全民攻笛
本實驗主要是研究閉管駐波的發聲原理。何謂「閉管駐波」?就是一個管子在相同長度下,用不同的力道吹,會有不同音高的聲音產生,這些音被稱為「諧音」。原管長所能發出的最低頻率稱作「第一諧音」,第二低的聲音稱作「第三諧音」,依此類推。在簫的演奏上,只要按住同樣的孔,用較大的力量吹,也同樣會發出較高的音;同樣地,在曲笛的演奏技巧上,有平吹、急吹等分別。為什麼吹越用力,音就越高呢?如果現在拿一個大吸管吹(要裝活塞),你會發現,只有在特定的位置(角度)下,才能吹出聲音。那麼,角度對於聲音也有影囉?這些現象的幕後黑手,就是在管口產生的「渦流」,渦流頻率也會隨著風速而增加;而且,渦流的頻率在特定風速下,會有特定的範圍。經由實驗可以大略歸納出,影響閉管駐波的三個主要變因,分別是「風速」、「風吹角度」、及「吹口至管口的距離」。吹得越急,風速就越快,渦流頻率越高,越易使諧音躍遷;吹的角度越小,越易產生渦流,亦易引發聲音;吹的距離越小,渦流越不?定,越易產生其他的擾動。以上就是本實驗的概略。This project is aimed to fine out how the closed tube can produce a sound. We know what harmonics are. When we hold a big straw and blow with increasing strength (the bottom should be in water), it will generate a higher sound. The high sound is called “harmonic”. The lowest sound it can make is “the first harmonic”, the second lowest sound is “the third harmonic”, and so forth. Likewise, when we press the same key on vertical bamboo flute with increasing strength, it’ll also produce a higher sound. But why do we use the strong air stream to blow the tube to cause the tone to transfer? Now let’s blow a straw flute. You will find that you need to blow in the particular position, and then the sound will be produced. So, is there any relationship between the blowing angle and the frequency? Actually, all these sound are produced by “vortex in the mouthpiece.” The frequency of vortex will increase with the wind speed. Moreover, the frequency of vortex has a range. In sum, the higher the wind speed is , the higher the frequency of the vortex is , and leads to the higher frequency of the sound. The smaller the blowing angle is, the easier the vortex will be produced; the easier the frequency will be made. The smaller the distance between the blowing angle and the frequency is, the more unstable the frequency will be. The above is the most important research in this project.
海格的爆尾釘蝦-鹼性電池的探討
鹼性電池使用的電解液均為強鹼,電池中的鋅極會與其發生腐蝕反應,使得電池放電壽命降低,並產生氫氣,而大量氫氣使得電池有爆裂的危險,為了改善上述問題,我們自行設計了氣體觀測儀器,用來檢測銀鋅電池充放電與靜置時之氣體產生量,更藉由探討影響變因的過程找出銀鋅電池較合適之使用條件,其中包含電解液種類及濃度之選擇、電極面積與充電電流對使用效果之影響,並改善電池腐蝕程度;我們將鋅極以浸鍍處理(Sn:Pb =1:1 )並搭配電解液添加物(KOH:Zn(OH)42 -= 2:1) 可效率地抑制氣體產生;更用氯化銀粉末取代傳統氧化銀極片為正極,發現氯化銀可代替氧化銀電極,且有不錯的放電效果。;As we know, the electrolyte solution used in an alkalinebattery is a concentrated alkaline solution, which corrodes the zinc electrode in a battery of this kind. The corrosive reaction not only reduces the lifespan of the battery but also produces hydrogen, causing the battery to explode. This study is intended to help us design a device to measure the quantity of hydrogen gas generated in the charging of a zinc-silver battery. We have studied several factors affecting zinc-silver battery, including the variety of electrolyte, the concentration of alkaline solution, the surface of electrode, and the density of charging current, etc. To reduce the corrosion of zinc electrode, we plate the zinc electrode by the immersion electroless plating method, using several kinds of low-polluting anti-corrosive additives (metallic compounds such as lead and tin). We also add zincate ion into electrolyte solution to further reduce the quantity of hydrogen produced. The experiments show a zinc-silver alkaline battery works most efficiently, if the powder of silver chloride is used instead of silver oxide.
生生不息-正五邊形的繁衍法則
This study was to explore the nature of two basic constitutes of the regular pentagon,With these two constitutes, the regular pentagon could be multiplied into any times. We used four multiplication methods (m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) to show how the regular pentagon could enlarge and to verify that the enlarged regular pentagons derived from computer did exist. By integrating these four multiplication methods, we were able to arrange regular pentagon of any length of side, and evidenced the equation was
( If the side length of a regular pentagon is a form of m,n is the number of A,B respectively )
We further proved that the first multiplication method could be developed into a new modified method, which could divide a regular pentagon with a given side length into a combination of A and B. But only when the x and y of side length of a regular pentagon could be divided by a natural number, k, and made x/k into an item of the Fibonacci Sequence and y/k a successive item.
When we tried to verify if any regular pentagon could be constituted by other smaller regular pentagons, we also found that it was un-dividable only if the length of pentagon side were ( the number of A, B were the 2n and 2n-1 item of Lucas Sequence). Otherwise, any regular pentagon might be able to be constituted by other smaller regular pentagons.
本研究是以正五邊形的兩個基本組成元素(B)作為討論對象,利用此二元素可以將正五邊形做任意倍數的放大。我們共使用4種繁殖法則(m2 = 2m1 + n1 、n2 = m1 + n1 、m2= k2m1 、n2= k2n1、a2 = a1 + 1、a2 = a1 + ) 來說明正五邊形的放大情形,並利用此4 種繁殖法驗證電腦運算出的放大圖形確實存在。利用這4 種繁殖法則的改良與整合,已達到能排出任意邊長之正五邊形的目標,並能計算並證明出其通式為。
(若正五邊形的邊長為形式,m、n代表、的個數)
更特別的是,我們能用第一繁殖法反推出一種方法,將給定邊長的正五邊形利用簡單的切割方式分成由A、B 組合成的形式,但只有正五邊形邊長之x、y 值可同除以任一自然數k 而使 x/k 為費波那契數列之一項且 y/k 為其後一項者才可以使用。
將此想法推廣至一個正五邊形能否由比他小的其他五邊形組合而成時,我們也發現當正五邊形之邊長為時(其A、B 個數為盧卡斯數列之第2n,2n-1 項),不可分解,否則應該皆可將一個正五邊形分解成比它小的其他五邊形組合(我們也可以利用這些質形檢驗出其他正五邊形是否也為質形)。但其分解形式,不只一種,而我們推測只用兩種較小的正五邊形就能達成,我們期待能找出一或多種分解方法,能將正五邊形分解成標準的分解形式。
漩渦也有形
流體旋轉時,外圍及底部流體,因槽壁及槽底摩擦力的影響,流速較慢,相對的壓力也較大,導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中,探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小,隨著f 的增大,可觀察到的形狀邊數越多;反之,若y、R 愈小、H 越大,則f 愈高,所形成的圖形半徑愈大,易超過轉盤,不易觀察。依白努利方程式,外層水流的流速較慢,而內層水流的流速較快,故外層壓力大而內層壓力小,水會由外往內流,而此渦動流於轉動液面產生的剪力,可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中,因轉動而產生流體離心力與內外層壓力差交互作用下,於某特定相關的因素條件下,形成特定角形數漩渦,是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.
黑龍仔知人間冷暖
為了瞭解黃斑黑蟋蟀叫聲和溫度之間的關係,我應用物理熱平衡原理,自製水浴槽控制環境溫度,以電腦錄音程式分別錄製15℃、20℃、25℃、30℃、35℃時的蟋蟀叫聲,利用Sound Forge軟體分析並比較不同溫度下的各種特性。結果發現所分析的chirp、chirp period、syllable period、pause均和溫度呈負相關,而單位時間內的叫聲次數則與溫度成正相關,並推導出15~35℃範圍內蟋蟀叫聲次數與溫度成正相關的公式。最佳直線為:﹙15秒內叫聲次數+19.385﹚÷2.483=當時溫度﹙℃﹚,呈高度正相關﹙相關係數:0.9398﹚。本實驗也比較母蟋蟀對不同溫度下雄蟋蟀叫聲的偏好程度,發現母蟋蟀較偏愛25℃時的雄蟋蟀叫聲,此結果可能與雄蟋蟀在25℃時叫聲的波形最為穩定有關。為探測蟋蟀觸角上的溫度感受器位置,我們曾將不同部位的觸角加以剪除,結果顯示觸角剪除面積越大的雄蟋蟀越不傾向鳴叫,但無法證實是否為溫度偵測異常所導致。本實驗除供學術研究外,因黃斑黑蟋蟀在世界各地均有分布,所以希望能藉由分析溫度與蟋蟀叫聲的相關性實驗,未來嘗試能探討其在不同環境的適應行為亦或種化的可能性。另外,全球暖化問題日益嚴重,也希望能藉由相關實驗探討暖化對蟋蟀生態上的影響。最後,我們的實驗證明了蟋蟀叫聲和環境溫度確實有極大的關聯性,未來或許能參考蟋蟀感覺溫度的機制,製作出一個天然零污染的溫度計。 To find out the relationship of cricket’s calling and temperature, we use a hand-made water-bath tank to control the temperature and record the callings with microphone and software, Sound Forge. After analyzing the collected data, we’ve found that cricket’s chirp, chirp period, syllable period, and pause are indeed affected by temperature (15 degrees - 35 degrees C). Moreover, we also compare female cricket’s preference to the callings, and the result indicates that female cricket’s preference is changing with temperature. In the last, we tried to find out where the thermoreceptors are by cutting out the antennae. After cutting, crickets tend to not to make any calls at all, so we conclude the antennae might play an important role in sensing and calling. The experiment proves that this communication system is temperature coupled. Because the cricket, Gryllus bimaculatus, is a worldwide species, we may learn the accommodation or the possibility of performing a new species by researching the relationship of temperature and cricket’s callings. By the way, the Green House Effect is getting more and more serious, so we want to search for the influences on crickets that are caused by Green House Effect. The last but not the least, according to the report, maybe we can investigate the mechanism of sensing temperature and then make a natural thermometer that is no pollution in the future.
探討太陽黑子與珊瑚生長速率之關連性
微孔珊瑚是優良的生物氣候記錄器,可準確記錄海水表面水溫、陸源沉積物通量和其他微量海水組成等,已成為熱帶氣候變遷研究的重要工具。然而,珊瑚成長速率則顯著受限於海水表溫影響(邱景星,1999)。太陽是地表能量最主要來源,其活動狀態能深遠掌控地球氣候變化,因此其週期性變動規律,已成為近期地球科學家探討環境變遷的重要資訊。 本研究以台灣東南外海綠島採集的微孔珊瑚骨骼樣本,藉由X-ray精確測量其年平均生長速率及觀察骨骼內微量腐殖酸螢光特性,並透過比對太陽輻射量、珊瑚生長與太陽黑子數目的相關性分析,以推倒百年來控制地表氣候變遷的主要因素。 本研究經由頻譜分析、主變量計算、平均標準差和太陽輻射角修正,獲得正確太陽黑子數目、地區性輻射、海水表面溫度和珊瑚生長速率等資料,並討論其間的相互關係。 結果顯示,太陽輻射、海水表面溫度和氣溫有高度正相關(r2>0.62),證實太陽對地球氣候系統的重要性。太陽黑子與輻射資料,則因大氣折射、日照時數等因素影響,正設法解決這些干擾效應;而珊瑚生長速率與海水表面溫度的相關性,則涉及雙極化效應(註)及其他未知因素影響,尚待進一步釐清。 (註):雙極化效應指珊瑚在過高或過低的環境下,生長速率皆會停止 The skeleton of Porites corals is one of the most useful biogenic recorders, which provide relevant information of abrupt climate change, such as sea surface temperatures (SSTs), riverine sedimentary flux, and seawater compositional variations. Information retrieved from coral skeleton, therefore, has become a powerful tool for studying tropical climate change. The annual growth rate of Porites corals, however, was affected strongly by local SSTs (Chiu, 1999). On the other hand, the climatic condition on Earth surface is regulated significantly by solar activity. Subsequently any intensity or periodicity variation in sunspot activity will cause major global environmental changes. This research aims to study coral skeleton collected from the Orchid Island (Lan-yu) offshore southeastern Taiwan for precise measurement of annual growth rate using X-ray density bands, as well as the luminous characteristics of trace humic acids in skeleton. A systematic comparison among solar irradiation, SSTs and coral growth rate will provide critical information on major factors that may affect environmental changes occurred during the last millennium. In this study, we apply spectrum analyses, principal component, mean standard error method, and modified sun irradiation angle to correct biases presented in the available data of observed sunspot number, local irradiation, SSTs and coral annual growth rate and to examine possible relationships among these factors. We have found excellent correlation coefficient (r2>0.62) in solar irradiation, SSTs and air-temperature, which support the importance of solar irradiation to the earth surface climate. However, effects on cloud and length of sun irradiation need further investigation to emphasize the importance of sunspot activity to the annual growth rate of Porites corals. No straight forward relationships were observed between coral growth rate and local SSTs due to complicated biological effect (1*) or other unknown factors, waits for further investigation in the near future. 1* Complicated biological effect means that coral may stop growing their skeletons when the temperature it lives in is over range for growth.
立體尺規作圖-PES 作球
In this study, we mainly explore the geometric construction in 3D. By conducting some problems about constructing circles, we define the PLC construction in 2D as constructing a circle, either passing through a given point (P), tangent to a given line (L) or tangent to a given circle (C). Besides, we aim to discuss the properties of the PLC construction and the relations between each other. We discover if we find a plane satisfying certain conditions in space, the properties in the PLC construction can apply to such a plane. Furthermore, we extend the properties in PLC to the PES construction in 3D, defined as constructing a sphere, either passing through a given point (P), tangent to a given plane (E) or tangent to a given sphere (S). Also we discuss the relations among them.這個研究主要在探討3D 的尺規實作。藉由歸納某些有關作圓的題目,我們定義2D 中的PLC作圖─作圓,過已知點(P)、切已知線(L)、切已知圓(C)。並探討PLC 作圖的性質及彼此的關聯性。而我們發現:在空間中只要找到滿足特定條件的平面,則2D 幾何作圖性質在該平面仍能沿用。此外,運用PLC 作圖性質,我們進一步推廣到空間中的PES 作圖─作球,過已知點(P)、切已知面(E)、切已知球(S),並探討各個類型間的關聯性。