2007年

席貝克效應〈Seebeck effect〉是熱能與電能之間的一種固態能量轉換方式，當兩種不同性質的金屬導線之端點連接形成封閉迴路時，若兩接點間有溫差，則兩接點間可測得電壓，而因單位溫差所產生的電壓差稱為席貝克係數〈Seebeck coefficient〉。由本實驗的結果發現：溫差大小、導線特性〈熱電係數〉、導線表面有無氧化層是影響席貝克效應中電壓值及席貝克係數大小的原因。溫差越大，電壓值越大。鉑〈Pt〉與其他金屬的熱電偶導線組合之熱電轉換效能為Pt-Fe > Pt-C > Pt-Al > Pt-Sn；導線的表層若有氧化層，會造成電壓在上升過程中穩定性不佳，產生高低起伏的跳動溫壓曲線，但在較高溫差時，溫壓曲線趨於穩定上升狀態。The Seebeck effect is one of thermoelectric effect. A voltage existed between two ends of different metal wires when a temperature gradient existed between the two junctions. This means the conversion of temperature differences directly into electricity. The voltage induced was called electromotive force, EMF. The EMF generated was dependent on the properties of the wires, which formed the thermocouple and the temperature difference between the junctions. This paper was to study the effect of variety of wire combinations and geomtric properties of wires in thermocouple on the Seebeck coefficient generated. The results indicated that temperature difference, wire properties, and absence or presence of oxidative layer on the surface of wires were the factors to affect the magnitude of voltage and the Seebeck coefficient. As the temperature difference between the junctions was increased, the voltage increased. The combination effiency of conversion of temperature difference into electricity of platinum was following： Pt-Fe > Pt-C > Pt-Al > Pt-Sn. The presence of oxidative layer on the surface of wires caused instability during the process of voltage increase. It made the temperature-voltage curve up and down. On the contrary, when the temperature difference was big, the temperature-voltage curve became increased stably. The temperature-voltage curve was independent of geomtric properties of wires.

This research mainly discusses an antibubble the interesting physical phenomenon that isn’t generally noticed .We use digital video cameras to obtain the experimental results, and pick up and analyze them with the computer. The experimental result as follow： (1) The formation of an antibubble mainly relates with the surfactant ingredients.The washing liquid, which has the surfactant characteristics the thinner its concentration; the lower the success rate of the antibubble. (2) The size scope of an antibubble is situated between 0.35 cm to 0.6 cm, and the size of the antibubbles produced by different densities of washing liquids are not obviously different. (3) The interior radius of an antibubble is approximately 3/4 times of the outer radius. (4) The survival time of an antibubble is mostly within 70 seconds, some minority surpasses for 100 seconds. Its average survival time is 40.65 seconds. (5) When the temperature of water the underneath liquid is between 20℃ to 90 ℃, the higher its temperature; the lower the success rate of the antibubble. After the temperature reaches 80 ℃, the success rate of the antibubble turns into 0. Besides, the higher the temperature of water; the shorter survival time of the antibubble. (6) Antibubble die by itself can be induced two kinds of types. One is centralism death, and another one is vibration death. Vibration death is less common and rare. Its dead process lasts longer time than the general antibubble, and also has 2 to 3 times back and forth vibration. 本研究主要要探討「反泡泡」（antibubble）這個一般不被注意到的有趣物理現象。我們用數位攝影機進行實驗結果的取得，並以電腦進行擷取與分析。實驗結果為：一、 反泡泡的生成主要與界面活性劑的性質有關。洗碗精這樣具界面活性劑特性的物質濃度越稀薄，反泡泡的成功越低。二、 反泡泡的大小範圍介於0.35cm 至0.6cm，不同濃度所產生的反泡泡大小並無明顯之差異。三、 反泡泡的內半徑約為外半徑之3/4。四、 反泡泡存活時間大多在70 秒之內，僅有少數超過100 秒，平均存活時間為：40.65 秒。五、 承接液體在20℃至90℃的範圍中，隨著溫度的增加反泡泡生成成功率越下降，在80℃之後，成功率降至0。且溫度增加會使反泡泡存活的平均時間下降。六、 反泡泡自行破滅可以歸納出兩大種類型。其一為：「集中破滅」；另一為「震盪破滅」。「震盪破滅」情形較為特殊少見，其破滅過程較一般反泡泡來得更久，且有2 至3 次的來回震盪。

本實驗以吸附染料之二氧化鈦奈米結構電極層為承載基材的太陽能電池為研究對象，旨在增進其光電轉換效率，促使染料有效地吸收光能後造成電荷分離，再經由二氧化鈦傳導帶向外傳出而形成電流，即所謂染料敏化太陽能電池。實驗主軸共分三：1、合成染料N3：觀察吸附度與浸泡時間之關係，發現在18~20 小時電池有最佳吸附；改變電解液濃度，求得最佳電解液濃度範圍；酸化二氧化鈦極板。2、天然植物色素：改變溶劑，得出高極性之丙酮對電池最佳；酸、鹼化植物色素；觀察電池隨著光照時間增加，性質趨於穩定。3、混合色素與染料：此實驗旨在印證不同吸能範圍之染料在極板混合浸泡後，電池吸能帶是否有疊加、擴充的效果，並觀察分開浸泡與混合色素一起浸泡之不同效應，量測IPCE 以玆比較。實驗結果可知，確實對於電池吸光範圍有所增加，且分開浸泡之效果較好。This experiment is mainly about the phtosensitization of Ti02 solar cell, aiming at improving the energy conversion efficiency, promoting the electric charge to separate from TiO2 and spread out through after the dye absorbs light. That is so-called dye-sensitized solar cell. The experiment mainly divides into three parts: 1. Ruthenium(II): Observing the connection between adsorption and dipped-time, find out that solar cell has best to adsorb in 18 to 20 hours; change the concentration of electrolyte; acidification TiO2. 2. Photosynthetic pigments: Change solvent, and get the conclusion that pigment has better adsorption in high polar solvents such as acetone; acidification/basification pigments; observe the changing of energy conversion efficiency while the illumination time increases. 3. Mixed the dye and pigment: This experiment is aim at proofing that the absorption spectrum of soaked-TiO2 may mix after dipped in different dye and pigment. Furthermore, we compares the differences between TiO2 dipped in one mix solution and dipped in several solutions separately, measure its IPCE. According to the experiment, the spectrum of soaked-TiO2 is certainly larger, and dipping in solution separately has better effect to the battery.

槐葉蘋(Salvinia natnas)生長於台灣低海拔淡水濕地，目前已列為嚴重瀕臨滅絕的台灣原生物種，為不具有根的植物，是世界珍稀的漂浮型水生蕨類。本研究是探討槐葉蘋形態、生活史及生存環境因子，實驗發現可藉由成熟浮水葉外部形態特徵來區別槐葉蘋與外來種之人厭槐葉蘋(Salvinia molesta)；槐葉蘋成熟浮水葉呈橢圓形，葉上毛被物是叢生且分岔，人厭槐葉蘋成熟浮水葉呈雙耳形，葉上毛被物則像打蛋器。當兩物種共存於同一個環境空間時，人厭槐葉蘋以平均11.6 cm2/week 的生長率將槐葉蘋完全取而代之，顯示人厭槐葉蘋之入侵對槐葉蘋生存影響之深遠。經由兩年的槐葉蘋物候觀察，發現3~11 月為抽芽成長期、3~12 月為成熟繁殖期、12 月~隔年2 月為冬枯期及孢子囊果出現期，12 月~隔年5 月為孢子囊果成熟開裂期。其繁衍策略可分為無性繁殖（頂芽及側芽生長）及有性生殖（異配子體交配）。探討環境因子（光照度、氣溫、濕度、水質、水溫、pH 值）分析結果，適合槐葉蘋生存環境的條件為(1)陽光間接照射（半遮蔭，遮蔭度58.33%）、(2)乾淨未受污染的水質(pH 6.5~8)、(3)通風性良好。生長環境符合以上條件即可達到移地保育的目的。Salvinia natans, a floating fern without roots, grows in low elevation fresh water wetlands of Taiwan, and is a critically endangered precious Taiwanese native species. This research investigates the life form, life history, and living environment of Salvinia natans. Our experiments show that we can differentiate Salvinia natans and Salvinia molesta, two easily mixed up species. The shape of matured floating leaves of Salvinia natans is elliptical and smaller, while it is twin-ear shape and larger for Salvinia molesta. Also, they can be distinguished by their leaf hairs. The hairs of Salvinia natans are tufted and separated at the tips, while the hairs of Salvinia molesta form an ‘eggbeater’ shape at the tip. When these two species lived together, Salvinia molesta grew in a rate of 11.6 cm2/week and will replace all Salvinia natans eventually. This shows the profound impact of invasion of Salvinia molesta. From the data of 2-year phenology observation, we concluded that budding took place from Mar. to Nov., growing and reproducing from Mar. to Dec., decaying from Dec. to Feb. (sporocarps were born in this period), and sporocarps matured from Dec. to May. There are two reproduction strategies: sexual reproduction (intergametophytic mating), and asexual propagation (by terminal and axillary growth). After investigating the environment factors (illuminance, air temperature, water temperature, humidity, pH), we found that ex situ conservation for Salvinia natans requires 1) indirect sunshine, 2) unpolluted water (pH 6.5 ~8), and 3) good ventilation.

磁粉探傷過程包含兩個重要的物理現象，其一是磁力線於工作瑕疵處的漏磁現象而形成邊緣磁場，其二是鐵粉顆粒受邊緣磁場的影響而向工作瑕疵處附近聚集現象分別反應出磁場在通過不同介質時所遵循的折射原哩，以及磁場分佈對鐵粉顆粒產生的磁力原理。本研究以電磁通電產生靜磁場，並利用兩電磁鐵間的氣隙來模擬工件瑕疵，因電磁鐵的磁導係數遠大於空氣之磁導係數而造成漏磁場方向機與漏磁面垂直，形成一單純的邊界條件使得邊緣磁通密度的解析解可直接利用馬克斯威爾方程式求得。我們亦導出空氣中的磁通分佈對微小的鐵粉顆粒所產生的磁力公式，發現鐵粉顆粒受靜磁力的大小與該顆粒的體積、磁通密度與磁通密度之梯度成正比，而其方向則與磁通密度之梯度一致，此結論與磁粉探傷過程中，鐵粉向工件瑕疵處聚集的現象吻合。實驗設計採用螢光粉混合鐵粉以獲致明顯的鐵粉顆粒運動軌跡，用數位錄影機紀錄後再擷取影像圖檔判讀其位置與時間之關係，進而反算鐵粉顆粒之位置與所受之靜磁力的關係，以定量的方式證實所推導的邊緣磁場分佈公式以及磁力公式。Two important physical phenomena are observed in the practice of magnetic particle inspection (MPI). The first one is that leakage flux is present in the defect area of the work-piece under inspection. The second one is that magnetic particles aggregate in the vicinity of the defect. These phenomena manifest the theory of flux refraction, which occurs in the intersection area of two different magnetic materials, and the theory of magneto-static force, which is experienced by the iron powder in a magnetic field distribution. Two electromagnets, made of cast steel, are aligned together such that the leakage flux in the air gap forms a fringing field distribution. It is this magnetic field distribution that simulates a defect area in a magnetized magnetic work-piece. Since the permeability of cast steel is far larger than that of air, the direction of the fringing field at the surface of the electromagnets is almost perpendicular to the surface. Such a simple geometry renders an analytical solution to the Maxwell’s equations. The magnetic force of the magneto-static field exerting on the magnetic particle, an iron powder in this case, can be derived by using the principle of virtual displacement. We obtain a formula of magnetic force, whose direction coincides with the gradient of the magnetic flux density and whose magnitude is proportional to the magnitude of the particle volume, the magnetic flux density and its gradient. This formula also agrees with the observation in MPI that the magnetic particles aggregate in the vicinity of the defect.

費曼曾說：There is plenty of room at the bottom。喬治亞理工大學的Mostafa El-Sayed 教授發表的癌細胞辨識、與科學月刊報導『台大抗煞一號』引發我們對膠體金粒子的興趣。膠體的性質主要是由界達電位 (zeta potential)決定。參考台科大、成大、中山…等超音波應用研究，提出改良篩選物理法製造之膠體金粒子的儀器設計與製作。經沉降過濾可達平均粒徑 100 nm；而離心式篩選機與超音波管式篩選機可達平均粒徑30 nm。篩選後的膠體粒子以電容原理調控膠體金粒子之界達電位 (zeta potential)，成功地從-30 mV 提升至-59 mV，並發展成電容超音波界達電位控制儀(Capacitor Ultrasonic Zeta Potential Controller)。以膠體金粒子與蛋白質鍵結量來測試調控界達電位的效果，發現蛋白質鍵結量之增加曲線與界達電位的增加曲線的增加趨勢相似；此功能的發現對於生物科技方面的應用應會有很大的幫助。透過界達電位控制系統，本研究達到費曼先生所期望的「在原子或分子的尺度上來加工材料和製造設備」。“There is plenty room at the bottom.” The words of Mr. Feynman are the beginning of nano technology. Mostafa El-Sayed, a professor of Georgia Institute Technology, identified cancer cells through nano gold-antibody complex. So, our study focuses on the zeta potential of colloidal gold particles. At first, the filtering method and equipments were developed. The theories were based on the ultrasonic studies of universities such as National Taiwan University of Science and Technology. Then the colloidal gold’s sizes were filtered to100 nm through settling. At last, by using Continual-Filtering Centrifuge (CoCe.) and Tube Well Mass (TW-MS), the mean particles sizes can be filtered to 30 nm. The most important results are: Zeta potential of the gold colloid was controlled with Capacitor Ultrasonic Zeta Potential Controller. The zeta potential can be raised from -30 mV up to -59 mV, which is -20 mV higher than the conventional pH-changing way. The function of zeta potential to protein binding quantity was tested. The increasing curves of zeta potential and protein binding quantity were similar. This property would be a significance of biotechnology. Thourgh Capacitor Ultrasonic Zeta Potential Control system, the zeta potential’s limitation of gold colliod, which is produced by SANSS (Submerged Arc Nanoparticles Synthesis System), can be controled in a wilder range. The study which is focused on nano-scale, like the wish of Mr. Feynman – “To manufacture material and produce equipment in atom and molecular scale”.

Thermal expansion exists in our daily life. However, thermal expansion is generally too slight to be seen by naked eyes. Therefore, in the present project, a dilatometer was assembled to enhance better sensitivity toward thermal expansion. Hopefully the self-assembled dilatometer could contribute to teaching purpose.The structure of our 4th generation dilatometer is showed below. Using an ‘L’ square to hang up the metal stick and a rolling needle with a mirror to reflect the laser light are the critical parts of this equipment. By using this special reflection mechanism, the slight expansion of a metal stick caused by heat can be enlarged to a large scale. This special mechanism is where our creativity laid. Measuring in millimeter (mm), the measurement precision of the equipment can be extended to 0.0001 decimal. Our dilatometer was used to measure the expansion of various metal sticks caused by the temperature changes. Results were drawn from analysis of the data: 1) The average relative deflection was within 1.0~1.8%; 2) The relative deviation of linear thermal expansion coefficient was within –1.2~-4.4%. 物質熱漲冷縮的特性普遍存在於我們的生活環境中，但因其變化量相對微小，一般並不容易直接觀察，爲了進一步研究這課題，我們組裝偵測熱膨脹的儀器，並希望儀器的靈敏度高，能推廣為教學器材，經過我們不斷努力與改良，終於有了令人愉悅的成果。 自製第四代熱膨脹儀的結構如圖，設計「角尺懸吊金屬棒」與「滾針及鏡面反射」是儀器的重要部份，利用滾針旋轉及鏡面反射雷射光，加乘放大熱膨脹的微量變化，這是我們主要的創意，以公厘（mm）為單位，儀器的精確值到小數第四位。 利用自製的熱膨脹儀，探討金屬熱膨脹的影響因素。分析實驗所得數據，平均相對偏差在1.0~1.8﹪，而線膨脹係數的相對誤差約-1.2~-4.4﹪。

設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve , Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P 為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。 Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.

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.

吹長笛時，按同一按鍵，以大小不同的力量去吹，會引發不同頻率的泛音，而通常越用力吹，引發泛音的頻率越高，所以我們想了解為什麼越用力，泛音的頻率會高，其間的關係究竟是什麼？風經過管口會產生各種頻率的噪音，其中某些特定頻率的聲音會因為會在管內形成駐波而放大，所以我們只能聽到某些特定頻率的聲音。當風速增加時，會在管口形成渦漩逸放的紊流現象。其渦漩頻率與流速成正比（註一）。我們以塑膠管實驗。發現以特定的風速引發該基音後，繼續增加風速，當風速達某一定強度時，才會躍遷為下一個泛音的頻率。這個現象告訴我們：在一封閉管下，風速與泛音的關係並非「線性遞增」，而是越「躍遷遞增」的關係。另一個實驗測量不同管長、其諧音之頻率的關係，我們可以得知，越短的管子，因為相鄰兩泛音間頻率差較大，越不易激發更高階泛音。經由這些實驗結果，我們能夠推論：當管子越長、基音頻率越低時，諧音間頻率的差距相對越小，繪出的風速－頻率關係圖應更加顯示了風速與頻率呈正比關係。未來我們可以以閃頻器觀測紊流渦漩的產生，再變化至不同吹入角度，及各式管口造形，這些實驗能協助我們更進一步了解樂器的發聲原理，甚至開發一個以聲音頻率測量風速的儀器。註一：林婉如、張?文2006 國際科工程組佳作作品。When we press the same key and blow a flute using different strengths, we can get different overtones. Usually, the harder we blow the flute, the high the frequency we get. We want to understand why we get a higher frequency when we blow harder into the flute and to understand the relationship between them. When wind passes through the mouthpiece, many kinds of noises will be produced. Some of the frequencies will expand because they will form standing waves in the tube. Therefore, we can only hear certain frequencies. As wind speed increases, a turbulence of the vortex shedding will be formed. The frequency of the vortex shedding and wind speed will be in a direct ratio. We experiment with plastic tubes. When we increase the wind speed and get certain magnitudes, the frequency will jump to the next overtone. The phenomenon shows that the relation, in a closed tube, between wind speed and harmonics is not a linear increase but a transition increase. In another experiment, we measured the relationship between wind speed and different lengths of tubes. We can infer that the shorter the tube, the higher high-frequency harmonics can be produced. Through these experiments, we come to the conclusion that the longer the tube, the lower frequency of the fundamental tone we get and the discrepancy in frequency between harmonics is smaller. Then we make a diagram between wind speed and frequency that indicates that there is a direct ratio between wind speed and frequency. In the future, we can use “” to observe the production of turbulence. Then we can switch to different angles when we blow into flutes. Otherwise, we can experiment with different shapes of mouthpieces. These experiments can assist us to understand more how the instrument sounds. We can develop a device measuring wind speed with frequency.