樂器聲波之探討(The Study of A Sound Wave on Musical Instruments)
演奏樂器時，是使發聲體產生駐波而發出各式各樣悠揚的聲音及音調；樂器主要分成振動體(發聲體)及共鳴器兩部分，依發音方式分為弦樂器(使弦振動產生駐波)、管樂器(利用空氣柱振動產生駐波) 及打擊樂器(利用板、膜或磚等彈性材料的固有頻率振動產生駐波)。聲音有三要素：振幅、頻率及波型，響度取決於振幅大小、音調與頻率有關、波型則由不同的頻率及響度組成。樂音多變的主因是音色及音調。音色是發聲體的發音特性，取決於該發聲體的聲波波型。音調即聲音的高低，與發聲體的振動頻率材質息息相關，頻率愈高，其音調愈高，而樂曲中的音階高低則是由音調高低所構成。樂曲的製作及演奏必涉及到律制，從駐波的產生、律制的探討、頻率的測量和琴鍵的振動模型建立與波形的觀察，我們使用計頻器、示波器及有限元素ANSYS 軟體、數學計算Mathematica 軟體，我們設計一系列實驗，企圖對樂器聲波操作技巧有更進一步的認知。從實地走訪樂器製造廠，了解到設計與改良仍是樂器工藝家重要課題，本文的實驗方法可提供大型演奏會現場調音、樂器調音師或樂器工藝家設計製造樂器時參考用，對於發展文化產業期待提供更經濟與實用的建議。;Playing musical instrument is to make sounding part produce stationary wave so as to give off various gentle sounds and tones. According to different modes of sound producing, musical instruments which comprise vibrator (sounding part) and resonator can be divided into stringed instruments (which vibrate the strings to produce stationary wave), wind instruments (which produce stationary wave with vibration of the air column) and percussion instruments (which produce stationary wave with natural frequency of boards, films or bricks). Three Essentials of sound include amplitude, frequency and waveform, in which the amplitude decides the volume, tones are related to frequency and the waveforms are composed of different frequency and volume. Various musical sounds are mainly due to different timbres and tones. Timbres, sounding characteristics of sounding part, is decided by waveform of the sounding part. Tone means pitch of the sound and is closely related to vibrating frequency of sounding part. Higher frequency makes higher tones and pitch of a musical scale is decided by different tones. Music composing and playing is necessarily connected with music temperament including producing of stationary wave, discussion of temperament, measurement of frequency, establishment of vibrating mode of keys and observation of waveform. We adopted frequency counter, wave inspector, ANSYS software and Mathematica software and designed a series of experiment to get further knowledge of technique of handling musical instrument wave. After visiting musical instrument manufacturers, we learnt that design and improvement are still the essential subjects for instrument craftsmen. Experimental method in his article can provide reference for on-the-spot tuning of large concert, musical instrument tuner and musical instrument designing and manufacturing by craftsmen, and more economic and practical suggestion for cultural industry development.
你喝下了多少？-台灣市售優酪乳乳酸菌生長力及抗酸性之探討
現今乳酸菌飲料風行，但是乳酸菌是否真能通過胃酸的考驗，到達腸道進行複製，利益人體？我們首先以市售乳酸菌粉（加拿大Rosell 公司，含二種菌，暫時命名為"小毛"及"小白"）為預測菌種，利用分光光度計測定乳酸菌於Thioglycollate 培養基中的生長能力（OD600）。小毛在pH 值 1、 3 、5、 7 時之生長力分別為0、 0.008 、0.682 、0.847 ，小白為 0、 0.015 、0.973、 0.636。若於培養基中添加不同濃度的螺旋藻熱分解物，如加入0.01%的添加物後，小毛在以上各種pH 值生長力分別為0.042、1.291, 、1.447, 、1.213 ，小白為 0.053、1.392、 1.531、 0.988，意外發現可大幅提升菌的生長力及抗酸力。再取台灣市售4 種廠牌優酪乳（以甲、乙、丙、丁代表之），分離乳酸菌，再於各種pH 值中培養。結果在pH 3 時，螺旋藻熱分解物僅對丙廠牌有效, 乙廠牌無效, 甲與丙則有無填加生長力都很差。在pH 1 時, 則對乙、丙、丁皆有效，故建議廠商慎選菌種，並於製程及成品中添加螺旋藻熱分解物。The yogurt is a popular drink. But whether the lactobacilli inside can resist the destruction of gastric acid and grow well in the intestinal tract is still questionable. We used pure lactobacilli powder (Rosell Company, Canada, containing two bacteria named in this report as "Little Hair" and "Small White") for pre-test. The growth ability in thioglycollate medium was determined by spectrophotometer (OD600). The results of bacterial growth at pH 1, 3, 5, and 7 for "Little Hair" were 0, 0.008, 0.682, and 0.847, respectively. Those for "Small White" were 0, 0.015, 0.973, and 0.636, respectively. After supplement with 0.01% of the boiled lysate of Spirulina algae (ProBio Biotech, Taiwan), growth abilities at pH 1, 3, 5, and 7 for "Little Hair" were 0.042, 1.292, 1.447, and 1.213, respectively. Those for "Small White" were 0.053, 1.392, 1.531, and 0.988, respectively. The algae extract amply promotes the growth and acid-resistance, especially at pH 3, of these bacteria. The lactobacilli isolated from four different products of yogurt in Taiwan, named as A, B, C, and D, were then tested as above. Results showed the supplement with the boiled lysate of Spirulina algae was very effective, at pH 3, for promoting growth of C, but not effective for B. Growth abilities of both A and D were very unsatisfactory with or without this supplement. At pH 1, algae lysate supplement significantly improved the growths of B, C, and D. Therefore, this supplement in culture and product for yogurt preparation was suggested.
金字塔附近的流體力學效應
陸地上的金字塔無時無刻沒有受到氣體的包覆，這個實驗透過風洞模擬金字塔模型，在流體中的壓力變化，並藉由煙線來觀察流體的移動情形，可具體看到當流體經過物體週遭時流場的改變。經由測量壓力，可更深入的探討風速與壓力的關係。在實驗中，可發現當流體迎面而來，在金字塔後方形成的流場變化中，以渦流最易觀察；且透過壓力的測量，發現模型的前、後方，會有明顯的壓差，會對模型造成力矩，可能會使金字塔結構不穩定。越往金字塔上方壓差越小，因此其受阻力所產生的合力矩應較同底面積、同高的長方體小，故金字塔可以長久在沙漠中屹立不搖。此外，流體流過模型兩側會產生分離的情況，分離點的位置會影響渦流區的大小；一般而言，分離點發生在物體的越後方，尾流的尺寸越小，壓差所造成的阻力越低，實驗中發現流速對分離點的位置影響不大，金字塔的擺放形狀卻會對分離點的位置產生明顯的影響，所以越流線型的物體，其受到壓差所產生的阻力越小。希望透過以上的研究，能夠對金字塔周圍複雜的流場有更深入的了解。The pyramid on land is constantly surrounded by gas. Using the wind tunnel, we can investigate the distribution of pressure surrounding the model of pyramid; furthermore, we can discuss about the relationship between pressure and wind velocity. In addition, with the smoke wire, we can visually observe the dynamic flow filed. In our experiment, we discovered that when fluid comes, there will be obvious difference of pressure between the front and the back of the pyramidal model, causing a torque to the model. At higher parts of the model, there is less difference of the pressure, so the resulting torques of a pyramid should be less than that of a cuboid. Therefore, a pyramid can stand in the desert for a long time. Besides, when the fluid flows through the two sides of the model, it will separate, and the position of the separation points will influence the size of the turbulence area. Generally speaking, the farther the separation points are to the back, the smaller the size of the turbulence area, and the less the drag caused by the difference of pressure. With the study above, I expect to have more understanding about the complex flow field of pyramid.
口琴簧片振動與氣流的影響
本研究主題在測量口琴簧片受到各種氣流因子影響後，所產生音色、音頻等變化之探討。在過去我們認為，一片簧片不論如何吹奏，其發出的頻率皆相同。但是事實上，演奏家控制氣流的強弱、方向、渦流等，便可吹奏出多樣的音頻。探討形狀因子對簧片頻率的影響，如：長度、寬度、厚度對頻率所造成的影響。自製口琴，利用變壓器控制送風機風速。探討氣流因子對簧片主頻之影響，利用各種不同的自製吹嘴，改變風速、角度、渦流…等，找出可能使簧片改變頻率的氣流因素。實驗結果發現改變風速會影響簧片主頻的變化，風速越大，頻率越大，為一條平滑線。但並非一直都會上升，當簧片頻率上升至某一極限，便無法再利用風速使頻率上升。例如實驗四吸音標準狀態下，風速大於8 Kt 後，頻率一直停在429Hz。在外加障礙物時(模擬吹奏舌頭時隆起)和標準狀態(正常零度入射)下頻率比較吹音和吸音有明顯的差異。吹音時，同風速下，其頻率比標準狀態高，發生音升；吸音時，同風速下，其頻率比標準狀態低，發生音降，具應用性。我們發現在頻率改變時，簧片的振動型態會有所不同，所以利用高畫素像機拍攝和電腦相位差算出簧片之曲折點至尾端的距離，發現頻率和簧片之曲折點至尾端的距離成正向關係。如實驗五中頻率從414 至419Hz，簧片的曲折點到振動端距離也明顯變大。我們發現吹嘴和口琴只要稍有一點空隙(大約在0.2cm 左右)，便會和完全吻合時有顯著的頻率差距(吻合後大約比有空隙低20Hz 左右)，此實驗頻率變化現象和現實壓音頻率變化極為相近。實驗過程中發現，改變簧片吹嘴的吻合程度，吹入口琴的風速相近，但頻率變化卻也有壓音的音頻變化。在實驗三加入各種氣流因子發現入射角度和標準情形差異不明顯，因此推論壓音的頻率變化和風力強度、入射角度關係不大，壓音主要為渦流所造成的現象。簧片振動模式改變，導致簧片振動頻率發生變化，且簧片的自然頻率不變。當壓音產生時，氣流在振動面造成妨礙簧片振動的抗力，但琴格內部同時也給簧片的風壓，使簧片產生一種非自然振動的頻率。The theme of the research is to explore the changes on its timbre and frequency after the harmonica reed is influenced by each kind of air current factor .In the past ,most people think no matter how to play the reed ,the frequency it produced was supposed to be the same. But in fact the frequency will be changeable under different direction, turbulent flow and air intension by the perform. First to explore the basic feature of harmonica reed, for example: The length, the width, thickness cause the influence on the frequency. To make the self-made harmonica, using the transformer control air feeder wind speed. To discussion the influenced caused by air current factors,and use each kind of different self-restraint to boast, change the wind speed, angle, turbulent flow ,in order to discover possible factors the reed causes to change the frequency of the air current factor. The experimental result discovered the change of wind speed can affect the change of basic frequency , the stronger speed cause the bigger frequency, It will be a curve. But it will not be rising continuously, when the reed frequency rise to some limit, it is unable to cause the frequency rise again by using the wind speed. For example experiment four sound absorption standard conditions, after the wind speed is higher than 8 Kt, the frequency continuously stops in 429Hz. To compare obstacle (simulation plays when tongue sticks out) and the standard condition (normal zero degree incidence) , comparison blows the sound agreement sound absorption to have the obvious difference. When blows the sound, under the same wind speed, its frequency is higher than the standard condition, has the sound to rise; When sound absorption, under the same wind speed, its frequency is lower than the standard condition, has the sound to fall. The harmonica terminology for presses the sound, extremely has the application. We discovered when frequency change, the reed vibration condition have differently, therefore use the camera photography and the computer phase different figures out the reed winding point to the end distance, discovered the frequency and the reed winding point relate to end distance is being connected. If tests five medium frequencies from 414 to 419Hz, the reed winding point is away from to the vibration end also obviously changes . The different reed vibration condition cause the frequency to change. Natural frequency is constant. When cause “bending” (the frequency is lower than the standard condition), the airflow make a force keep from reed vibration. But the chamber air pressure still drive reed. therefore cause the reed to give off not natural frequency sound
關於渦旋
A professor once told me that scientists have already known a lot about vortices, but less about how to tackle with them in here and there cases. As to my mind, this means knowing by halves. As a matter of fact, I gradually found that human may not know more than a dragonfly! A dragonfly flying in a figure of eight pattern does know about Vortices Recycling. The highlight of the experiment is the hovering ability upon a fixed point in the air. Who can stay longer will be the king of Vortices. Sometimes I am not so optimistic about mimicking a fly or a bat, but I am really very interesting in discovering which flying mechanism is more effective,『Fling Mechanism』 or 『In a figure of eight pattern』, if with the same weight and energy? How to implement their mechanism in our flying machine? It is always the best policy to do naturally with vortices. The conservation of vortices is found here and there. Vortex itself is energetic. To gain means to keep. The one who is able to keep vortices will be rewarded. As in life generation and the ability of hovering, the rule follows. Typhoons and tornados still threat us like the beasts. And what’s more, a jumbo-airplane was crashed as beaten by tip vortices of the former airplane. As the dragonflies, the beautiful acrobats of vortices , infuse in tip vortices. Not the strong contradistinction did we realize that it is time for vortices!研究渦旋已經四年。四年之中，涉獵了許多關於渦旋的實驗。當我越了解渦旋，就越佩服那些卓越的昆蟲朋友們，他們可說是調配利用渦旋的大師。從候鳥遷徙的V字型隊伍、海豚的渦旋氣球、到蜻蜓八字型的飛行機制，我很想知道：在一個固定的流場中，到底哪一種運動機制，能最有效率的提供上升的力量？而如何將昆蟲朋友們的高超技術，運用到人類飛行載具上？將是我有興趣的另一項課題。『關於渦旋』是一系列渦旋實驗，目的就是自基礎開始深入了解在地球這樣環境下渦旋的性質。（一）探討基礎的渦旋本質（二）產生相對運動下物體的的渦旋架構（三）物體取得升力和失去升力的要件（四）昆蟲飛行機制探密（五）未來展望與渦旋的運用經過長時間的觀察可以了解到：1、渦旋遵守動量守恆。是以渦旋出現時是成對的2、渦旋是具有能量的。在上升力取得方面，當攻角過大時，渦旋剝離，造成能量的損失；以至於飛行載具失速。而蜻蜓是保有渦旋並加以利用的高手，自然事半功倍。順勢而為，渦旋增強。
凸多邊形完美分割線的尋找
1) First, we studied the properties of lines and segments that bisect a triangle’s perimeter. By observing the properties, we found a “revolving center” what we defined. We employed the revolving center in the construction with ruler and compass to make “triangle’s perimeter bisectors” that pass the points we desire. Later, we found out the “envelope\r curves’” equations of the “perimeter bisectors” on the triangle’s two sides are parabolic curves. Moreover, the focus of this parabolic is just as same as the revolving center. 2) The curves envelope of area bisectors formed a hyperbolic curves. By similar method of constructing a “perimeter bisector”, we can also construct an “area bisector”’ by using the hyperbolic curve’s focus. We accidentally found out that we can construct the tangent of the conic by using our method, too. Different from the information we found, It supplies a easier method to construct the tangent of a conic. 3) With the rules of constructing perimeter (area) bisectors, we can expand the method to constructing the “perimeter (or area) bisectors” of any convex polygons. 4) We call the lines that bisect the convex polygon’s perimeter and area at the same time the "perfect bisect lines”. Based on the properties of the” perimeter bisectors” and the “area bisectors” in our research, we found out that the” perfect bisect lines” pass the intersection of the” perimeter bisector’s effective segment” and the hyperbolic. Thus, we can construct the “perfect bisect lines”. Moreover, we proved the esistence of the “perfect bisect lines.”1. 首先我們先探討三角形等分周長線的性質，利用性質及觀察等周線的變化，我們找到可利用本研究所稱的「旋轉中心」，以尺規作圖的方式，作出「任意點的三角形等分周長線」。接著我們導出三角形兩邊上等周線所包絡而成的曲線方程式為一條拋物線的曲線段。進而發現上述的旋轉中心，即為等周線所包絡而成拋物線的焦點。2. 三角形兩邊上等積線所包絡出的曲線是一條雙曲線的曲線段。利用等周線的尺規作圖，我們找到同樣可利用焦點當旋轉中心做出等分面積線。意外的發現出圓錐曲線的切線作圖，皆可利用我們的研究方式(有別於已查出的文獻上記載)，較快速的作出切線。3. 利用三角形等周線(或等積線)的尺規作圖，可擴展到「過任意定點作出凸多邊形的等周線(或等積線)」。4. 我們將同時分割凸多邊形等周長與等面積的分割線稱為「完美分割線」。利用三角形研究出的等周線與等積線相關性質，我們找出完美分割線必通過同角的等周有效段與等積曲線段之交點。利用這結果可作出完美分割線。並進一步，我們證明出凸多邊形完美分割線的存在性。
東沙島海灘的變遷與復育：由龍擺尾停擺說起
政府最近公佈在東沙群島設立第一個國家海洋公園，顯示國人重視海洋資源的保育與復育；但是東沙島特殊的自然景觀「會擺動的沙嘴」—龍擺尾，卻因興建八座消波塊構築的突堤而消散停擺。本研究以一個高中生的觀點，設計及進行一系列的模型實驗，探討東沙島的形成機制、各種環境因素對海灘及龍擺尾的演化、驗證龍擺尾的現況及如何讓龍擺尾復活，再由東沙島海灘復育看世界的海岸問題。雖然設備很克難，但都能完成預定的目標，證實東沙島的海灘演化。希望此次對東沙島海灘的研究成果與初步探討，能應用於世界上遭受侵蝕而需復育的海岸。In 2007, our government proclaimed Dongsha archipelago as the first national marine park, signifying her emphasis on the conservation and restoration of marine resources. However, the sand spit on Dongsha island, a unique natural wonder commonly referred to as the “swaying dragon tail”, has become motionless since the construction of a total of eight groins along its SE and NE coast during the period between 1993 and 1996. This study has conducted a series of model experiments to verify several fundamental issues, ranging from the formation and the factors affecting the stability and the status quo of Dongsha island and its spit. The experimental results find several favorably outcomes, giving the coast evolving evidences of Dongsha island. Furthermore, strategy to stabilize the coast and revitalize the spit are then considered, which could hopefully benefit the coast suffering erosion on the world’s coastline.
網路監控與家庭自動化系統之研究
The paper presents a new technique for the Internet monition and control system. The user not only can “watch” the current operation of remote home appliances from the client computer, but also directly control the behavior of remote home appliances through the Internet network. In the mean while, concerning the interface between users and appliances, the virtual reality is combined into the system so that users operate the system easily. First, virtual reality, CGI , HEML . I/O control code, 8255 I/O card and CCD are applied in the server computer to control and “watch” home appliances. Next, the client computer is connected to the sever computer through the Internet WWW(World Wide Web) network. Then, the user can control remote home appliances directly through the homepage. Finally, the experiment results are presented and discussed.本研究提出一種高效率且易維護的網路監控技術，從遠端確實“看”到監控系統現場動作，並下達控制指令。同時顧慮到使用者操作介面，結合虛擬實境，讓使用者可更輕鬆操作。首先，伺服端結合VR(虛擬實境)、CGI技術、基本的HTML、I/O控制指令、8255 I/O介面卡及CCD(網路攝影機)，應用於家用電氣，接著用戶端透過WWW全球資訊網連上伺服端首頁，然後依首頁之畫面，來達到遠端監控與家庭自動化之目的。