Investigation in Acoustics of Wine Glasses

Investigation in Acoustics of Wine Glasses Introduction Resonance is extremely important in engineering and structural design. It directly relates to the way buildings, bridges and other structures sway with disturbance. In the case of wine glasses used in the Glass Harmonica invented in 1761 by Benjamin Franklin, varying the amount of water contained within the glass will vary the resonant frequency of the glass.[1] The purpose of the task is to investigate how frequency varies as height of water increases in a range of wine glass diameters before making recommendations regarding the ideal height and diameter for a given frequency. Collection of data is not a simple task as the height of water must be measured under great scrutiny and the wave produced needs to be constant in order to accurately record frequency. However, alterations have been made to the design of the experimental setup and will account for error through these avenues. For example, volume of water will be increased in increments and the heights measured as increasing volume is easier than increasing height. Once the collection and processing of data has been completed, recommendations can be made about the use, manufacture and efficiency of the Glass Harmonica. Essentially, the aim of the investigation is to scrutinize the Glass Harmonica and make recommendations about other structures through extrapolation. Background Theory A.P. French’s Formula While the Glass Harmonica is not the most commonly played instruments, the physics behind the way it works has been investigated a number of times. A journal paper describing the resonance on wineglasses was written by the late A.P. French, a Ph. D. and former President of the American Association of Physics Teachers.[2] In the paper, French derived a general formula for how the frequency of a singing wineglass could vary with the volume of water in the glass.[3] While French’s general formula was derived to describe the behaviour of ideal cylindrical glasses, it was found that any type of glass would approximately fit the formula. The formula is shown below: Resonant Frequency The main factor at play in the experimental investigation is resonant frequency. According to The Physics Classroom, â€Å"resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others.†[4] The system’s resonant frequency is the frequency where the system demonstrates its relative maximum amplitude, that is, the system exhibits greatest oscillation.[5] Figure 1 illustrates the resonant frequency of a general system. When its rim is rubbed by a moistened finger, the glass emits its resonant frequency. This is due to the crystals in the glass vibrating together which leads to one clear tone. As water is added to the glass, its resonant frequency changes. Resonance is important on a bigger scale than just the use of the Glass Harmonica. It relates to the way structures and other man-made objects oscillate in the outside world. For example, the Takoma Narrows Suspension Bridge in Washington collapsed due to wind that was gusting at the exact resonant frequency of the bridge.[6] Furthermore, acoustic resonance is important for instrument builders, as many instruments use resonators, for example, strings on a guitar, the length of a tube and the tension on a drum membrane. ‘Slip-Stick Effect’ The slip-stick phenomenon is defined as â€Å"the spontaneous jerking motion that can occur while two objects are sliding over each other.†[7] The friction between two surfaces leads to a ‘stick’ effect. The ‘stick’ effect is due to the applied force not being great enough to overcome the friction. However, as the force applied becomes greater, one of the surfaces begins to ‘slip’. When the surface ‘slips’, the force applied increases the second surface’s velocity. As the velocity increases, the frictional force increases too, until the frictional force is greater than that of the force applied, leading to another ‘stick’. The process continues and is named the ‘slip-stick effect’. The constant frictional jerking of the finger on the rim of the wine glass causes vibrations within the wall of the glass, leading to the oscillation of the glass and essentially, the tone produced. How does the glass vibrate? The glass begins to vibrate in a very special way when affected by the slip-stick phenomenon. When a moistened finger rubs along the glass, the rim begins oscillating into an elliptical shape due to its relatively elastic nature. Figure 2 portrays an exaggeration of the deformation of the rim of the glass. The rim’s shape oscillates between the two elliptical shapes shown several hundred times per second, producing an audible tone. Hypothesis In context of the investigation to be undertaken, it is hypothesised that as height of water increases in each of the three glasses, the frequency produced by each of the glasses will fall. The glass that can contain the greatest volume of water will reduce the least over the course of the experiment. Additionally, both other glasses will have a greater rate of frequency decrease. Under test conditions, it is predicted that as the glasses get fuller, the frequency reduction will become greater as the stem of the glass supports the glass, hindering it from vibrating as much. Correlation Using French’s formula, a linear relationship can be established between the frequency produced and the height of water: The value has been substituted into the equation as is built up of a number of constants representing the density of liquid, density of glass and glass thickness. Thus, plotting the following as and should present a linear relationship: Graphing the above equation should present a value as gradient. Ideal Graphs Ideally, the graphs should be as depicted below: The graph on the left depicts the reduction in frequency as height of water increases. The frequency slowly decreases in the first part before rapidly diminishing as height increases. The graph on the right has been manipulated using the raw data into a straight-line graph. Its gradient is the value. Method Clear the area and prepare the test glass and all other equipment used in experimentation. Place test glass flush on the desk before adopting silence in the room. Moisten index finger and begin softly rubbing the rim of the glass. Continue rubbing the rim of the glass until a standing wave appears. Begin recording sound in the room for a period of 10 seconds. If the standing wave is lost before the end of 10 seconds, stop the recording, delete the recording and repeat the procedure. If the standing wave continues, stop the recording at 10 seconds and stop rubbing the rim of the glass. Open the ANALYSE drop-down menu and select PLOT SPECTRUM. Trace along the graph until the peak is reached and record the frequency of the peak. Close the spectrum and delete the recording. Repeat 3 times. Measure out 20ml of water in a surgical syringe and add this liquid to the glass. Repeat the method outlined above. The setup of the experiment is pictured below: Results The results of the experiment are tabulated below: Raw Data Analysis Frequency Reduction (Hz) Glass 1 Glass 2 Glass 3 Linear Relationship Graphs Glass 1 Glass 2 Glass 3 ‘-Value’ for Different Glasses Error Analysis There are three forms of error in this experiment: Straight line error Measurement error Expected error Straight Line Error Measurement Error Measurement error can be calculated using the smallest division of every piece of equipment used to measure values. These are presented below: Vernier: 0.01mm Audacity’s Frequency Spectrum: 0.5 Hz Syringe: Negligible as the volume increments are not factored into the French’s formula Substituting various values into a rearranged version of French’s formula will find the various amounts of measurement error in each trial. The calculations are available below: Formula Glass 1 Therefore, measurement error is 0.52 Hz Glass 2 Therefore, measurement error is 0.52 Hz Glass 3 Therefore, measurement error is 0.52 Hz Expected Error Expected error can be found by substituting the value for various glasses into the manipulated formula used for the measurement error. The result of graphing this is the expected frequency decrease curve. The graphs are presented below: Glass 1 Glass 2 Glass 3 Average Difference Throughout the Duration of the Experiment Maximum Difference Discussion Interpretation of Results According to the results, the previously formulated hypothesis was proven correct. This is true since the frequency produced by each of the glasses fell as the height of water in each of the three glasses increased. Furthermore, Glass 2, which has the greatest capacity, also followed suit as it had the least frequency reduction. Moreover, stem of the glass acted as an excellent support for each of the glasses, ensuring that the raw graphed data followed a similar pattern to that expected. Another noteworthy trend was that the taller glass with the smallest capacity and radius had the greatest reduction in frequency. On the other hand, the shortest glass has the most stable and predictable decrease. Following French’s formula, justification can be made as to why the values didn’t increase as height of glass increased. The values of each of the glasses is made up of the following: Where the only variable factors between glasses are , radius of the glass and , thickness of the glass at water level. Thus, as increases, as with Glass 2, the value increases too. Naturally, as decreases, as with Glass 3, the value increases. Glass 3 had a higher value than Glass 1 simply due to the thin nature of the glass. Furthermore, Glass 2 had the highest value due to its large radius and almost spherical shape. While it was not a part of this experimental investigation at all, it must be noted that the glass with the greatest value produced the loudest sound, that is, the wave with the greatest amplitude. An interesting observation can be made through linking the nature of the glass, the value and the amplitude of the sound wave produced. As the glass becomes thinner and rounder, the value increases, which in turn, leads to a louder sound being produced. While the results obtained from the experiment are as were hypothesized, the outcome for the overall investigation is not as straightforward. The varied frequency decrease in the three glasses indicates which would be the most efficient in a Glass Harmonica with limited glasses. The dissimilarity also shows which glass would be able to play a specific small range more precisely than others. There are distinct advantages/disadvantages regarding high/low frequency reduction. The main advantage of the greater variation in frequency is that one can play a whole range of notes with only a few of the same type of glass. Additionally, the primary disadvantage of a great frequency decrease is that subtle changes in frequency cannot be easily made. A method of eliminating this disadvantage is simply using glasses that have a slower frequency reduction, such as Glass 2. However, this has its own advantages and disadvantages. The key advantage is that more specific notes in a small range can be played. Nevertheless, a disadvantage of this is that a large number of glasses need to be used, to play each specific note. In the real world, when a Glass Harmonica is used, a whole range of glasses are used due to the fact that more precise notes can be played in a while range of frequencies. This is what makes these instruments so expensive. Usually, the higher notes are played using thinner glasses and lower, deeper notes are played using rounder, wider glasses. Comparison with Expected Results The results obtained from conducting the experimental investigation are slightly deviant from those expected. It was expected that the values of the various glasses would be ordered the same way as the retention of frequency, and in the following order, from greatest to smallest frequency retention: The results obtained are divergent from these and follow the pattern as shown below: However, when comparing the data collected to the expected data, there is a trend on all the graphs as they all begin almost exactly on par with the expected results. Glass 3 had the greatest amount of difference from the expected graph. On average, every frequency measured was 32.25 Hz above or below the value it should have been at. In addition, Glass 2 began on par wuth the expected curve before reducing frequency slightly slower than expected. Nevertheless, the graphs were most consistent in both the beginning and end of each glass. As visible on the all three of the â€Å"difference in frequency† graphs, the true data began and ended almost exactly equal to the expected values. While results obtained were fairly accurate, the maximum difference between the expected values and true data in the three glasses was 68.04 Hz. Mistakes, Uncertainties, Errors While the investigation undertaken does not blatantly show evidence of any significant mistakes/errors, there are certainly a number of anomalies. For example, Glass 3 had a greater value than Glass 1 even though it has a minute radius. The values of the various glasses differ by only a small amount and the reduction of frequency differ by a fairly large amount. Both these must be duly noted. When analysing the raw data, there is a distinct anomalistic middle of all 3 of them. This is a clear indication of a large error caused by either measuring incorrectly each glass was further tested or simple inconsistencies in the peaks of Audacity’s frequency spectrum. Regardless, this error in all 3 experiments caused a deviance from the trendline. Unfortunately, it was not possible to avoid the influence of this error as values had to be calculated using those sections of data. There are a number of errors, caused by the method, which could have influenced the results. Firstly, when measuring the values of height of water and height of glass through the Vernier, there existed a chance of parallax error as the readings may be slightly deviant from the true values. Secondly, increasing volume of water instead of height of water for ease of measurement may not have had the correct effect and it may have been easier to simply measure heights in standard increments. Lastly, the standing wave may have broken at points, leading to the peaks of the frequency spectrum having an effect on the validity of the results, for example, the raw data and it’s difference to the expected data wou

Dramatic Monologue Essay

Black, black, black, that is all I can see. My cold, legs froze as I attempted to walk forward through the icy mist of the darkness. The darkness didn’t frighten me, my eyes focused on the beam of light that reflected of the tips of my shoes. To take my mind off the thought of being alone, I closed my eyes, and thought of what I could be here for. I continued to close my eyes but the idea of being alone made it hard to concentrate. The air around me felt lifeless, I clenched my fist, to give me the feeling as if someone else was here with here with me. I could only hear the accelerated speed at which my heart was beating. I have never felt like this since I was in high school, when I tried out for the school cross country team. My legs became stiffer than they were before. I bit my tongue and drew back a breath; relieving myself of the pain I could feel riding up the sides of my legs. The pain then became too much for myself to handle, I bit my tongue harder and harder as the pain got worse. Suddenly the pain was gone and the feeling of relief over whelmed me. I sat on the floor, the beam sat beside me; it seemed the light was my only source of comfort in dark. My memory of home, the place I once was, is hazy but kept me from losing touch with reality. The thoughts of Catherine waiting for me after work and Beatrice preparing dinner on the stove warmed my heart. But not all my memories were like this, they were once filled with fear and disappointment. Back home, in Sicily, I once had dreams of coming to America and living the American dream, which the people of my village used to speak of. But being the oldest it was hard to be positive, and living in house for 3 with a family of 8 didn’t help either. My village was poor because of the war so it made it harder for people to find work. While my father worked during the day, as a fisherman, I and the other children played in fields behind my house. The feelings I experienced playing in the fields were nothing like feelings I felt at home. I laid on my back, head pumping as though I had been trying to study last minute for a test. The gash on my chest, which was oddly shaped like an ear, was stinging under the pressure of my shirt. I tried to remember what I had thought about before the pain kicked in. The dream of me dying felt so real†¦. there was me on the floor surrounded by people I knew †¦Ã¢â‚¬ ¦ I thought harder†¦. there people from around the block, and some I have never seen before†¦.. and the warm voice†¦. the voice of Beatrice stood out from the rest. I thought harder and tried to remember what was going on †¦.. all I could remember was the sound of people screaming my name and a pool of blood, that was spread from the bottom of my stairs to the side of the pavement. I was then clear of what I was here for. I stood up, tore the picture of Katie I had around my neck and tossed it into the light. The light then vanished and it became completely dark. It was her †¦ Katie†¦ she is the reason why I’m here. It was wrong, the feelings I felt for her that is the reason I’m here. I was supposed to look after her not fall in love with her. The jealousy I felt when I saw her with Rodolfo drove me to become this way it was the thought of her being taken away from me really got to me. But I can’t put the blame on him. It was me. All me. I laid back on my back, closed my eyes and laid completely still. If I was to wake and find myself in the pits of hell I wouldn’t be surprised. But if I were to wake up, wrapped in the arms of my love, I would take my own life then and there. So that my family could live on happy and not have to worry about how I could screw up their lives. This is the gift I give to you, my family a life to live without the thought of me.

The Unexposed Secret of Questbridge Essay Samples

The Unexposed Secret of Questbridge Essay Samples The Importance of Questbridge Essay Samples Nobody is supposed to take a person's life since they didn't give life. If you don't feel as if you have enough time to write essays by yourself, we will assist you, any instance of the day, seven days per week. To steer clear of these, take time to consider about what makes you unique. Unfortunately, there'll never be enough space to inform your complete story. It is possible to come across narrative essay examples wherever you locate a great story. The way the topic affected you'll play a huge part in the way you will write your essay. Make certain to read your essay and make certain it is logical. Writing a high school essay if you've got the tips about how to do essay effectively. Our aim is to supply you with a professionally written essay on this issue you require. It is far better read through several narrative essay examples in order to get the one which best matches the format which you're writing your essay in. Questbridge Essay Samples Secrets Remember that a misspelled word may itself be the right spelling of a different word your spell check may not catch these kinds of errors. For instance, some of them just have zero time to deal with dozens of assignments that keep bombarding from every side. You have to find the most suitable resources for your essay along with patience when finding the proper inspiration to write. An essay with major errors or even consistent minor mistakes will make it hard for readers to concentrate on the story you're trying to let them know about yourself. If your aim is to pass the GED, then you have to learn about test-taking strategies. Admitted students who choose to enroll will be asked to submit official score r eports. Have a look at our very first instance of how to answer Why Northwestern here. Scholarship college freshman most essential part of narrative writing. It doesn't need to be explicit you don't need to explain how every paragraph is related to the typical thread. There's no fixed number of body paragraphs for an essay and a great paragraph has one central point. This is done most effectively when there's a frequent thread that's concluded at the conclusion of your essay. You need to read the example answers to acquire ideas about what are good forms of answers and what are bad varieties of answers. First and foremost it's vital to ensure that you comprehend the essay question fully and your essay answers each part of the question adequately. First of all, we suggest narrowing your focus to a couple important ideas or topics. Sometimes you might not know that you've strayed off topic. Also, try to remember that a topic does not need to be especially thrilling to be unique. This experience can help you make strategic decisions about which subject lessons you must learn. Let's say your topic is to explore an extracurricular activity that has played a massive effect on your life. The progression of the disease differs for each patient and at times contributes to an early death, but almost always results in big disabilities. The reasons might be absolutely different. When you finish the Common Application, you are going to select people to offer your recommendations. Untimely delivery It's mostly marked that these services are difficult to rely upon because of their untimel y shipping. Adoption is an alternate solution. It is a better alternative in this case.

The Philosophy of Avenue Q Lyrics - An Analysis

In traditional Punch and Judy shows, the anti-hero Punch insults, pesters, and beats his fellow characters, much to the delight of the audience. Punch and Judy shows were a glorious display of political incorrectness. Londons Covent Garden features a large plaque on the walls outside of St. Pauls church announcing it as the location of the the famous Punch and Judy Shows performed during the 1600s. Thats right, Shakespeares plays competed with puppet shows. Today, the tradition of puppets delivering obnoxiousness and social commentary continues with Avenue Q. The Origin of Avenue Q The music and lyrics of Avenue Q were created by Robert Lopez and Jeff Marx. The two young composers met in the late 90s while involved in the BMI Lehman Engel Musical Theater Workshop. Together, they have written songs for Nickelodeon and the Disney Channel. However, they wanted to create a puppet-friendly show that was strictly for adults. With the help of playwright Jeff Whitty and director Jason Moore, Avenue Q was born—and has been a hit Broadway show since 2003. Sesame Street for Grown Ups Avenue Q could not exist without Sesame Street, the long running childrens show that teaches kids letters, numbers, and practical life-lessons. The premise of Avenue Q is that adolescents grow up without learning the truth of adult life. Like the puppet protagonist Princeton, many new grown-ups experience anxiety and confusion when entering the Real World. Avenue Q offers many practical life-lessons, too. School / College Doesnt Prepare You for Real Life With songs like What Do You Do with a B.A. in English? and I Wish I Could Go Back to College, Avenue Q lyrics portray higher education as an extended stay in the carefree land of adolescence. Princetons main conflict is that he is drifting through life, trying to discover his true purpose. One would hope that college would establish this sense of purpose (or at least a sense of self-sufficiency), but the puppet croons to the contrary: I cant pay the bills yetCause I have no skills yet.The world is a big scary place. The ensemble of characters, both human and monster, wistfully recall the days when they lived in a dormitory with a meal plan, a time when, if things got too difficult, they could just drop a class or seek an academic advisors guidance. This criticism of the education system is nothing new. Philosopher John Dewey believed that public education should proactively prepare students with useful critical thinking skills rather than just facts from books. Modern day critics such as John Taylor Gatto further explore the failures of compulsory learning. His book, Dumbing Us Down: The Hidden Curriculum of Compulsory Schooling, explains why many people feel the same social/intellectual impotence lyrically expressed in Avenue Q. The Freedom to Find Our Own Purpose Princeton decides that he should seek his purpose in life. At first his quest for meaning is guided by superstition. He finds a penny from the year he was born and considers it a supernatural sign. However, after a couple a false-start relationships and dead-end jobs, he realizes that discovering ones purpose and identity is a difficult, never-ending process (but an invigorating process if one chooses to make it so). Steering away from lucky pennies and mystical signs, he becomes more self-reliant by the musicals conclusion. Princetons resolution to find his own path would be smiled upon by existential philosophers.The main component of existentialism is the assumption that humans are free to determine their own sense of personal fulfillment. They are not bound by gods, destiny, or biology. When Princeton laments, I dont even know why Im alive, his girlfriend Kate Monster replies, Who does, really? A rather existential response. There Are No Selfless Deeds Perhaps there are good deeds, according to Avenue Q, but there seem to be no purely selfless deeds. When Princeton decides to generate money for Kates School for Monsters, he does so because it feels good to help others. But he also hopes to win her back, thereby rewarding himself. The lyrics from Money Song explain: Every time you do good deedsYoure also serving your own needs.When you help othersYou cant help helping yourself. This bit of wisdom would please Ayn Rand, author of controversial classics such as Atlas Shrugged and The Fountainhead. Rands concept of objectivism specifies that ones purpose should be the pursuit of happiness and self-interest. Therefore, Princeton and the other characters are morally justified in performing good deeds, so long as they do so for their own benefit. Schadenfreude: Happiness at the Misfortune of Others If youve ever felt better about your life after watching the miserable guests on a Jerry Springer rerun, then youve probably experienced schadenfreude. One of the Avenue Q characters is Gary Coleman, a real-life child star whose irresponsible family squandered his millions. In the show, Coleman explains that his personal tragedies make others feel good. Ironically, it becomes a virtue (or at least a public service) to be a wretched failure or a victim of calamity. (By the way, this would would be frowned upon by Ayn Rand). Characters such as Coleman and the recently homeless puppet, Nicky, improve the self-esteem of the mediocre masses. Basically, these lyrics make you feel better about being a loser! Heterosexual puppet Nicky tries to help the sexually repressed puppet Rod come out of the closet. He sings: If you were queerI’d still be hereYear after yearBecause you’re dear to me. A bit more devious (in a good way) is the song â€Å"Everyone’s a Little Bit Racist.† During this number, the characters proclaim that â€Å"everyone makes judgments based on race,† and that if we accepted this â€Å"sad but true† premise society could â€Å"live in harmony.† The song’s argument might be specious, but the audience’s self-deprecating laughter throughout the musical number is very telling. Everything in Life Is Only For Now â€Å"Spiritual† books such as Eckhart Tolle’s have been asking readers to focus on the present, to embrace â€Å"The Power of Now.† Does this message anger historians? Either way, this seemingly modern concept stems from ancient times. Long ago, Buddhists described the impermanence of existence. Avenue Q follows the Buddhist path in its final song, â€Å"For Now.† These cheerful Avenue Q lyrics remind the audience that all things must pass: Each time you smileIt’ll only last a while. Life may be scaryBut it’s only temporary. In the end, despite its zaniness and crude jokes, Avenue Q delivers a sincere philosophy: We must appreciate joy and endure any sadness we currently experience while acknowledging that all is fleeting. Learning this lesson can makes life seem all the more precious. Why Puppets? Why use puppets to deliver the message? As Lopez explained in a New York Times interview, â€Å"Theres something about our generation that resists actors bursting into song on the stage. But when puppets do it, we believe it.† Whether it’s Punch and Judy, Kermit the Frog, the cast of Avenue Q, puppets make us laugh. And while we are laughing, we usually wind up learning at the same time. If a regular human were on stage singing a preachy song, many folks would probably ignore the message. The creators of Mystery Science Theater 3000 once explained, â€Å"You can say things as a puppet that you can’t get away with as a human.† That was as true for MST3K as it was for the Muppets. It was true for the bombastically cruel Punch, and it is eloquently true for the ever-insightful show Avenue Q.