Forced Vibrations Of Simple Systems English Language Essay

Forced Vibrations Of Simple Systems English Language Essay Mechanical, acoustical, or electrical vibrations are the sources of sound in musical instruments. Some familiar examples are the vibrations of strings violin, guitar, piano, etc, bars or rods xylophone, glockenspiel, chimes, and clarionet reed, membranes (drums, banjo), plates or shells (cymbal, gong, bell), air in a tube (organ pipe, brass and woodwind instruments, marimba resonator), and air in an enclosed container (drum, violin, or guitar body). In most instruments, sound production depends upon the collective behavior of several vibrators, which may be weakly or strongly coupled together. This coupling, along with nonlinear feedback, may cause the instrument as a whole to behave as a complex vibrating system, even though the individual elements are relatively simple vibrators (Hake and Rodwan, 1966). In the first seven chapters, we will discuss the physics of mechanical and acoustical oscillators, the way in which they may be coupled together, and the way in which they radiate sound. Since we are not discussing electronic musical instruments, we will not deal with electrical oscillators except as they help us, by analogy, to understand mechanical and acoustical oscillators. According to Iwamiya, Kosygi and Kitamura (1983) many objects are capable of vibrating or oscillating. Mechanical vibrations require that the object possess two basic properties: a stiffness or spring like quality to provide a restoring force when displaced and inertia, which causes the resulting motion to overshoot the equilibrium position. From an energy standpoint, oscillators have a means for storing potential energy (spring), a means for storing kinetic energy (mass), and a means by which energy is gradually lost (damper). vibratory motion involves the alternating transfer of energy between its kinetic and potential forms. The inertial mass may be either concentrated in one location or distributed throughout the vibrating object. If it is distributed, it is usually the mass per unit length, area, or volume that is important. Vibrations in distributed mass systems may be viewed as standing waves. The restoring forces depend upon the elasticity or the compressibility of some mater ial. Most vibrating bodies obey Hookes law; that is, the restoring force is proportional to the displacement from equilibrium, at least for small displacement. Simple harmonic motion in one dimension: Moore (1989) has mentioned that the simplest kind of periodic motion is that experienced by a point mass moving along a straight line with an acceleration directed toward a fixed point and proportional to the distance from that point. This is called simple harmonic motion, and it can be described by a sinusoidal function of time, where the amplitude A describes the maximum extent of the motion, and the frequency f tells us how often it repeats. The period of the motion is given by That is, each T seconds the motion repeats itself. Sundberg (1978) has mentioned that a simple example of a system that vibrates with simple harmonic motion is the mass-spring system shown in Fig.1.1. We assume that the amount of stretch x is proportional to the restoring force F (which is true in most springs if they are not stretched too far), and that the mass slides freely without loss of energy. The equation of motion is easily obtained by combining Hookes law, F = -Kx, with Newtons second law, F = ma =. Thus, and Where = The constant K is called the spring constant or stiffness of the spring (expressed in Newtons per meter). We define a constant so that the equation of motion becomes This well-known equation has these solutions: ) Figure 2.1: Simple mass-spring vibrating system Source: Cremer, L., Heckl, M., Ungar, E (1988), Structure-Borne Sound, 2nd edition, Springer Verlag Figure 2.2: Relative phase of displacement x, velocity v, and acceleration a of a simple vibrator Source: Campbell, D. M., and Greated, C (1987), The Musicians Guide to Acoustics, Dent, London or From which we recognize as the natural angular frequency of the system. The natural frequency fo of our simple oscillator is given by and the amplitude by or by A; is the initial phase of the motion. Differentiation of the displacement x with respect to time gives corresponding expressions for the velocity v and acceleration a (Cardle et al, 2003): , And . Ochmann (1995) has mentioned that the displacement, velocity, and acceleration are shown in Fig. 1.2. Note that the velocity v leads the displacement by radians (90), and the acceleration leads (or lags) by radians (180). Solutions to second-order differential equations have two arbitrary constants. In Eq. (1.3) they are A and; in Eq. (1.4) they are B and C. Another alternative is to describe the motion in terms of constants x0 and v0, the displacement and velocity when t =0. Setting t =0 in Eq. (1.3) gives and setting t = 0 in Eq. (1.5) gives From these we can obtain expressions for A and in terms of xo and vo: , and Alternatively, we could have set t= 0 in Eq. (1.4) and its derivative to obtain B= x0 and C= v0/ from which . 2.3 Complex amplitudes According to Cremer, Heckl and Ungar (1990) another approach to solving linear differential equations is to use exponential functions and complex variables. In this description of the motion, the amplitude and the phase of an oscillating quantity, such as displacement or velocity, are expressed by a complex number; the differential equation of motion is transformed into a linear algebraic equation. The advantages of this formulation will become more apparent when we consider driven oscillators. This alternate approach is based on the mathematical identity where j =. In these terms, Where Re stands for the real part of. Equation (1.3) can be written as, Skrodzka and Sek (2000) has mentioned that the quantity is called the complex amplitude of the motion and represents the complex displacement at t=0. The complex displacement is written The complex velocity and acceleration become Desmet (2002) has mentioned that each of these complex quantities can be thought of as a rotating vector or phase rotating in the complex plane with angular velocity, as shown in Fig. 1.3. The real time dependence of each quantity can be obtained from the projection on the real axis of the corresponding complex quantities as they rotate with angular velocity Figure 2.3: Phase representation of the complex displacement, velocity, and acceleration of a linear oscillator Source: Bangtsson E, Noreland D and Berggren M (2003), Shape optimization of an acoustic horn, Computer Methods in Applied Mechanics and Engineering, 192:1533-1571 2.4 Continuous systems in one dimension Strings and bars This section focuses on systems in which these elements are distributed continuously throughout the system rather than appearing as discrete elements. We begin with a system composed of several discrete elements, and then allow the number of elements to grow larger, eventually leading to a continuum (Karjalainen and Valamaki, 1993). Linear array of oscillators According to Mickens (1998) the oscillating system with two masses in Fig. 1.20 was shown to have two transverse vibrational modes and two longitudinal modes. In both the longitudinal and transverse pairs, there is a mode of low frequency in which the masses move in the same direction and a mode of higher frequency in which they move in opposite directions. The normal modes of a three-mass oscillator are shown in Fig. 2.1. The masses are constrained to move in a plane, and so there are six normal modes of vibration, three longitudinal and three transverse. Each longitudinal mode will be higher in frequency than the corresponding transverse mode. If the masses were free to move in three dimensions, there would be 3*3 =9 normal modes, three longitudinal and six transverse. Increasing the number of masses and springs in our linear array increases the number of normal modes. Each new mass adds one longitudinal mode and (provided the masses move in a plane) one transverse mode. The modes of transverse vibration for mass/spring systems with N=1 to 24 masses are shown in Fig. 2.2; note that as the number of masses increases, the system takes on a wavelike appearance. A similar diagram could be drawn for the longitudinal modes. Figure 2.4: Normal modes of a three-mass oscillator. Transverse mode (a) has the lowest frequency and longitudinal mode (f) the highest Source: Jaffe, D and Smith, J (1983), Extension of the Karplus-Strong plucked string algorithm, CMJ 7:2, 43-45 Figure 2.5: Modes of transverse vibration for mass/spring systems with different numbers of masses. A system with N masses has N modes Source: Beranek L (1954), Acoustics. McGraw-Hill, New York As the number of masses in our linear system increases, we take less and less notice of the individual elements, and our system begins to resemble a vibrating string with mass distributed uniformly along its length. Presumably, we could describe the vibrations of a vibrating string by writing N equations of motion for N equality spaced masses and letting N go to infinity, but it is much simpler to consider the shape of the string as a whole (Bogoliubov, and Mitropolsky, 1961). Standing waves Consider a string of length L fixed at x=0 and x= L. The first condition y (0,t) = 0 requires that A = -C and B = -D in Eq. (2.9), so Using the sum and difference formulas, sin(xy) = sin x cos y cos x sin y and cos(x Y = 2A sin kx cos = 2[A cos The second condition y (L, t) =0 requires that sin kL =0 or . This restricts to values Thus, the string has normal modes of vibration (Obrien, Cook and Essl, 2001): These modes are harmonic, because each fn is n times f1= c/2L. The general solution of a vibrating string with fixed ends can be written as a sum of the normal modes: and the amplitude of the nth mode is. At any point Alternatively, the general solution could be written as Where Cn is the amplitude of the nth mode and is its phase (Keefe and Benade, 1982). 2.5 Energy of a vibrating string McIntyre et al (1981) has mentioned that when a string vibrates in one of its normal modes, the kinetic and potential energies alternately take on their maximum value, which is equal to the total energy. Thus, the energy of a mode can be calculated by considering either the kinetic or the potential energy. The maximum kinetic energy of a segment vibrating in its nth mode is: Integrating over the entire length gives The potential and kinetic energies of each mode have a time average value that is En/2. The total energy of the string can be found by summing up the energy in each normal mode: Plucked string: time and frequency analyses According to Laroche and Jot (1992) when a string is excited by bowing, plucking, or striking, the resulting vibration can be considered to be a combination of several modes of vibration. For example, if the string is plucked at its center, the resulting vibration will consist of the fundamental plus the odd-numbered harmonics. Fig. 2.5 illustrates how the modes associated with the odd-numbered harmonics, when each is present in the right proportion; add up at one instant in time to give the initial shape of the center-plucked string. Modes 3,7,11, etc., must be opposite in phase from modes, 1, 5, and 9 in order to give maximum displacement at the center, as shown at the top. Finding the normal mode spectrum of a string given its initial displacement calls for frequency analysis or fourier analysis. Figure 2.6: Time analysis of the motion of a string plucked at its midpoint through one half cycle. Motion can be thought of as due to two pulses travelling in opposite directions Source: Gokhshtein, A. Y (1981), Role of air ¬Ã¢â‚¬Å¡ow modulator in the excitation of sound in wind instruments, Sov. Phys. Dokl. 25, 954-956 Since all the modes shown in Fig.2.6 have different frequencies of vibration, they quickly get out of phase, and the shape of the string changes rapidly after plucking. The shape of the string at each moment can be obtained by adding the normal modes at that particular time, but it is more difficult to do so because each of the modes will be at a different point in its cycle. The resolution of the string motion into two pulses that propagate in opposite directions on the string, which we might call time analysis, is illustrated in Fig.2.6 if the constituent modes are different, of course. For example, if the string is plucked 1/5 of the distance from one end, the spectrum of mode amplitudes shown in Fig. 2.7 is obtained. Note that the 5th harmonic is missing. Plucking the string  ¼ of the distance from the end suppresses the 4th harmonic, etc. (Pavic, 2006). Roads (1989) have mentioned that a time analysis of the string plucked at 1/5 of its length. A bend racing back and forth within a parallelogram boundary can be viewed as the resultant of two pulses (dashed lines) travelling in opposite directions. Time analysis through one half cycle of the motion of a string plucked one-fifth of the distance from one end. The motion can be thought of as due to two pulses moving in opposite directions (dashed curves). The resultant motion consists of two bends, one moving clockwise and the other counter-clockwise around a parallelogram. The normal force on the end support, as a function of time, is shown at the bottom. Each of these pulses can be described by one term in dAlemberts solution [Eq. (2.5)]. Each of the normal modes described in Eq. (2.13) has two coefficients and Bn whose values depend upon the initial excitation of the string. These coefficients can be determined by Fourier analysis. Multiplying each side of Eq. (2.14) and its time derivative by sin mx/L and integrating from 0 to L gives the following formulae for the Fourier coefficients: By using these formulae, we can calculate the Fourier coefficients for the string of length L is plucked with amplitude h at one fifth of its length as shown in figure.2.8 time analysis above. The initial conditions are: y (x,0) = 0 y (x,0) = 5h/L .x, 0 x L/5, = 5h/4 (1-x/L), L/5 x L. Using the first condition in first equation gives An=0. Using the second condition in second equation gives = = The individual Bns become: B1 =0.7444h, B2 =0.3011h, B3 =0.1338h, B4 =0.0465h, B5 =0, B6= -0.0207h, etc. Figure 2.7 shows 20 log for n=0 to 15. Note that Bn=0 for n=5, 10, 15, etc., which is the signature of a string plucked at 1/5 of its length (Shabana, 1990). Bowed string Woodhouse (1992) has mentioned that the motion of a bowed string has interested physicists for many years, and much has been written on the subject. As the bow is drawn across the string of a violin, the string appears to vibrate back and forth smoothly between two curved boundaries, much like a string vibrating in its fundamental mode. However, this appearance of simplicity is deceiving. Over a hundred years ago, Helmholtz (1877) showed that the string more nearly forms two straight lines with a sharp bend at the point of intersection. This bend races around the curved path that we see, making one round trip each period of the vibration. According to Chaigne and Doutaut (1997) to observe the string motion, Helmholtz constructed a vibration microscope, consisting of an eyepiece attached to a tuning fork. This was driven in sinusoidal motion parallel to the string, and the eyepiece was focused on a bright-colored spot on the string. When Helmholtz bowed the string, he saw a Lissajous figure. The figure was stationary when the tuning fork frequency was an integral function of the string frequency. Helmholtz noted that the displacement of the string followed a triangular pattern at whatever point he observed it, as shown in Fig.2.7: Figure 2.7: Displacement and Velocity of a bowed string at three positions along the length: a) at x = L/4; b) at the center, and c) at x = 3L/4 Source: Smith, J (1986), Efficient Simulation of the Reed-Bore and Bow-String Mechanisms, Proc. ICMC, 275-280 The velocity waveform at each point alternates between two values. Other early work on the subject was published by Krigar-Menzel and Raps (1891) and by Nobel laureate C. V. Raman (1918). More recent experiments by Schelleng (1973), McIntyre, et al. (1981). Lawergren (1980), Kondo and Kubata (1983), and by others have verified these early findings and have greatly added to our understanding of bowed strings. An excellent discussion of the bowed string is given by Cremer (1981). The motion of a bowed string is shown in Fig.2.8: Figure 2.8: Motion of a bowed string. A) Time analysis of the motion showing the shape of the string at eight successive times during the cycle. B) Displacement of the bow (dashed line) and the string at the point of contact (solid line) at successive times. The letters correspond to the letters in (A) Source: McIntyre, M., Woodhouse, J (1979), On the Fundamentals of Bowed-String Dynamics, Acustica 43:2, 93-108 Dobashi, Yamamoto and Nishita (2003) have described that a time analysis in the above figure 2.8 (A) shows the Helmholtz-type motion of the string; as the bow moves ahead at a constant speed, the bend races around a curved path. Fig. 2.8 (B) shows the position of the point of contact at successive times; the letters correspond to the frames in Figure 2.8(A). Note that there is a single bend in the bowed string. Whereas in the plucked string (fig. 2.8), we had a double bend. The action of the bow on the string is often described as a stick and slip action. The bow drags the string along until the bend arrives [from (a) in figure 2.8 (A)] and triggers the slipping action of the string until it is picked up by the bow once again [frame (c)]. From (c) to (i), the string moves at the speed of the bow. The velocity of the bend up and down the string is the usual . The envelope around which the bend races [the dashed curve in Figure 2.8 (A)] is composed of two parabolas with maximum amplitu de that is proportional, within limits, to the bow velocity. It also increases as the string is bowed nearer to one end. 2.6 Vibration of air columns: According to Moore and Glasberg (1990) the familiar phenomenon of the sound obtained by blowing across the open and of a key shows that vibrations can be set up in an air column. An air column of definite length has a definite natural period of vibrations. When a vibrating tuning fork is held over a tall glass is pured gradually, so as to vary the length of the air column, a length can be obtained which will resound loudly to the note of the tuning fork. Hence it is the air column is the same as that of the tuning fork. A vibration has three important characteristics namely Frequency Amplitude Phase 2.6.1 Frequency:- Frequency is defined as the number of vibration in one second. The unit is Hertz. It is normally denoted as HZ. Thus a sound of 1000 HZ means 1000 vibrations in one second. A frequency of 1000 HZ can also be denoted as 1 KHZ. If the frequency range of audio equipment is mentioned as 50 HZ to 3 HZ it means that audio equipment will function within the frequency range between 50HZ and 3000 HZ. 2.6.2 Amplitude:- Amplitude is defined as the maximum displacement experienced by a particle in figure will help to understand amplitude. Let us consider two vibrating bodies having the same frequency but different amplitudes. The body vibrating with more amplitude will be louder than the body vibrating with less amplitude. The following figure represents two vibrating bodies having the same frequency but different amplitudes (Takala and Hahn, 1992). 2.6.3 Phase:- Phase is defined as the stage to which a particle has reached in its vibration. Initial phase means the initial stage from which the vibration starts. The following will help to understand the concept of phase. From the source travels in the form of waves before reaching the ear sound cannot travel in vacuum. Sound needs medium for its travel. The medium may be a solid or liquid or gas (Brown and Vaughn, 1993). Support a glass tube open at both ends in a vertical position, with its lower and dipping into water contained in a wider cylinder. Hold over the upper end of the tube a vibrating tuning form. Adjust the reinforcement of the sound is obtained. Adjust the distance of the air column till we get actually the resonance or sympathetic note. Repeat the adjustments and take the average of the results from the observation. It will be found from the repeated experiments, that the longer the air column is produced when the tuning fork becomes identical. Vibration of air column in a tube open at both ends:- Obrien, Shen and Gatchalian (2002) have described that if they think of an air column in a tube open both ends, and try to imagine the ways in which it can vibrate; we shall readily appreciate that the ends will always be antinodes, since here the air is free to move. Between the antinodes there must be at least one node, and the ends, the moving air is either moving towards the center from both ends or away from the centre at both ends. Thus the simplest kind of vibration has a node at the centre and antinodes at the two ends. This can be mathematically expressed as follows: Wave length of the simplest kind of vibration is four times the distance from node to antinode 2L where L is the length of the pipe. Vibration of air column in a tube closed at one end: The distance from node to antinode in this case is L, the whole length of the pipe, the wavelength is therefore = 4L. 2.7 Resonance-sympathetic vibration Sloan, Kautz and Synder (2002) have described that everybody which is capable of vibration has natural frequency of its own. When a body is made to vibrate at its neutral frequency, it will vibrate with maximum amplitude. Resonance is a phenomenon in which a body at rest is made to vibrate by the vibrations of another body whose frequency is equal to that of the natural frequency of the first. Resonance can also be called sympathetic vibrations. The following experiment will help to understand resonance: Consider two stretched stings A and B on a sonometer. With the help of a standard tuning form we can adjust their vibrating lengths [length between the bridges] to have the same frequency. Thus we can place a few paper riders on string B and pluck string A to make it vibrate. The string B will start vibrate and paper riders on it will flutter vigorously and sometimes A can be stopped simply by touching it. Still the string B will continue to vibrate. The vibration in the string B is due to resonance and it can be called as sympathetic vibration. If instead of the fundamental frequency one of the harmonics of string B is equal to the vibrating frequency of string A then the string B will start vibrating at that harmonics frequency. But in the case of harmonics the amplitude of vibration will be less. In Tambura when the sarani is sounded the anusarani also, vibrates thus helping to produce a louder volume of sound. The sarani here makes the anusarani to vibrate. In all musical instrum ents the material, the shape of the body and enclosed volume of air make use of resonance to bring out increased volume and desired upper partials of harmonics. 2.8 Intonations Spiegel and Watson (1984) have described that during the course of the history of music, several of music intervals were proposed aiming at a high degree of maturing consonance and dissonance played important role in the evolution of musical scales. Just intonation is the result of standardizing perfect intervals. Just Intonation is limited to one single-key and aims at making the intervals as accordant as possible with both one another and with the harmonics of the keynote and with the closely related tones. The frequency ratio of the musical notes in just Intonation is given below. Indian note Western note Frequency ratio r C 1 K2 D 9/8 f2 E 5/4 M1 F 4/3 P G 3/2 D2 A 5/3 N2 B 15/8 S C 2 Ward (1970) has mentioned that most of the frequency ratios are expressed is terms of comparatively small numbers. Constant harmonics are present when frequency ratios are expressed in terms of small numbers. The interval in frequency ratio are: Between Madhya sthyai C[Sa] and Tara sthayi c[sa] is 2 [1*2=2]. Between Madhya sthyai C[Sa] and Madhya sthayi G[pa] is 3/2 [1*3/2=3/2]. Between Madhya sthayi D[Ri] and Madhya sthayi E[Ga] is 10/9 [9/8*10/9=5/4] Between Madhya sthyai E[Ga] and Madhya sthayi F[Ma] is 16/15-[5/4*16/15=4/3]. Between Madhya sthyai F[Ma] and Madhya sthayi G[Pa] is 9/8-[4/3*9/8=3/2]. Between Madhya sthyai G[Pa] and Madhya sthayi A[Dha] is 10/9[3/2*10/9=5/3]. Between Madhya sthyai A[Dha] and Madhya sthayi B[Ni] is 9/8-[5/3*9/8=5/8]. Between Madhya sthyai Sa[C] and Ri2[D] there is a svarasthanam [CH]. Hence the interval between Sa[C] and Ri2[D] and Ga2[E] is known as a tone. But there is no svarasthanam [semitone] between Ga2[E] and Ma1[F]. Hence the interval between Ga[E] and Ma1[F] is known as a semitone. Between Pa[G] and Dha[A] we have a tone. Between mathya styayi Ni2[B] and Tara sthyai C[Sa] we have a semitone. In just Intonation we find that tones are not all equal. But the semitones are equal. In just Intonation the modulation of key of musical notes will be difficult for example, if the keynote is changed from Sa[C] to Pa[G] then the frequency of etatusruthi Dhairatam [A] will change from 1.687, time the frequency of Sa[c]. A musical instrument tuned in just intonation to play sankarabaranam ragam cannot be used to play kalyani ragam. Hence the modulation of key of musical notes will be difficult in just Intonation (Doutaut , Matignon, and Chaigne, 1998). Equal temperature Lehr (1997) has described that the above mentioned problem in just Intonation can be solved in the Equal Temperament scale. In Equal temperament all the 12 music intervals in a sthayi [octave] are equal. The frequency ratios of semitones in Equal temperament scale was first calculated by the French Mathematician Mersenne and was published in Harmonic Universelle in the year 1636. But it was not put into use till the latter half of seventeenth century. All keyboard instruments are tuned of Equal Temperature scale. Abraham pandithar strongly advocated Equal Temperament scale and in his famous music treatise karunamitha sagaram he tried to prove that the Equal Temperament scale was in practice in ancient Tamil music. A simple mathematical exercise will help to under the basis of Equal Temperament scale. Equal Temperament Madhya sthayi Sa[c] frequency ratio=1=2 ÃÅ'Ã…  . Tara sthayi Sa[i] frequency ratio = 2=212/12=2. Frequency ratios of 12 svarasthanams are given below. S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" à ¢Ã¢â‚¬  Ã¢â‚¬Å" 20 21/12 22/12 23/12 24/12 25/12 26/12 27/12 28/12 29/12 210/12 2n/12 S à ¢Ã¢â‚¬  Ã¢â‚¬Å" 212/12 All semitones are equal is Equal Temperament scale. Each represents the same frequency ratio 1.05877. The great advantage in Equal Temperament scale is that music can be played equal well in all keys. This means that any of the 12 semitones can be used as Sa in a music instrument tuned to Equal Temperament scale. There is no need to change tuning every time the Raga is changed. Since keyboard instruments are pre-tuned instruments they follow Equal Temperament. 2.9 Production and transmission of sound:- According to Boulanger (2000) the term sound is related to quite definite and specific sensation caused by the stimulation of the mechanism of the ear. The external cause of the sensation is also related to sound. Anybody in vibration is an external cause of the sensation. A veena [after plucking] or violin [after blowing] in a state of vibration is an external cause of the sensation. A body in a state of vibration becomes a source of sound. A vibration is a periodic to and fro motion about a fixed point Iwamiya and Fujiwara (1985) have mentioned that the pitch of a musical sound produced on a wind instrument depends on the rate or frequency of the vibrations which cause the sound. In obedience to Natures law, the column of air in a tube can be made to vibrate only at certain rates, therefore, a tube of any particular length can be made to produce only certain sounds and no others as long as the length of the tube is un-altered. Whatever the length of the tube, these various sounds always bear the same relationship one to the other, but the actual pitch of die series will depend on the length of the tube. The player on a wind instrument, by varying the intensity of the air-stream which he injects into the mouthpiece, can produce at will all or some of the various sounds which that particular length of tube is capable of sounding; thus, by compressing the air-stream with his lips he increases the rate of vibration and produces higher sounds, and by decompressing or slackening the inte nsity of the air-stream he lowers the rate of vibration and produces lower pitched sounds. In this way the fundamental, or lowest note which a tube is capable of sounding, can be raised becoming higher and higher by intervals which become smaller and smaller as they ascend. These sounds are usually called harmonics or upper partials, and it is convenient to refer to them by number, counting the fundamental as No. t, the octave harmonic as No. 2, and so on. The series of sounds available on a tube approximately 8 feet in length is as follows: Tsingos et al (2001) has mentioned that a longer tube would produce a corresponding series of sounds proportionately lower in pitch according to its length, and on a shorter tube the same series would be proportionately higher. The entire series available on any tube is an octave lower than that of a tube half its length, or an octave higher than that of a tube double its length ; thus, the approximate lengths of tube required to sound the various notes C are as follows : Fundamental Length of tube C, 16 feet C 8 ,. c 4,, c 2,, c I foot c 1/2,, Shonle and Horen (1980) has mentioned that the addition of about 6 inches to a 4-foot tube, of a foot to an 8-foot tube, or of 2 feet to a i6-foot tube, will give the series a tone lower (in B flat), and a proportionate shortening of the C tubes will raise the series a tone (D) ; on the same basis, tubes which give any F as the fundamental of a series must be about midway in length between those which give the C above and the C below as fundamental. Examples: Trumpet (modern) in C-length about 4 feet ,, in F ,, ,, 6 ,, ,, (old) in C ,, ,, 8 ,, Horn in F ,, ,, 12 ,, ,, ,, C ,, ,, 16 ,, It will be noticed that the two lower octaves of the harmonic series are ve

The Lady of Shalott Essay -- essays research papers

1.  Ã‚  Ã‚  Ã‚  Ã‚  Introduction This paper will try to analyze the growth of consciousness of the Lady of Shalott. Ranging from her state of mind in total isolation, her 'childhood', to her changing 'adolescence' and eventually reaching 'adulthood' and death, all in a sort of quick-motion. It will further deal with the development of tension throughout the poem. By making a distinction between tension through formal aspects, such as rhyme scheme, and tension through content it will try to show the interconnection between both of them. Additionally, the paper will deal with the possible effect of tension on the reader and how the poem might be perceived by him/her. 2.  Ã‚  Ã‚  Ã‚  Ã‚  Growth of Consciousness and Development of Tension 2.1.  Ã‚  Ã‚  Ã‚  Ã‚  Initial Isolation Lord Alfred Tennyson's poem starts out with the total seclusion of the beautiful, young Lady of Shalott surrounded by '…four grey walls, and four grey towers…';. (Tennyson, line 15). She is largely unaware of the world outside and of her own existence as a woman, only being able to see shadows of reality, which are reflected by her magic (?) crystal mirror and worked into her web. At this point of time it is unknown to the reader whether the Lady of Shalott is forced to be in this situation or chose to live this life of isolation. Reasons for a self inflicted seclusion might be homophobia, the fear of rejection by the exterior world, or simply a lack of interest for it. However, the Lady of Shalott is quite content with what she has and what she does. Her life of art in front of the loom and the crystal mirror is all she needs singing her ';…song that echoes cheerly…'; (30) throughout the land. She is as innocent as a careless child giving little thought about her future. The Lady of Shalott has no urge to leave her own interior world because she is not aware of any other options. Little is known about her outside '…many-towered Camelot.'; (5) and apparently she intends to keep it that way: But who hath seen her wave her hand ? Or at the casement seen her stand ? Or is she known in all the land, The Lady of Shalott ? (24-27) By now the reader might ask him-/herself why the Lady of Shalott is stuck in such a dreadful situation and why she does not attempt to do anything about it. There is a cons... ...martyrdom and so the story ends, leaving the reader in anger about the carelessly spoken words of Lancelot. 3  Ã‚  Ã‚  Ã‚  Ã‚  Conclusion   Ã‚  Ã‚  Ã‚  Ã‚  'The Lady of Shalott'; was and is subject for countless interpretation by readers and artists, especially pictorial. Although, or maybe because the whole setting is quite vague and shadowy there have been many attempts to explain why the Lady of Shalott was cursed. Maybe she was not cursed al all. What was this whisper she heard ? Was she schizophrenic, hearing voices inside her head ? Another question is why she had to die in the end. Is it possible she eventually commit suicide, because she had realized that her love for Sir Lancelot was futile ? These are some questions that stay in the back of your head after reading Tennyson's poem. Even today you can feel the infinite struggle the Lady of Shalott had to undergo. Tennyson impressively shows the development of a young woman who is faced with one of the most difficult times in life- growing up in a world full of restrictions and rules and becoming a woman. His subtle description of a girls problems at his time is, slightly altered, even valid today.

United States Men’s National Soccer Team

While rival drug cartels warred in the streets and the country’s murder rate climbed to highest in the world, the Colombian national soccer team set out to blaze a new image for their country. What followed was a mysteriously rapid rise to glory, as the team catapulted out of decades of obscurity to become one of the best teams in the world. Central to this success were two men named Escobar: Andrà ©s, the captain and poster child of the National Team, and Pablo, the infamous drug baron who pioneered the phenomenon known in the underworld as â€Å"Narco-soccer.† But just when Colombia was expected to win the 1994 World Cup and transform its international image, the shocking murder of Andres Escobar dashed the hopes of a nation. Through the glory and the tragedy, The Two Escobars daringly investigates the secret marriage of crime and sport, and uncovers the surprising connections between the murders of Andres and Pablo. Personal Statement Our films tend to focus on disenfranchised communities in the process of rising up and transforming their political and economic circumstances. We choose these stories due to the scale of their historic importance—this is where societies are shaped. By comparison, sports have often felt like mere diversion, games limited to the playing field. At times, we have both drifted from the passion for sports we shared as young athletes and fans, engaging ourselves in other endeavors as seasons of professional competition passed by. Then, invariably, definitive moments in sports history would grab our attention and turn our logic upside down. Like in 1994, when an athlete named Andres Escobar was murdered for accidentally scoring an own goal that cost the Colombian National Team a chance at winning the World Cup and transforming its negative image on the international stage. Here was a country with a national identity so integrally connected to the success of its soccer team that one mistake on a playing field dashed the pride of an entire nation and cost a man his life. Looking into the incident, we learned that the dramatic rise and fall of Colombian soccer was inextricably tied to the rise and fall of Pablo Escobar’s Medellà ­n Drug Cartel, considered by many the ‘ruling party’ of Colombia at the time. Sport in Colombia was not only mirroring the personality and politics of society, but also an inseparable part of that society – the playing field an extension of the streets and offices where influential decisions are made. On our journey through diverse walks of Colombian society during production, it became clear that this was far from a classic â€Å"deal-with-the-devil† narrative. Rather, this was the story of the passions and dreams of a people intrinsically tied to the rise and fall of a team. Stories such as this revive our childhood fascination with sports and confirm the fundamental role they play in shaping our world.

Implementation on Solid Waste Management of Boarding Houses Essay

Introduction Solid Waste Management, the collecting, treating, and disposing of solid material that is discarded because it has served its purpose or is no longer useful. Improper disposal of municipal solid waste can create unsanitary conditions, and these conditions in turn can lead to pollution of the environment and to outbreaks of vector-borne disease—that is, diseases spread by rodents and insects. The tasks of solid-waste management present complex technical challenges. They also pose a wide variety of administrative, economic, and social problems that must be managed and solved.the unwanted or useless solid materials generated from combinedresidential, industrial and commercial activities in a given area. It may be categorizedaccording to its origin (domestic, industrial, commercial, construction or institutional);according to its contents (organic material, glass, metal, plastic paper etc); or according to hazard potential (toxic, non-toxin, flammable, radioactive, infectious etc) .Management of solid waste reduces or eliminates adverse impacts on the environmentand human health and supports economic development and improved quality of life. Anumber of processes are involved in effectively managing waste for a municipality.These include monitoring, collection, transport, processing, recycling and disposal.Solid waste refers to wastes from households, municipal services, construction debris andthe agricultural sector. This also includes non-hazardous, non-liquid wastes from institutions andindustries. (RA 9003) According to the World Bank (2001), its generation is greatly affected by acountry’s development. Read more:  Waste Disposal in the Philippines Generally, the more economically prosperous a country is, the more wasteis generated per capita. Table 1.1 presents a comparison of municipal waste generation of differentcities in the world.Solid waste management (SWM), on the other hand, pertains to the control of theâ€Å"generation, storage, collection, transfer and transport, processing and disposal (RA 9003)† ofsolid waste in a fashion that is in accordance to societal and economic needs while at the same timecompliant to environmental standards and principles.Solid waste is a telltale sign of how citizens’ lifestyles change as a result of economicdevelopment. Furthermore, the distribution of waste generation in the different regions of a countryis indicative of its degree of urbanization. In cities, where standard of living is higher, there isusually a higher waste output compared to rural areas. This is reflective of the case of thePhilippines where its capital and largest urban centre, Metro Manila, generates a lmost a quarter ofthe country’s total waste generation (WB, 2001).The issue of solid waste in Metro Manila gained international attention in the 1980s throughthe Smokey Mountain dumpsite, which became representative of poverty in the Philippines(Gonzales, 2002). It used to be the country’s largest dump and is also one of the largest slums in the world (Yashwant, 2002). The government was concerned about the negative image that thisgave the country that it was eventually closed in 1995.The matter of solid waste and its management had, once again, catapulted itself into thelimelight in 2000, during which a number of issues plagued the solid waste management (SWM)sector. First came the ‘Payatas Tragedy’ in July when a huge amount of garbage in Payatas, the largest active open dumpsite in the Philippines, was loosened by heavy rains and caved in on thecommunity of scavengers living around it. Next came the impending premature closure of the SanMateo Waste Disp osal Facility (SMWDF), which took in majority of Metro Manila’s solid waste atthat time, at the end of the year which aroused panic and concerns among the Local GovernmentUnits (LGUs) and the Metro Manila Development Authority (MMDA), the bodies responsible forSWM in Metro Manila. They scurried around, desperate for alternative dumpsites and solutions. They also rallied for the repeal of the Clean Air Act (Republic Act 8749), passed the year before,under which incineration of solid wastes was banned.During this time, the Ecological Solid Waste Management Act (RA 9003), a landmark lawwhich addresses SWM issues was in the final stages of formulation. It was finally approved inJanuary of 2001 after delays due to the political perturbation at that time. The passing into law ofRA 9003 was met by much enthusiasm by political leaders and non-governmental organizations(NGOs) alike as it was the first law in the country that addressed SWM in a non-piecemeal manner.Despite the initial optimism after RA 9003’s approval, 2001 turned out to be the year of theMetro Manila garbage crisis. The LGUs and the MMDA provided neither alternative dumpsites norsolutions by the time SMWDF was shut. Garbage dumps were literally growing everywhere in themetropolis – roadsides, waterways, vacant lots, rivers and other public places. The problem got soout of hand that Metro Manila was declared as under a ‘state of emergency’ to obtain assistancefrom the national government (The Manila Times, 2002). The crisis also caught the attention of theWorld Bank, thus its focus on the growing problem of solid waste in the Philippines in the 2001Philippine Environment Monitor (WB, 2001).Things had momentarily quieted down with the opening of the Montalban Solid Waste Disposal Facility (MSWDF) in mid-2002. The issue of SWM, however, has not completely fadedinto the background as earlier events had inspired the activism of several NGOs. Unfortunately,though, it also escalated the growing not-in-my-backyard (NIMBY) problem, making the task ofsearching for locations for future solid waste disposal facilities for the LGUs and the MMDA abigger problem. These are just a few of the challenges that face the SWM sector. By looking at itas a system, its relationships and effects with the different elements in the sector can be identi fied.With this, improvements can be proposed and evaluated. 1. Strategies to implement Solid Waste Management of the owner in boarding houses from waste disposal facilities through reuse, recycling, and composting activities. 2. Factors of advantages to implementation of Solid Waste Management Plan decision. The improvement of specific area in implementing process of strategies of Solid Waste Management Plan. Figure 1 Present the Schematic Diagram which shows the process of this study. Conceptual Framework The conceptual framework maps the entire process of the researcher study. The study is entitle, Implementation on Solid Waste Management of Boarding Houses. Figure 1 is the schematic diagram. The Geometric figures presented the following: First Box The study aims to assess the profile the people who respondent in selected area conducted study of research in Boarding Houses. Second Box The second box focuses on the Strategies to implement Solid Waste Management of the owner in boarding houses from waste disposal facilities through reuse, recycling, and composting activities and factors of advantages of Solid Waste Management Plan decision. Third Box The third box is the determination of the improvement of specific area in implementing process of strategies of Solid Waste Management Plan. Statement of the Problem This study aims to answer the following questions based on what is the reality in present time when it comes to implementing Solid Waste Management in Boarding Houses. 1. What is the profile of the people who respondents in specific area to conduct study research of implementing the Solid Waste Management? 2.1 Age 2.2 Gender 2.3 Civil Status 2.4 Occupation 2.5 Religion 2.6 Nationality 2.7 municipality 2. What are the Strategies to implement Solid Waste Management of the owner in boarding houses? What are factors of advantages to implementation of Solid Waste Management Plan decision? 3. What is the improvement of specific area in implementing process of strategies of Solid Waste Management Plan? Significant of the Study This study is significant to the following sectors, for the reason that Solid waste management is strongly grounded in the need to safeguard the environment, conserve and recover material and energy resources, and protects public health and safety. Students The students are the individuals whose focus of the mind is in learning and digesting different knowledge. The students have ample time in studying than the parents, thus, knowing this reality, this work be somehow important or even extremely important for the students. If they will be using their might and time to implant the significance of this study to the people, surely the result will be good as expected. Students could appreciate the native literature because it a sign of being patriotic and showing love into the country. Teachers Teachers could also benefit the meat of this work, they are facilitators and they are the ones that will implant o the student’s mind the importance of the native culture and the wholeness of being a Filipino. This is also significant to the teachers for the reason of they as teachers must also know the culture of this indigenous people and understand them of what life they are having. Thus, understanding their life, teachers could easily teach the students to stop the discrimination against their brothers and sisters that are also Filipino. Government localgovernments are responsible for ensuring that solid waste generated in their jurisdictions is managed in an environmentally and economically sound manner that protects public health and safety. Giving attention and lending ears to the literary pieces of the Manobo people, Government could understand the feelings of the nomadic people. The government should look and give importance to the areas where nomadic people are living. Some of the nomadic people are living with great poverty just because of the reason that their homes are far away from the progress, far away from the industries, far away from the market place to buy foods and other necessities, and most of all, far away from love and care of the other tribes which are thinking that they are superior than the others. The government shall see the reality of these people, so that their life will become easier and their livelihood products will also be easy to deliver. Scope and delimitation Definition of Terms CHAPTER II Assumption Antipolo takes pride in calling its campus a ‘’green zone’. With Apostolate that aims to take care of God’s creation, the Environmental　Education Program is an integral part of the curriculum. The program as a whole installs in the student a deeper commitment to environmental stewardship. It makes use of the SEE-DISCERN ACT process to develop in the student a lifestyle of steward ship where caring is a commitment. To SEE allows the student to observe environmental realities, to DISCERN is to reflect and use her personal understanding to seek God’s plan anchored on prayers, leading her to ACT in response to God’s will. The Solid Waste Management for Schools is a guide or a step-by-step instruction or manual on how solid waste management should be implemented, and who among the school community would be the key players in the immersion process. The goal is to foster participation among children and adults, and put schools in action for the welfare of Mother Earth. The program is a cross-curriculum area of learning, wherein all subject areas can integrate environmental issues and mater ials in their encounters, thus helping students make informed decisions. Assumption Antipolo students also engaging in a proper waste disposal, or proper way to segregate different solid waste around the school. The school also have a Zero Waste Campaign the Canteen and cafeteria upholds the schools advocacy promoting zero waste. Therefore, the following are practiced: Encouraging the use of biodegradable materials whenever possible, minimizing the use of plastics and briging reusable container for food and drinks.   

Letter from hospital

I thought I should write to let you know IM safe and IM recovering. I miss you and the rest give everyone a hug from me and tell Rosier I hope she's being good. The hospital Is constantly got new soldiers coming In suffering from nervous exhaustion and shell shock too so IM not the only one, the doctor said It Is an Injury to the nerves and told me to rest and they are putting In place electric shock treatment.All the nurses are very sympathetic but sometimes when they think we can't hear them they call us all weak and say we are cowards. Im not suffering as much as most, a young gentleman has been learning to walk again yet he still wants to get back to the frontline. Yes, am returning to the frontline soon so that's why I took this opportunity to write. We had strict orders not to take prisoners, no matter if wounded my first Job was when I had finished cutting some of their wire away, to empty my magazine on 3 errands that came out of one of their deep dugouts they was bleeding ba dly begging for them to be put out of their misery.They cried for mercy, but I had my orders, they had no feeling what so ever for us†¦ It makes my head Jump to think about It. One time I was In serious danger I was almost completely paralyses with fear. I was slating with Taylor (a fellow soldier) on the fire-step of a trench during an intense bombardment,when it seemed certain that we must be killed at any moment. Shots fired around us; each moment threatened to be the last. I was conscious of biting the fabric on my top to prevent my teeth from chattering.If I had been alone on that occasion I believe that I would be dead now; it was the presence of others that saved me. It's not all been like that, one evening me and Owen was in the barracks and I received a letter from you for my birthday and it kept me going for so long, but everyone has a breaking point: weak or strong, courageous or cowardly- war frightens everyone my breaking point has now unfortunately came. Give my l ove to everyone, Yours sincerely

Research Paper on Abortion

The ethics of abortion is one of the most controversial topic that has been continually argued over years and probably many years to come. The main controversy is the question of legalization of abortion, which ties into ethical issues, emotions, and political issues or laws. Before I discuss the many sides to abortion, it is critical to define the term. The Webster’s Dictionary defines abortion as the termination of a pregnancy after, accompanied by, resulting in, or closely followed by the death of the fetus. Despite the liberal attitudes toward abortion, it still remains an important political issue. Even in societies where abortion has been legalized, many actions are being raised by the anti-abortionists. These anti-abortionists believe in â€Å"pro-life† and their religious perspectives are responsible in their arguments against abortion. They believe that â€Å"it is equally as heinous intentionally to kill a human being in existence at fertilization, as to kill a larger pre-born child. † On the other hand, there are reasons for legalization of abortion. Most people agree with the concept of reproductive freedom—the fundamental right of every individual to decide freely and responsibly when and whether to have a child. Human life is defined as â€Å"any living entity that has DNA from the species homo sapiens. This includes an ovum, spermatozoon, zygote, embryo, fetus, newborn. It also includes an infant, child, adult, elder. It also includes a breast cancer cell and a hair follicle and a skin scraping. Some forms of human life have little or no value; others are the most valuable and precious form of life in the known universe†. Because an unborn fetus is considered to have a human life, abortion should not be legalized. It is a definitely a crime to kill a living and breathing fetus even though the embryo may not take the form of a human structure. If abortion is permitted, the dignity of human will be destroyed. In the medical field, the doctors prescribe the baby before 15 days after conception as dividing cells. But after this short period, abortion is prohibited from the principal of identifying. This is because the fertilization process contains many cell divisions by zygote progressing into a human being. Many people assert the right that women do not have a baby because they have the right to choose. But it is neglecting the right of the baby who has his or her own life. Just because an unborn fetus is not capable to express his or her feelings, is it morally right to end its life? Considering moral issues, abortion is definitely equally termed a murder. However, I do understand the other point of view for legalizing abortion. The exception to abortion is considered when the mother bearing the child has illnesses or diseases that can be transmitted to the baby genetically. Also, financial issues are often being raised by the parents whom are not able to support another family in the house. In this case, abortion may be permitted because it is rather better to not be alive than be living under such poor conditions. Furthermore, abortion is considered as a rightful act when the women get pregnant from rape. Some people may generally think that a crippled person is pessimistic about the world. But in fact, they thank their parents who gave life to them. The life as a handicapped person could be better than not experiencing life at all. If it’s not by the force of other one, people must take the responsibility for their behavior. Every action you make comes in consequences and therefore, it is important to choose birth controls if pregnancy is not wanted. If the reason that causing abortion is merely a problem of foster, it is never permitted. We must keep in mind that life is most precious thing in the world. It is estimated that the number of aborted babies is almost 4000 in a month. Vast majority of abortions are done for convenience, by women who simply want to terminate an unwanted pregnancy. But abortion is a murder. So, now is the time for us to think about the abortion again and to search for the best solution. In any circumstances, the life must be admired. Work Cited http://www.religioustolerance.org/abortion.htm http://abortion-alternatives.adoption.com/ http://www.friesian.com/abortion.htm

James C. Curtis, Andrew Jackson and the Search for Vindication Essay

James C. Curtis, Andrew Jackson and the Search for Vindication - Essay Example Throughout the start of the book, Curtis widely relates Andrew’s early encounters with his prospective motivations both in political and personal thoughts. Andrew Jackson personally participated in important national and international events within the period between, 1767 and 1845. For one, it is within this period that Andrew Jackson was the seventh president of the U.S. serving between 1829 and 1837. During this period, he remained a polarizing figure and controlled the Second Party System. As a president, he demolished the national bank and repositioned most Indian tribes to the west of river Mississippi. Before this, Jackson had served as a politician and an army general who was able to defeat the Indians during the 1814 battle of Horseshoe Bend. Similarly, Andrew defeated the British forces during the 1815 battle of New Orleans. It is during this period that Jackson became a rich slaveholder and appealed to the United States’ common people. He is also known for po litically fighting against what he referred to as closed and undemocratic aristocracy, hence, the era of Jacksonian democracy. Another event that marks this period in Jackson’s life is the Nullification crisis. This crisis was characterized by the tariff issue that evidently established one of the most important elements of Jackson’s term as a president. ... Andrew Jackson was extraordinarily successful in national politics as he played a major role in it. For instance, the Americans viewed Jackson as the embodiment of success as he was a man who could overcome inseparable opposition through determination. Hence, he was referred to as the Man of Iron Will .One of his remarkable characteristics as president was his well-known inflexibility of purpose. Andrew Jackson has remained extraordinary, as he was able to close the second Bank of the United States. He did this in order to avoid the destruction that would befall the bank due to corruption. Another noticeable success of Jackson was his famous duel with Charles Dickson, as suggested by O'Brien (89). In the duel, he was able to use his wisdom and ended the life of Dickson. Hence, his behavior in the duel gave an example of animal courage and demonstrated his ability to conquer battles. Jackson also alleged in rights of the states. He asserted that there were firm limits in the constitut ion in as far as federal government authority was concerned. As a result, he supported the state of Georgia in its jurisdictional disagreement with the federal government concerning the Cherokees. Moreover, Jackson strived to advance the common person interest against his almost equally corrupt opponents. Andrew Jackson also had outspoken commitment to particular principles that led him to shaping his party. He was also consciously and honestly dedicated to working people whether in agriculture or industry and to the America’s democratization. As a result, he insisted to limited public economy and government apart from where the President’s power was required to defend the interest of the