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我们的参赛队号为：1570我们选择的题目是：A参赛队员(签名) ：队员1：魏祯队员2：李兴队员3：高安森参赛队教练员(签名)：无数学建模国际赛编号专用页参赛队伍的参赛队号：（请各个参赛队提前填写好）：#1570 竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：The most resounding whistleAbstract:In this report, through the analysis of factors affecting the whistle sounding loudness, we build gas unitary flow model and multi structure model. In model 1, using the mass conservation equation and continuity equation of flow of energy conservation in, obtained the density, velocity, relationship quality force was established, so that the energy to keep the optimal combination of maximum; in model 2, through the method of control variables, to study the impact of different mouth size on loudness, simulate and repeated experiments, the structure and size of the whistle body that the strongest sound. Combined with the model two and model, we design the loudest whistle.Key words: sounding loudness gas unitary flow modelenergy conservation the mass conservationIntroduction:The whistle ,a device which is through the air quickly pressed into a narrow space within the device caused by the airflow disturbance, sounding device to send a strong sound. Whistle in the life and production have been widely used. Traffic police using whistles to guide the vehicle through, soldiers through the emergency buzzer to achieve the aim of urgent collection, sports events, refereeing to decisions and guidance game by whistle, when people are in danger, they send out a signal of distress through an intense whistle . So often the high quality of whistles can play an important role in production and life. So can we design a sufficiently loud whistle is the key to improve the quality of life and production efficiency?Assumptions:●The whistle sound is caused by air turbulence caused by the vibration,the airflow of different intensity will affect the intensity of the sound a whistle.●Humidity and velocity of sound and the air whistle, the humidity ofthe air will cause varying degrees of impact on air quality, sound quality, different velocity of air will send out different sounds.●The sound and the gas whistle by friction. Will cause friction whistleacoustic energy body loss, would seriously weaken the intensity of sound.●Flow fields disturbance affected by the whistle sound, different airwill take different routes, so that the formation of the flow field of different distribution, will cause the pressure differences occur, which affects the intensity of the sound.●Sound and whistle on the materials, different materials have differenttimbres, different timbres will also affect the intensity of the sound change, so, change material can also cause the intensity of sound.●About the reflectivity of sound and acoustic whistle acousticreflectivity assembly, reduces energy loss is reduced in the process of communication, which will increase the intensity of the sound.●The structure and size of sound and the whistle body ,whistle, whistlebody concerned, different structure, its internal air flow will form different can also cause the occurrence of different strengths, whistling size will affect the airflow reversal form, cause significant influence on the frequency of sound and vibration, so the structure and size of the whistle body Will affect the intensity of the sound a whistle.Problem analysis:◆Problem1The mechanism of whistle is a complex process, improve whistle sound intensity also need some practical ways. Whistle sound intensity internaland external factors. We simulate the sound of a whistle relationship between the factors and the strength through modeling approach. We will whistle the air velocity is coupled to the energy equation and the quality equation, caused by differences in the energy flow rate established for different correlation equation between the two. Through a comprehensive analysis of all aspects, and a discussion of the simulation results of the model, and thus more targeted to improve the strength of the whistle sound.◆problem 2Through the whistle sound intensity analysis of the actual situation, we found that many factors will affect the whistle sound intensity. Whistle sound velocity gas intensity, structure and whistle of the material, as well as the degree of airflow disturbances related to whistle, but the impact of the size of the whistle sound intensity is more obvious, therefore, our impact on the sound of the whistle dimension of intensity were appropriate model simulation, and made a further in-depth study. We have to study through the use of modeling, and control variables method, to explore the extent of the impact on the size of whistle whistle sound intensity. By controlling the whistle body make the same amount of gas entering and sonic vibration image issued by software simulation whistle. Variable Declaration:V Local mean velocityτTotal friction caused by viscous and turbulent nq Heat flux intensityF Unit mass forceP Local pressureρLocal air densityT The local temperatureV The study on the volume of fluid within the given time t S Surface volume Vv The normal velocitynF The area of the side cross sectional area of A1F The area of the side cross sectional area of A2μSpecific internal energyεPer unit time per unit mass release of heatd WidthA AmplitudeModel establishments:As everyone knows, there are a lot of reasons affecting the whistle sound, sound and gas flow velocity of the whistle gave a whistle whistle, structure, materials, elements of sound reflectivity and the turbulence degree have close relationship. The occurrence of waveform figure whistle, we can know the whistle waveform is some continuous sinewave, so how to increase the wave crests or troughs has become the key to increase the whistle sound.Figure 1: the energy trendModel 1Through the analysis ,we know that the air velocity will affect the intensity of the sound of the whistle whistle, through different velocity of air would directly into the whistle caused by different energy, different energy will cause the intensity of the sound emitted by a marked change, so, through the analysis of the simulation result can formula of different the flow velocity and sound intensity. Below is the three-dimensional simulation maps between acoustic frequency and sound decibels by below, we can analyze the frequency of sound, the greater the greater the decibel of sound wave, the frequency of sound is small and its acoustic decibels is smaller, therefore, appropriate frequency can increase the frequency of sound, so as to increase the loudness of sound.In flowcalculation process, in order to simplify the calculation, sometimes low-flow suddenly its slightly compressible processed by an incompressible fluid[3].Figure 2Through the method of control variables, control the flow velocity, to study the effect of gap size on the whistle whistle sound intensity, through the experimental study, guarantee the same velocity, made of the same material whistle, whistle has different size control exhaust port, through the DB tester, measuring the sound intensity under different gap whistle the size of the gap, find suitable can enhance the intensity of the sound a whistle.Through a simple analysis of the problem and the model, our group has qualitative obtains the effect of each factor and the intensity of the sound relationship, derivation and computation of gas velocity we detailed below influence on sound intensity formula [1][2] .Figure 3: gas unitary flow diagramthe principle of conservation of mass ，0=+∂∂⎰⎰ds pv dv t p sn v ds v dF v dF v ds v An F x F x s n⎰⎰⎰⎰++-=ρρρρ21, therefore012=+-+∂∂⎰⎰⎰⎰ds v dF v dF v dv tA n F x F x V ρρρ, Both sides of the equation is divided by dx, the limit take dx to 0，dF v x dF v dF v dx Fx F x F x dx ⎰⎰⎰∂∂=-→ρρρ)](1[lim 120, And dx=dFdx ，derived0=∂∂++∂∂⎰⎰⎰dF v xds v dF t F x s n F ρρρ 0=∂∂+∂∂⎰⎰dF v xdF t x F F ρρ The principle of generating the whistle is caused by turbulence, and equation analysis and gas turbulence unary flow problems are similar, so we use the continuous equation of gas unitary flow to analyze the whistleoccurs changes in energy and conservation in the process, in order to study the influence to calculate the energy change of intensity of sound. The law of conservation of energy=+++∂∂⎰⎰ds v v jdv v t n s v )2()]2([22μρμρ-⎰⎰⎰⎰⎰++++vs n v s n s dv ds q dv ds ds fv v nv ρερρτ)()(-, Type change,])2()2()2([)]2([22212ds v v dF v v dF v v dv v t n A x F x F v ⎰⎰⎰⎰+++-+++∂∂μρμρνρμρBoth sides of the equation is divided by dx, from dx to 0 to limit})2()2()2()]2([{1lim 2222012ds v v dF v v dF v v dv v t dx n A x F x F v dx ⎰⎰⎰⎰+++-+++∂∂→μρμρμρμρ⎰⎰+∂∂++∂∂F x F dF v v x dF v t )2()2(22μρμρ If the whistle side is free surface, then the friction is zero, if whistle side is rigid, then the velocity is zero. Based on the above assumptions and simulation, we established a conservation equation between the change of normal stress and the speed and intensity of sound derived:0)(=⎰ds v nA τ Assuming the mass force with potential energy ϕ∇=f ,dv dv v dF VV V v v v fv ⎰⎰⎰∇-∇==)]()([)()(ρϕρϕϕρρ Continuous equation by the conservation of mass 0)(=∇+∂∂v tρρ, dv t dv dv V V V v fv ⎰⎰⎰∂∂+∇=ρϕρϕρ)()(Through the discussion of flow propagation in subsonic blowing the whistle, whistle in the air energy, and then draw the side effects on the energy loss of the internal parameters of the whistle, to analyze the optimal scheme to reduce energy losses. According to one yuan the gas continuity equation, momentum equation is obtained the relationship between the various parameters affecting the sound. Conclusions are drawn as follows:●the size of the fluid compressibility effect to a certain extent,sonic;●the whistle materials (communication media) has a directinfluence on the energy;●the sonic flow of gas is a function of state parameters;●in the transmission medium to maintain consistent case, sonicvelocity increases with the temperature.Model 2Strength: We use the model 1 group using physics equation analysis of the relationship between the flow velocity and sound, and the whistle is sound because of the high-speed airflow from a relatively narrow gap flow caused turbulence, the structure size hypothesis whistle will affect the acoustic intensity. In order to analyze the relationship between them, we establish the model of 2: in the control of gas flow rate is constant, by changing the width and diameter of the whistle, the determination of therelationship between sound intensity and their. Intensity depends on the vibration amplitude of the acoustic sound of the size, the larger amplitude, the greater the intensity; the smaller the amplitude, the weaker the strength. We use virtual instrument software through computer microphone measuring amplitude, in order to reduce the error, we use the average value obtained in successive, change the width and diameter size case, multiple measurements of amplitude and the average values.Table 1 Width(mm)Amplitude(mm) 3.00100 5.00450 10.00 650 15.00400 20.00200 25.00851004506504002008501002003004005006007000102030Amplitude/cm Width/mmThe amplitude and widthThe amplitude and width Figure 4: the amplitude and widthWe simulated the relationship between the data through the MATLAB, clearly drawn from the diagram:●whistles width effect on amplitude of the whistle sounding: wideror narrower, smaller sound amplitude.●whistles diameter affected the vocal amplitude: whistle diameterbigger or smaller, the smaller the sound amplitude.●the same width as the whistle, diameter is larger, the lower thesame sound amplitude; the inner diameter of the whistle, the greater the more width, low sound amplitude.●when the whistle width and diameter of between 6 and 12 mmlarger amplitudeModel application and result analysisThrough the analysis on the model and the principle of calculus and analytic, we conclude that can adjust the high whistle sound loudness measures, according to the needs of different environments or sites, to whistle sound loudness will have different requirements, so we rang, the relationship between degree and elements according to the whistle sound, guide us choose according to their own needs and select the highest whistle in his loudness by the application of the place[4].Analysis based on above model, we considered the optimal combination of various factors, but also with reference to the previous design, designed the loudest voice whistle, whistle Tongti snail shape, length 8cm, width 6cm, thickness 3cm, shape with gentle curves, the man-machine engineering science based on, we fully considered hand comfort, so will be the mostharmonious curve used in the periphery of the body of the whistle. The mouth of the circular design, like this is advantageous when used with strict enough contact opening, reduce the blow out gas leak, the mouth and the whistle body with 1.8cm distance, this distance is conducive to the stability of air flow, reduce the disturbance, this is very helpful to the entry and exit gas blow out from a more stable, thus the sound of loud, continuous, concentration. Ample whistle body space, so that you can make more air into, when these gases will be discharged from whistling have enough loudness. At the same time, must be adequate space is stable airflow, whistling into from the gas accumulation in this sufficient space, then the steady flow in this space, minimize the flow disturbance, help to issue more forceful voice, this enough space for storing enough gas store up enough energy, which must be so it is with enough sound whistle. Then the air outlet, in this place we post to this period of material outlet gradually thinning, making the outlet near the whistle body is thin enough, so from the whistling into the whistle and accumulation of airflow can more quickly through the air outlet, and the airflow can stable is the whistle body cutting, voice frequency this produces higher, louder, with what we want a strong enough loudness.Figure 5: whistle stereo modelFigure 6: entity profileStrengths and weaknessesAccording to the analysis of our qualitative and quantitative, and the formula for the calculus and derivation, we clearly analyze the influence of each factor on loudness, verify that such more clear, accurate and amend our hypothesis, but also help us draw the correctformula. Through the analysis of the other factors directly affect thechange of image, we have drawn the effect of the change of elements on the sound loudness.Although we change in analyzing the various factors of influence on the sound loudness is already very full, but there are still some factors that we did not take into account, there are some factors we do approximate processing, so it is bound to cause some errors on the results, although the error is in the allowable range, but also with the real situation have some differences, therefore, our model has a lot of can improve and enhance the placeReferences[1] YiZhong WuXuan Zhou Lizhen ,Low-speed aerodynamics Metallurgical Industry Press P189-196.[2]Qian YiJi, Aerodynamics Beijing University of Aeronautics andAstronautics Press P34-36.[3] Xiong Yifu, Equation of Flowed Energy and its Appliction.[4]Y ue MinYi Li RongHang, Introduction to CombinatorialOptimization Technology Press.[5]Journal of the American Mathematical Society ,/jou rnals/.[6]New York Journal of Mathematics,:8000/nyjm. html.。