Thursday, November 28, 2019

Standing Waves on a String Essay Example

Standing Waves on a String Paper The objective of this experiment is to study the resonance modes of a stretched string by measuring directly in order to test the theoretical formula which relates the tension in the string to its length, mass, resonance frequency, and mode of vibration.  Definition of Standing Waves:  An oscillation pattern that has an outline which is resulting from the superposition of two identical waves traveling in opposite directions. Superposition occurs when two or more  waves are moving through a same linear medium at any point that the algebraic sum of the waves will be the resultant wave. Standing waves are produced from transverse sinusoidal waves having the same amplitude, frequency, wavelength, but traveling in the opposite directions in the same medium.  Sinusoidal Wave  Standing Waves at Fixed Ends:  When a string is put at two fixed ends and a tension is applied, waves are set up in the string as a superposition of waves that are reflected from both ends. Under a tension the string will oscillate and can reach several nodes of vibration. Nodes occur where there is not any amplitude, motion, in the string (wave). Antinodes occur where there is maximum amplitude and motion in the string (waves). The fixed ends of string are each nodes on the string. The distance between two nodes is equal to   where is the wavelength. The distance between a node and antinode is equal to 4. In the figure indicated below, the nodes and antinodes of the wave are labeled. We will write a custom essay sample on Standing Waves on a String specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Standing Waves on a String specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Standing Waves on a String specifically for you FOR ONLY $16.38 $13.9/page Hire Writer In a wave, the distance between the nodes (1) and antinodes (2) is given by the formula:  (1) X = n (? / 2) n = 0, 1, 2n, where n can be any real number  Ã‚  (2) X = n (?/ 4) n = 1, 3, 52n+1 where n can be any real number  In a string that is fixed on both ends, no vertical oscillation will take place at the points of nodes. However, for the rest of the points in the medium of the wave there will be the same frequency, and vertical displacements will differ for each point throughout the medium of the wave. The string can have several patterns of oscillation. Each pattern is unique in its own form, and there is a different frequency for each pattern. These different patterns of oscillation are referred to as normal modes or harmonics. The length L of the string between the fixed ends of each different pattern of oscillation is given by the formula:  It was observed that the mass of the string per unit of length () can be found by knowing the frequency of a string, tension and the mode of vibration. In this experiment the mass of the string per unit of length was measured with two different methods. In the first method, the mathematical formula was used to calculate the for different patterns of created standing waves. In this formula, slope can be found from the à ¯Ã‚ ¿Ã‚ ½ vs. n graph. Then the final result was found by calculating the average of obtaineds. The second method was measuring the directly by using the formula , where the mass of the string was determined by using the electrical balance. The average that was calculated in the first method was (4.84 0.05) 10-4 Kg/m, and The value of by using the direct measurement was 5.1010-4 Kg/m 1.03   10-6 Kg/m. These two results are close to reach other, but the result by using the second way is more accurate because of the fact that in the second method an electrical balance was used to measure the weight of the string which is relatively more accurate. Since the mass of the string per unit of length values obtained through the both methods had minimum differences, this experiment was relatively a success. When finding resonance frequencies it was also known that the 2nd mode of vibration should be double the fundamental frequency. For example3 = 1 and so on. Although the values obtained for higher modes of vibration were close to being multiples of one another, they were not exact. The causes of why these errors have occurred are due to a number of reasons. The air resistance could have affected the standing wave of the string which consequently affects the frequency of the wave. When the string reaches higher modes of vibration becomes more difficult to sense where the nodes are which will impact the frequency. There also could have been some errors in weighing and measuring the length of the string. To reduce the errors of this experiment it could have been performed several times.

Monday, November 25, 2019

Ultimately Responsible For His Downfall Essays - Free Essays

Macbeth/Ultimately Responsible For His Downfall Essays - Free Essays Macbeth/Ultimately Responsible For His Downfall William Shakespeares Macbeth is a tragedy about a war hero named Macbeth, who follows his ambition with evil and who is repaid with evil. Macbeth has influenced many works of literature through its conflicts between good and evil; heroes and villains; loyalty and treachery; and ambition and morality. In the story, Macbeth is ultimately responsible for the actions that lead to his fate. Although the witches predictions are responsible for influencing Macbeths thoughts, no one tells Macbeth to kill Duncan. Macbeth is responsible for putting power into the hands of Lady Macbeth and letting her influence him. Finally, Macbeth acknowledges his guilt of wrongdoing and is thereby responsible for his actions. Macbeths ambitions spur him on to follow an unstated yet clearly understood plan to kill Duncan. Although the witches predictions initiate Macbeths desire to become king, no one tells him to kill Duncan. When the second prophecy becomes a reality, Macbeth immediately thinks of murdering Duncan. I am of Cawdor: / If good, why do I yield to that suggestion / Whose image doth unfix my hair (I, iii, 143-145). For the first time in the story, we see a dark side to the brave and courageous Macbeth. Macbeth sees himself kill his ruler. Macbeth is horrified by the idea but his thoughts of going after his destiny still remain. Another example of Macbeths early thoughts of treachery occurs when Duncan formally names his son Malcom as his successor. Stars, hide your fires; / Let not light see my black and deep desires: / The eye wink at the hand! yet let that be, / (I, iv, 57-59). Macbeth is vexed at the Duncans choice of successor and wishes to overleap the situation with murder. No one helps Macbeths thoughts to prepare for the murder of Duncan. It is Macbeth and Macbeth only who is resp onsible for his own ambitions. Macbeth is eager to become king and wishes to reach his goal by any means, even if this means letting himself be influenced by others. Macbeth is responsible for putting power into the hands of Lady Macbeth and letting her influence him. Lady Macbeth tries to persuade Macbeth to kill Duncan but it is Macbeth who listens to her demands. This nights great business into my dispatch; / Which shall to all our nights and days to come / Give solely sovereign sway and masterdom (I, v, 75-77). Macbeth could have told his Lady to stop her plans. Instead, he lets himself be influenced. Macbeth puts power into the hands of Lady Macbeth by letting her arrange Duncans murder. Will it not be received, / When we have markd with blood those sleepy two / Of his own chamber, and used their very daggers, / That they have donet? (I, vii, 82-85). Macbeth agrees with the plan, determined to win the throne. If Macbeth truly did not want to commit evil, he could have refused his Ladys arrangements. Instead, Macbeth accepts the plans and goes further by asking Lady Macbeth to mock the time with fairest show (I, vii, 91). Although sometimes M acbeth wants the murder of Duncan, other times his thoughts show the contrary. Macbeth recognizes the thoughts of killing Ducan are immoral. Macbeths is conscious that is thoughts are evil, yet he does nothing to correct the situation. My thought, whose murder yet is but fantastical, / Shakes so my single state of man that function / Is smotherd in surmise; and nothing is / But what is not (I, iii, 149-152). If Macbeth were mentally deranged he would not be responsible for the outcome of his actions. However, Macbeth shows that he has a conscience and that he can differentiate good from evil. In privacy, Macbeth re-thinks his plans to kill Duncan. Macbeth, reveals that he knows what he is about to do is immoral, and that justice will be repay him with evil. We still have judgment here; that we but teach Bloody instructions, which being taught return To plague the inventor: this even-handed justice Commends the ingredients of our poisond chalice To our own lips. Hes here in double trust: First, as I am his kinsman and his subject, Strong both against the deed: then, as his

Thursday, November 21, 2019

Literary Analysis of The Tell-Tale Heart Essay Example | Topics and Well Written Essays - 1500 words

Literary Analysis of The Tell-Tale Heart - Essay Example This paper aims to analyze this marvellous and excellently written short story by discussing the characters, themes, symbols, textual details and imagery. The Tell Tale Heart may be categorized as a horror short story. The story is written in a first-person narrative style. The story opens with the explanation of horrified feelings and terror. These feelings if observed more closely are the remembrance of those terrifying events and things from the past (Quinn 1998, p. 394). The tell tale heart, is a story narrated by a mentally unstable and over suspicious man. It determines the mental conflicts within the narrator's mind but eventually ends up in murdering his innocent housemate, a pale blue eyed old man. Yet he claims his sanity and stability of mind and tries to bring logic in his cruel act. He kept on insisting about not being crazy and talks about his cold blooded and vicious planning of murder (Bloom 2002, pp. 70-71). He does try to satisfy himself by admitting killing the old man due to fear of his pale blue coloured eyes but he could not get rid of the guilt of his actions due to which he kept hearing old man's loud heart thumping sound and blows his own cover in front of the officers by confessing his crime. The narrator of The Tell Tale Heart seems and convincingly was a mentally unstable person who was dangerous and lost his control in his life, his obsession led to his destruction eventually. He felt hostile about his identity and wanted to stay anonymous. From the beginning he tried to protect his view about life as correct and his over imaginative and suspicious nature as peculiar sensitivity of sensing danger around. The narrator of â€Å"The tell tale heart† is a killer of an innocent man. The narrator of the story seemed well planned and gave acute time to his course in action, leaving no choice for the victim at all. The Tell Tale heart’s narrator waited for 7 nights and murdered the already scared man randomly on the 8th night. The factor of fear is even involved here; he could not stand the fear of his pale blue eyes. The tell tale heart’s narrator was a confused mind person who refused to be insane but did admit the fact that his actions were of a right cause and planned until he chopped the body and hid it under the floorboards. Due to his heighten sensitivity of listening to different sounds, he was unable to distinguish between the real and imaginative sounds so he confessed his crime and but did call the police officers villain as he could not distinguish between his own actions which were vicious. The Tell Tale Heart is the story which describes the feelings of conflict within a person. The use of unambiguous sentence structures and incompleteness of the narrations the author clearly illustrates the conflicts that are prevalent in the narrator’s mind. The unstable mental condition of the narrator is also obvious from the choice of words, unstructured sentences and improper expressing ways by the narrator. The story is tense and the narrator keeps this tension increasing gradually throughout the story until the end when the narrator accepts his sin of killing an innocent person. The story portrays violent act of murdering someone due to the inner obsession with the old man’s eyes. The insanity of the narrator is exposed through the extreme reaction of that obsession in killing him. The narrator does not have control over his actions and reactions which is also a predictor of an