that of the formal the hierarchical institutions of power. Social Environment of the Aboriginal The social environment is affected by the length of the tenure of the neighbourhood. This is treated as the important indicator of the social environment of the Aboriginal that affects their growth. The Aborigine makes frequent movements and the frequent relocation has adversely affected their education. The group of people are deprived of the educational opportunities. They are deprived of the link to the community and as well as to the services. They are also deprived of the social support networks. That has adversely impacted on reducing the three major types of the social capital. Due to the low level of income, the Aborigine people experience unemployment. These people are obliged to relocate very frequently in order to find out jobs for the support of the housing that can be afforded. The Aboriginal Victorians get less help from their families. This shows that there is a very low level of bonding of social capital. Families are treated as the most important source of favour. The lack of the support of the family increases the individual vulnerability and this is a major issue during the crisis in the stress periods. This is more important during the time of health problems. The high levels of the social capital bonding have to be taken care by making more provisions for the health centres so that the Aborigine families will be supported. There have been no differences between the two groups in the group meeting. Both the Aboriginal non-aboriginal people access the community services resources. The Aboriginal people are more concerned about the community group. Healthcare practices for the Aborigine of Australia The Aborigine has the poor health. There are more possibilities of blood pressure and mental health-related problem among the people of the Aborigine. The people receive fewer services of the healthcare than the required amount. This has been found that Aborigine people have strong resistance for the use of mainstream health care services during the time when there is a failure of services that cannot address the cultural security (Maru YT, 2011). This brings a lot of difficulty and challenges in gaining the trust of the people of the aborigine. The people of Aborigine do not find the similar kind of mainstream health care services in comparison to the non-aborigine people of the country. The Aboriginal of the Australia receives less key medical investigation treatment when they are hospitalised for coronary heart disease and aborigine with lung or prostate cancer also receive less surgery. Lifestyle risk factors There is also a need of studying the lifestyle risk of the aborigine of the Australia. The smoking, consumption of excessive alcohol, heavy body weight, poor diet insufficient physical activity are also some of the factors that determine the poor health condition of the people of the aborigine (humanrights.gov,au, 2017). The evidence shows that poor health condition of the aborigine people of Australia accounts approximately 26% of the aggregate health loss due to the death, disease injury. The policies of the government focus more on the lifestyle risk factors than important social determinants. The health issues related to the smoking, obesity and the appropriate food intake are relatively small in comparison to the social determinants (Purdie, et al., 2010). Conclusion The focus on the mainstream preventive systems interventions should not remain around the factors of the lifestyle risk. There is a need of addressing the distress related to the psychology of the people of the aborigine. The focus on the improving the mental state is more effective than the improvement policies for the lifestyle risk factors. This will also contribute to the lifestyle risks factors such as smoking. Thus it will be more effective if more focus is given on the psychological distress and effective strategy is required to be framed for developing the standard of the aborigine (Pyett Waples, 2008). For the lifestyle risks, it is important to intervene health education social marketing. This will contribute to the development of the aborigine and they will be aware of the health disorder. There has been a negative societal belief that people of aborigine engage more in the excessive consumption of alcohol and that continues to aggravate prejudice racism. Thus it is ve ry important to formulate a strategy for the improvement of the health of aborigine of Australia. Bibliography AIHW, 2011. Life Expectancy and Mortality of Aboriginal and Torres Strait Islander people. AIHW, Canberra, Volume 51. Awofeso, N., 2011. Racism: a major impediment to optimal Indigenous health and health care in Australia.. Australian Indigenous Health Bull, Volume 11, pp. 1-13. Clark, D., 2008. Intel Takes Step Into Home Health Care.?. The Wall Street Journal, p. B3. Govindarajan, V., 2007. The Importance of Strategic Innovation.. [Online] Available at: https:/www.vijaygovindarajan.com/2006/03/the_importance_of_strategic_in.htm. [Accessed 15 02 2017]. Grose, T. K., 2008. Life Support Systems.. Prism Magazine.org,, pp. 35-39. humanrights.gov,au, 2017. Social determinants and the health of indigenous peoples in Australia - a human rights based approach.. [Online] Available at: https://www.humanrights.gov.au/news/speeches/social-determinants-and-health-indigenous-peoples-australia-human-rights-based] [Accessed 10 05 2017]. Hurley, C., Baum, F., Johns, A. Labonate, R., 2010. Comprehensive primary health care in Australia: findings from a narrative review of the literature.. Australas Med J, 1(2), pp. 147-152. Landro, L., 2008. The Hospital Is Watching You.?. The Wall Street Journal, p. D4. Lehoux, P. et al., 2008. ?What leads to better health care innovation? Arguments for an integrated policy-oriented research agenda.?. Journal of Health Services Research policy,, 4(13), pp. 251-254. Markwick A, H. S. V. L. A. Z., 2011. The Health and Wellbeing of Aboriginal Victorians. Victorian Population Health Survey 2008 supplementary report., Melbourne: State Government of Victoria, Melbourne. Maru YT, D. J., 2011. Supporting cross-cultural brokers is essential for employment among Aborignal people in remote Australia. Rangeland J, Volume 33, pp. 327-338. Omachonu, V. K. Einspruch, N. G., 2009. Innovation: Implications for Goods and Services.. International Journal of Innovation and Technology Management.. Priest NC, P. Y. G. W. C. S. S. S., 2011. Racism as a determinant of social and emotional wellbeing for Aboriginal Australian youth.. Medical Journal Australia, pp. 546-550. Priest N, P. Y. S. P. L. J., 2011. Racism and health among urban Aboriginal young people. BMC Public Health, Volume 11, pp. 568-. Purdie, N., Dudgeon, P. Walker, R., 2010. Working Together: Aboriginal and Torres Strait Islander Mental Health and Wellbeing Principles and Practice., Canberra: Department of Health and Ageing. Pyett, P. Waples, C., 2008. Challenging our own practices in indigenous health promotion and research. Health Promote Journal, Australia, Volume 19, pp. 179-183. Riezenman, M. J., 2008. Robots in Rehab.. The Institute, p. 6. Varkey, P., Horne, A. Bennet, K. E., 2008. Innovation in Health Care: A Primer.. American Journal of Medical Quality, Volume 23, pp. 382-388. Vos, T., Barker, B., Stanley, L. Lopez, A., 2007. The Burden of Disease and Injury in Aboriginal and Torres Strait Islander peoples 2003. 2007,, Brisbane: School of Population Health, The University of Queensland, Brisbane. WHO, 2008. Closing the Gap in a Generation: Health Equity through Action on the Social Determinants of Health, Geneva: World Health Organsisation.

The Russian Revolution

The Russian revolution refers to a series of events that took place in Russia in the 1917. The Russian revolution has remained one of the most notable events of recent history.Advertising We will write a custom essay sample on The Russian Revolution specifically for you for only $16.05 $11/page Learn More This revolution was important because it led to the successful struggle over democracy. Tandem to this, it also promoted the independence of the non-Russian people. This paper highlights the causes of the Russian revolution. This paper will also highlight the events that took place during the revolution. The Background and Cause of the Russian Revolution Different studies have shown that the Russian revolution was, initially, a political movement that brought down the monarchy of Tsar Nicholas II and made the establishment of a new government system a key problem of the revolution. Nicholas II came into power in 1894, when there were rapid changes in Ru ssia. Russia was going through hard times; therefore, it needed enthusiastic and ingenious administration to push it through the hard times. However, Nicholas and his government were unable to provide that. Nicholas lacked the ability to implement radical policies. His government, therefore, was ineffective, as it could not carter for the needs of the Russian citizens. As a result, there was a mass protest in Russia that led to the formation of different movements, which later on overthrew Nicholas II government. Events That Took Place During the February and October Revolution The February Revolution In February 1917, the Tsarist autocracy collapsed in the face of popular revolution and the withdrawal of elite support for the regime. Revolutionary historians agree that the events of this revolution took place in the environment of intense military setbacks during World War I. It was during this revolution when the members of Duma assumed control of Russia and formed the Provisional Government.Advertising Looking for essay on history? Let's see if we can help you! Get your first paper with 15% OFF Learn More Revolutionary historians reveal that, in the February revolution, the dual relationship of the Provision Government and the Petrograd soviet emerged spontaneously, and the government accepted it largely because it had no choice. The provisional Government represented the elite revolution while the newly revived Petrograd soviet represented the popular revolution. The dual relationship was formed because there were many strikes, rebellions and protest, particularly among workers, who were demanding for better pays and good working condition. Therefore, while the provisional Government was concentrating on the war with other countries, such as Germany, the Bolshevik party and other soviets were intensively campaigning against the conflict in the country. October Revolution Lenin overthrew the Russian Provisional Government during the October re volution. Lenin had observed that the Provisional Government was ineffective and was not addressing the needs of the majority. Therefore, on 25 October, he led many revolutionaries against this Government. This happened after the move by Lenin to reverse the stance taken under Kamenev and Stalin’s direction became successful. Stalin and Kamenev had taken over Pravda editorial board and adopted a conciliatory position towards the Provisional Government. However, Lenin, in his famous â€Å"April theses† rejected this move. He claimed that Kamenev and Stalin’s strategies were not effective. As was indicated in his April Theses, Lenin repudiated the Provisional Government and called for workers and peasants’ state, based on the soviets.Advertising We will write a custom essay sample on The Russian Revolution specifically for you for only $16.05 $11/page Learn More This revolution, therefore, overturned the Provisional Government and established the Soviet Union. Conclusion While the February revolution overturned Tsar Nicholas II and established a Provisional Government. The October revolution led to the establishment of the Soviet Union. Therefore, the two revolutions created a massive transformation in Russia. This essay on The Russian Revolution was written and submitted by user Vivienne Hull to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.