Expressions for Velocity of Sound in Different Media

Expressions for Velocity of Sound in Different Media VELOCITY OF SOUND WAVE IN STRINGS: The velocity, V of a sound wave in strings is given by the expression. V= , = mass per unit length or linear density = Where r =radius of the wire, = density of material of the string or wire and T = tension VELOCITY OF SOUND WAVE IN SOLIDS The velocity, V of a sound wave in a solid is given by the expression: Where E = Young’s modulus of the material, = density of the solid or material. VELOCITY OF SOUND WAVE IN LIQUID The velocity, V of a sound wave in a liquid is given by the expression: Where B = Bulk Modulus of the liquid, = density of the liquid. VELOCITY OF SOUND WAVE IN A GAS The velocity, V of a sound wave in a gas is given by the expression Where M = molecular mass, R = molar gas constant, = ratio of the two specific heat capacities of a gas, P = pressure and = density VELOCITY OF WATER WAVE For deep water waves, V = For shallow water waves, V= For surface ripples, V = Where = wavelength, d = depth of water, = surface tension, =density of water, g = acceleration due to gravity. The Harmonic Oscillator Consider a simple pendulum consisting of a mass-less string of length ‘l’ and a point like object of mass ‘m’ attached to one end called the bob. Suppose the string is fixed at the other end and is initially pulled out at an angle from the vertical and released from rest from the figure below. Neglect any dissipation due to air resistance or frictional forces acting at the pivot. Diagram Note Is defined with respect to the equilibrium position. When, the bob has moved to the right. When, the bob has moved to the left. Coordinate system free-body force diagram Tangential component of the gravitational force is (1) Note The tangential force tends to restore the pendulum to the equilibrium value. If and if . The angle is restricted to the range . the string would go slack. The tangential component of acceleration is (2) Newton’s second law, , yields (3) T= (4) Simple Harmonic Motion Diagram The object is attached to one end of a spring. The other end of the spring is attached to a wall at the left in the figure above. Assume that the object undergoes one-dimensional motion. The spring has a spring constant k and equilibrium length (l). Note x>0 corresponds to an extended spring. x Therefore (5) Newton’s second law in the x-direction becomes (6) Equation 6 is called the simple harmonic oscillator equation. Because the spring force depends on the distance x, the acceleration is not constant. is constant of proportionality Energy in Simple Harmonic Motion Diagram (7) (8) It is easy to calculate the velocity for a given t value (9) And the energy associated with (10) A stretched or compressed spring has certain potential energy. Diagrams ( Hooke’s law) in order to stretch the spring from O to X one need to do work; the force changes, so we have to integrate: W= (11) Note This work is stored in the spring as its potential energy U. So, for the oscillator considered, the energy U is: U= (12) Therefore, the total energy is: (13) (14) (15) (16) Equation (16) is a famous expression for the energy of a harmonic oscillator. Note Where A is the maximum displacement. The total energy is constant in time(t), but there is continuous process of converting to kinetic energy to potential energy, and then K back to U. K reaches maximum twice every cycle (when passing through x=0)’ and U reaches maximum twice, at the turning point. Diagram0 In this graph time(t) was set to zero when the mass passed the x=0 point. Finally, we can use the principle of conservation of energy to obtain velocity for an arbitrary position by expressing the total energy position as (17) (18) (19) Example 1 A 200g block connected to a light spring for which the force constant is 5.00N/m is free to oscillate on a horizontal, frictionless surface. The block is displaced 5.00cm from equilibrium and released from rest. Find the period of its motion Determine the maximum speed of the block What is the maximum acceleration of the block? Express the position, speed and acceleration as function of time. Example 2 A 0.500Kg cart connected to a light spring for which the force constant is 20.0N oscillates on a horizontal, frictionless air track. Calculate the total energy of the system and the maximum speed of the cart if the amplitude of the motion is 3.0cm What is the velocity of the cart when the position is 2.00cm? Compute the kinetic energy and the potential energy of the system when the position is 2.00cm. Energy in waves Note Waves transport energy when they propagate through a medium. Consider a sinusoidal wave travelling on a string. The source of the energy is some external agent at the left end of the string, which does work in producing the oscillations. We can consider the string to be a non-isolated system. As the external agent performs work on the end of the string, moving it up and down, energy enters the system of the string and propagates along its length. Let us focus our attention on an element of the string of length and mass . Each element moves vertically with SHM. Thus, we can model each element of the string as simple harmonic oscillator (SHO), with the oscillation in the y direction. All elements have the same angular frequency and the same amplitude A. The kinetic energy K associated with a moving particle is: K= (20) If we apply this equation to an element of length and mass, we shall see that the kinetic energy of this element is (21) is the transverse speed of the element. If is the mass per unit length of the string, then the mass of the element of length is equal to. Hence, we can express the kinetic energy of an element of the string as (22) As the length of the element of the string shrinks to zero, this becomes a differential relationship: (23) Using the general transverse speed of a simple harmonic oscillator (24) (25) (26) If we take a snapshot of the wave at time t=0, then the kinetic energy of a given element is: (27) Let us integrate this expression over all the string elements in a wavelength of the wave, which will give us the total kinetic energy in one wavelength: (28) (29) (30) (31) (32) Note In addition to kinetic energy, each element of the string has potential energy associated with it due to its displacement from the equilibrium position and the restoring forces from neighbouring elements. A similar analysis to that above for the total potential energy in one wavelength will give exactly the same result: (33) The total energy in one wavelength of the wave is the sum of the potential energy and kinetic energy (34) (35) As the wave moves along the string, this amount the energy passes by a given point on the string during a time interval of one period of the oscillation. Thus, the power, or rate of energy transfer, associated with the wave is: (36) (37) (38) (39) Note This expression shows that the rate of energy transfer by a sinusoidal wave on a string is proportional to The square of the frequency The square of the amplitude And the wave speed. Put differently, Is the rate of energy transfer in any sinusoidal wave that is proportional to the square of its amplitude. Example A taut string for which is under a tension of 8.00N.How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0Hz and an amplitude of 6.00cm? STANDING WAVES Stationary Waves Stationary wave is produced if the waveform does not move in the direction of either incident or the reflected wave. Alternatively, it is a wave formed due to the superposition of two waves of equal frequency and amplitude that are travelling in the opposite directions along the string. Note You can produce stationary wave on a rope if you tie one end of it to a wall and move the free end up and down continuously. Amazingly the superposition of the incident wave and the reflected wave produces the stationary wave in the rope. A standing wave is produced when a wave that is travelling is reflected back upon itself. Antinode is an area of maximum amplitude Node is an area of zero amplitude. COMPARISON BETWEEN PROGRESSIVE (TRAVELLING) WAVE AND STATIONARY (STANDING) WAVE. Example3 A wave is given by the equation y= 10sin2. Find the loop length frequency, velocity and maximum amplitude of the stationary wave produced. solution

Psychology Project Racism Essay

Racism People see it every day across the world. A group of whites burn down a black , someone gets hurt or murdered from a racial insult, or fights break out at school or in public. These are the extremes of racism. Racism is definitely not a good thing; it’s a power that has taken over through the present daytime. What will the future bring for Racism? What are the main problems of racism? Can we get a hold on racism throughout the world or will we self-destruct in our own hate? Racism is everywhere, as much as today tries to hide it or say that we resolved it years ago. Racism is still all over the place. Definition of Racism: Racism is the belief that a particular race is superior or inferior to another, that a person’s social and moral traits are predetermined by his or her inborn biological characteristics. Racial separatism is the belief, most of the time based on racism, that different races should remain apart from one another. Racism has existed throughout human hist ory: It may be defined as the hatred of one person by another — or the belief that another person is less than human — because of skin color, language, customs, and place of birth or any factor that supposedly reveals the basic nature of that person. Prejudice: If someone is a racist they are of course, prejudiced. Prejudice is when someone doesn’t like someone else for the way they look.. It flies right over their heads – schools, the workplace, our community, our friend’s  house, even our homes. Racist or prejudice jokes are not harmless and it is a reality today. Racist jokes are just the start of it. Many people think the jokes are funny. Maybe they are, but they still hurt the people the jokes are about. Superiority: Superiority is a big part of racism. Every race thinks that they are superior to other ,that they are the best . The power issue may make the difference, that’s one of the main reasons. Each race thinks they are a better race.. Therefore, they fight and create violence to justify who is the greater race. But the reality is, that it doesn’t matter who you are or what color you are. Forms of Racism: †¢Individual Racism takes the form of individual attitudes, beliefs, value s and behaviors. Some examples of racist attitudes are racial prejudice, belittling, jealousy and bigotry. †¢Institutional or Systemic Racism takes the form of the practices, customs, rules and standards of organizations that unnecessarily disadvantage people because of their race, color or ethnicity. †¢Cultural Racism is the cultural values and standards that disadvantage people because of their race, color or ethnicity. . Bio-psycho-social-spiritual phenomenon of racism: Racism is the outward manifestation of an inward system. This system justifies power of position by placing a negative meaning and value on perceived or actual biological/cultural differences. This system gives biological differences, such as skin color, texture of the hair, physical features; or cultural differences, such as language, religion, ethnicity, or accent, a negative value and meaning. In real they are merely biological or cultural necessities. Thus, there is nothing wrong with the color black, brown or yellow. It is not skin color that forms the basis for discrimination, but the negative meaning and value given to the color of skin. â€Å"Color is neutral; it is the mind that gives it meaning.† Neither are women discriminated against because of their gender. If gender were the problem then the solution would also be to have a sex-change operation. But the problem is not gender but value systems.. Women are discriminated against because of the negative meaning and value given to their gender. How one defines a situation depends on how one perceives it. That’s the psycho pattern. The meaning that  people therefore give to their reality, whether or not true, causes people to behave in a manner that makes the original meaning actually come true. The interpretive meaning called â€Å"perception.†. The same goes with the spiritual dimension, the fourth factor. In order to justify such evil use of power, people will appeal to those moral systems which give them a sense of meaning, rightness, and ultimate value in life, their ideological belief systems, which serve as the highest authority in thei r lives, the moral basis of their existence. Like this the bio-psycho-social-spiritual framework works -and how it shapes our world. Common factors of Racism: †¢Color: Prejudice or discrimination in which human beings are treated differently based on the social meanings attached to skin color †¢Religion: Religious discrimination involves treating a person (an applicant or employee) unfavorably because of his or her religious beliefs. Religions, such as Buddhism, Christianity, Hinduism, Islam, and Judaism, but also others who have sincerely held religious, ethical or moral beliefs. †¢Gender: Granting or denying rights or privileges to a person based on their gender. No Boundaries: Victims and perpetrators of racial prejudice are not confined to any period in history, place, skin color, income group or other boundary. No one is immune! But the images we associate with the term racism depend largely on the part of the world in which we live. For instance, in different countries most commonly think of tension between whites and blacks, or increasingly, Hispanics and blacks or whites. Further back, though, other forms existed. Racism –different countries: Racism world-wide is manifested in every continent. In Europe, extreme racist groups have gained more and more acceptability in countries like France, Germany, and Austria. In Australia, the Aborigines have lost much of their land and have been the victim of extreme prejudice. Not only has Apartheid — legalized separation — been practiced in Australia, it has been a well-publicized condition in South Africa. Many African countries have endured long-term civil wars, some beginning shortly after that nation’s freedom from former colonial  countries. In Asia, Cambodians harbor extreme prejudices against the Vietnamese, and Chinese students have been forbidden access to higher education in Malaysia. In the Middle East, antagonism between the Israelis and the Palestinians continues to exist. Racism in Pakistan: In Pakistan people do face problem regarding racism and its done on the following bases. †¢Socio economic status †¢Gender †¢Color †¢Religion †¢Cast †¢Provincial Causes of racism: Major causes of racism common in all societies are: †¢Lack of self love †¢feeling of unworthiness †¢desire to feel superior †¢Fear of loss and displacement †¢lack of understanding †¢false perceptions †¢Ignorance, †¢Xenophobia †¢Brainwashing †¢ upbringing, †¢negative experiences with individuals of a given race, †¢negative images portrayed in media and societal stereotypes, †¢hate †¢ lack of education, †¢distorted thinking †¢ fear †¢Selfishness †¢Environmental Factors Effects of racism: It is said that â€Å" Racism always breaks a country and spoils a society.† The effects that are commonly observed are: †¢Self hate †¢ Suicide †¢Self harm issues †¢Eating disorders †¢Fear of going to school/public places (agoraphobia) †¢Bullying †¢Knife and gun crime †¢Panic attacks †¢Violence †¢hate crimes †¢inequality †¢inhumanity †¢intolerance †¢trade imbalance †¢depression †¢self loathing Racism and future: Today we are living in a load of social issues that we have to deal with and racism is one of them. People blame their faults and disappointments against society and the whole race in which they live in. but anyone can do good or excel if they put their mind to it. The future, when you hear the word – Racism – you start to think about advancing our technology and furthering science. You think of exploring new boundaries and seeing new places. A better world, but a worse world is what we see. The technology may improve as we go deeper into the next century, but what about the children of today that are responsible for the future? Right now, we are only hurting ourselves with racism and hate. We have taken many steps in controlling this disease, but like most diseases, they spread. Does God do favoritism? God is the  Creator of all the races—yellow, black and white (with brown and red). Each has strengths and gifts as well as weaknesses. For our better future it is important to finish this discrimination. If He has created everyone equally then who are we to judge? Who are we to complain? Who are we to discriminate? We being a Muslim, how can we do such a thing? Our religion has a clear concept about equality. It’s clearly written in the Holy book that no one is superior to another. Our God has created everyone equally. Its His choice how and what He do†¦ What Can We Do? â€Å"Racism isn’t born, it’s taugh† Where there is a problem, there is a solution. The only solution that seems to be found is to stop the hate. Dr. Martin Luther King said: â€Å"I have a dream that my four children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character. I have a dream today.† He had a dream.Its up to us that how and what we make a world without racism†¦. Changes: self-awareness†¦Ã¢â‚¬ ¦ Reengineering our attitudes about race means that we must examine ourselves. †¢Closely examine your values and beliefs; why do you think, believe, and behave toward others as you do. †¢Remember, one of the bases of prejudice is ignorance. Try not to ignore but to know other. †¢Measure your words carefully before you speak to others. †¢Try to be a human first . Society is formed by us †¦Ã¢â‚¬ ¦.society changes can be . †¢Do not tolerate prejudiced people, prejudiced talk, or racist action. †¢Give good literature, recommend films, lectures, meetings to your friends and family. †¢Write letters to newspapers, magazines, and TV sponsors giving your opinion on statements and actions that demean people. †¢Organize a cleanup or rebuilding campaign †¢Make an effort to support minority cultural events †¢ Make an effort to teach the value of equality and tolerance For Institutions-Effecting Change: †¢For institutions to change, their culture, vision, values, and ideology must change. All policies must be based around a single ideology. †¢Examine an institution’s deep belief and value systems †¢Hold training seminars in intercultural competence: †¢self-acceptance. †¢Put people to work and interact in interracial learning teams so as to develop positive attitudes and cross-ethnic friendships. †¢Make a commitment and act on it! Things You Can Do in the Schools: This can be done in a school or university setting. †¢sponsor panel discussions †¢awareness activities †¢cultural †¢projects that will promote cultural understanding and inclusiveness. †¢anti-racism education in your school’s curriculum †¢events relating to a variety of cultures.. †¢Ã¢â‚¬ Example: The â€Å"Book of Dreams† To sum it up: Figuring out what to do about the ugly reality of racism in our communities presents a difficult challenge. There is no single or easy set of instructions that will eliminate racism once and for all. Instead, it is something we must continually work against — choosing the strategies and actions that will be most effective in our own individual communities. In this resource, we’ve suggested such strategies and actions, and shown examples of how many of them have been put into practice in real communities. When you start deciding how to reduce racism in your own community, feel free to use any of these ideas, but also feel free to be creative and come up with your own solutions as well. Remember: â€Å"Rainbows aren’t just one color. They’re every single color. Be a rainbow. Enjoy all of the colors in the world.†

Lord of the Flies †An Alternative Ending Essay

Ralph looked up. He knew he was imagining things, and that had to stop. He focused on the essential things in life. Pigs. Sharpening sticks. Killing. Ralph stood and, set with a determination to fuel his desires, he exited the cave. He had been living in the cave for the past month. There was nothing left on his body save for a loincloth and markings on his body. He had been different from the other people since discovering the power. The power to kill the remaining survivors. Ralph walked down to the beach. The palm trees and sandy beaches were once a haven to the boys. Once. Now they were just obstacles in a war for both sides. Since Simon had died, and Piggy had disappeared, the â€Å"hunters† were fighting a war against Ralph. But luckily, none of the boys had been brave enough to kill Ralph ever since that fateful night. Ralph closed his eyes and let his memories take over. ***** It was dark that night. The boys had given up trying to chase down Ralph. Ralph had retreated to a cave, but he was too impatient to wait till the morning. He wanted to try to persuade the Hunters to change their allegiances to him. He was walking towards the sandy beach towards the rocky outcrop, taking his time, anything to delay persuading the hunters. His new found conscience was urging him along. â€Å"Go, Ralph! You might never get another chance like this!† â€Å"No!† Ralph cried! The conscience retorted, â€Å"What happened if you were bullied by a boy? Would you go confront the boy, or run away like a coward?† â€Å"This is different! These are boys, humans, like me!† yelped Ralph. â€Å"Just do it. Get it over with.† The conscience insisted. Ralph considered, â€Å"5 minutes only.† When he reached the rocky outcrop, Ralph decided to climb up the steep and potentially hurtful rock in secret for fear that the hunters would see him and not allow Ralph up to discuss matters. As he climbed to the top, the rock he was reaching for suddenly came loose and gravity took hold. Ralph prayed that the rock that hit the bottom wouldn’t make a sound. Luckily, it hit the waves and was dragged out by the tide. As Ralph struggled over the top, he saw 5 spears pointed at him, like deadly stakes. â€Å"Why are you here?† spat a savage. â€Å"I need to talk †¦ to all of you†¦Ã¢â‚¬  gasped Ralph, tired from climbing up the rock. â€Å"Get lost†¦ We don’t need to talk to you. You and us have nothing to do with each other!† snarled a savage. Roger, Ralph guessed from the intensity of the words. â€Å"It concerns about being rescued.† Ralph said with the ferocity of being a leader. â€Å"How ’bout we just kill you?† â€Å"Because I want to speak with Jack!† Ralph said the last three words ferociously, hurling himself over the edge. â€Å"What do you want?† spoke a quiet, bored voice from the darkness. â€Å"I have come to offer a treaty† â€Å"Get out.† Ralph’s anger, hatred and bitter emotions flowed out of his body in a rush of fury. â€Å"No.† he spoke with hatred about Piggy. â€Å"Get out before I kill you!!† roared Jack. thump. thump. thump. â€Å"Ignore th-!† screamed the conscience. The savages jeered â€Å"We’ll just roast you on a spit, just like a pig!† thump. Thump. THUMP. â€Å"KILL THEM!!!† shrieked the conscience with a sheer overwhelming force of hatred and cunning. Suddenly, Roger lunged for Ralph. Without warning, Ralph’s hands came up †¦ and found them on Roger’s throat. Ralph could feel this reborn conscience taking over his body†¦ and his mind. He was powerless to do anything or stop his hands. He felt the conscience growing bigger, and making him weaker. Soon, he was the conscience, and vice versa. â€Å"STOP!!!† Ralph screeched, â€Å"You’re meant to be my conscience, not take it over!† The conscience laughed â€Å"Too late, Ralph. You missed your chance. What goes around, comes around.† With a growing sense of horror, Ralph was watching, through his own eyes, the terror that unfolded. He felt the conscience becoming more and more confident, and he closed his hand on the neck. Of course, Roger struggled, however, he was no match for somebody who was strangling him with two hands. After a few seconds, Roger stopped moving. Subsequently, everybody in the vicinity could hear a sharp snap. Suddenly, panic broke out. Everybody but Ralph and Roger started screaming, and all of them were in a frenzy trying to escape – from the monster that had become Ralph. The horror of killing something worse than just a pig, about killing Roger simply for absolutely no reason, or that Ralph was always the one to uphold justice but was practicing otherwise. Feeling the blood gushing down his hands, the screams of the littleuns and biguns, the feeling of a cold hard body in his hands. His heart beat faster and faster, and he screamed. His head spun and he dry heaved. He was becoming more and more nauseated as he plummeted into the abyss. Claws grabbed him from below and tried to rip his skin. Blood materialized in his vision, but it wasn’t Ralph’s – it was Roger’s blood. He felt a searing pain on his arms and his head hurt so much†¦ ***** Ralph painfully opened his eyes. He wasn’t used to the amount of sunlight on his face – not anymore. He climbed up the rock leading to the savages’ hideout, intent on inflicting pain onto them, not caring about being rescued, about the honor of the fire, or the conch. For he, had become the Beast.

Sonnet 12 Essay - 934 Words

In modern times, youth and beauty is an image seen everywhere. For example, a Versace billboard, magazine ad, TV commercial, all of which displays images of beautiful people. But what happens when this beauty fades? Shakespeare in his 12th sonnet talks about his experience and fading beauty. The purpose of this poem is to encourage a young man to not lose his beauty to the ravages of time. In order to do this, one must reproduce so beauty will live. In the first quatrain, Shakespeare begins his meditation on the process of decay. He begins the poem with quot;Iquot;, which signals that Shakespeare will later give his own experience and account. The first object presented in this sonnet is a clock, which is to set the mood of the poem.†¦show more content†¦The idea Shakespeare tries to convey is that death takes everything. The violet was once beautiful and strong but as time passes, the violet will age and become frail. Shakespeare proceeds to speak of black sable curls hiding behind white. I have two observations about this line; the first being that as a man ages he will notice more white hairs on his head. The man will lose the vibrant black curls he once had as a young man. Second, Shakespeare may be implying to the young man that his hair too will become gray. Proceeding on to quatrain two, the poet continues to meditate by using images of decay; lofty trees, barren of leaves, white and bristly beard. Just as time progresses, day changes to night, and the young become old, summer becomes winter. In the warm weather, the trees were leafy and bountiful. They served as a canopy that sheltered herd of animals from the blazing sun (L.6). In winter, however, the lofty trees are now barren and stripped of their leaves. The outward appearance of the tree is pathetic and unsightly. The herd of animals will no longer seek shelter under the trees because they look lifeless. 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In the octet at the beginning of the poem Millay uses images that give a sense of transience and in the ending sestet of the sonnet she contrasts the sense of impermanenceRead MoreAnalysis Of St. Vincent Millay s Love Is Not All ( Sonnet Xxx )784 Words   |  4 PagesScansion and Analysis In Edna St. Vincent Millay’s â€Å"Love is Not All (Sonnet XXX),† the poem’s writer originally discredits the value of love, claiming that it is not essential because it does not support life; however, later Millay describes that love has some value. Love Is Not All is a Italian or Petrarchan sonnet, with fourteen lines of rhymed iambic pentameter. It has one stanza and it uses the rhyme scheme of a Shakespearean sonnet with three quatrains and a couplet. Each line contains betweenRead MoreThomas Grays Sonnet on the Death of Mr Richard West - an Analysis888 Words   |  4 PagesAnalysis – Poetry Sonnet on the Death of Mr. Richard West Thomas Gray 1. Communicative Situation, Theme and Figurative Speech a) Communicative Situation In the poem â€Å"Sonnet on the Death of Mr. Richard West† by Thomas Gray, the speaker can be identified by the use of personal pronouns of the first person singular â€Å"me† (l.1) and â€Å"I† (l.13), as well as the possessive pronoun â€Å"my† (l.7,8). It can be assumed that the speaker is male, since he mentions