小提琴琴橋主要將琴弦的振動傳遞到琴體上，並且能夠藉由琴橋的共振來強化振動的力量。在本文中，首先應用有限元素法，當琴腳為剛體固定時，計算修剪琴橋的自然頻率，並找出為何修剪琴橋可以增加小提琴音色明亮性，其琴腳反作用力與明亮性的關係。第二，改變琴橋材料性質的方向來比較對自然頻率的變化，並且依據挑選木材好壞的準則，個別改變三個材料性質來比較對琴腳反作用力的影響。第三，在琴橋中加入琴體來計算驅動點導納，並比較單獨琴橋與加入琴體後的琴橋之間有何差異。綜合以上結果，製琴師修剪琴橋到適當的形狀主要依據三個目的，頻率比、人耳的敏銳性、明亮性。

The violin bridge transfers vibration of the strings to the corpus, and the vibration can be reinforced by using the characteristics of the resonance frequencies. In the paper, we perform the finite element analysis to calculate the natural frequencies of trimming bridges when the feet are fixed. The relation between the reaction forces of bridge feet and the brightness will be discussed to specify the reasons why trimming bridges can increase brightness of the violin sound quality. We change the direction of material properties and compare the variation of natural frequencies. In addition, three material properties are changed individually to understand their effects on the reaction forces of the bridge applied on the corpus. The roles of the bridge with or without the corpus played on the vibration of the violin are also investigated by calculating the response of driving point mobility. In conclusion, expert violin repairman trims the bridges to a favorable shape depending on three major purposes: the natural frequency ratios, human ear’s sensitivity and the brightness.

Bucur, V., “Varieties of resonance wood and their elastic constants”, Catgut Acoust. Soc., Vol. 47, pp. 42-48, 1987

Bretos, J., Santamaría, C. and Moral, J. A., “Vibration patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis”, J. Acoust. Soc. Am., Vol. 105, No. 3, pp. 1942-1950, 1999.

Bissinger, G., “The role of radiation damping in violin sound”, ARLO 5(3), pp. 82-87, 2004.

Bissinger, G., “The violin bridge as filter”, J. Acoust. Soc. Am., Vol. 120, No. 1, pp. 482-491, 2006.

Chafe, C., “A comparison of timbres inherent in traditional violoncello playing”, Catgut Acoust. Soc. Newsletter 29, pp. 19-23, 1978.

Dunlop, J. I., “The acoustic properties of wood in relation to stringed musical instrument”, Acoustics Australia, Vol. 17, No. 2, pp. 37-40, 1989.

Duennwald, H., “Deduction of objective quality parameters on old and new violins”, Catgut Acoust. Soc. J., Vol. 1, No. 7 (Series II), pp. 1-5, 1991.

Fletcher, N. H. and Rossing, T. D., “The physics of musical instruments”, Springer-Verlag, New York, pp. 1-286, 1991.

Green, D. W., Winandy, J. E. and Kretschmann, D. E., “Mechanical Properties of Wood”, USDA, U.S.A., Chapter 4, p. 2, 1999.

Gough, C., “The violin: Chladni patterns, plates, shells and sounds”, Eur. Phys. J. Special Topics, 145, pp. 77-101, 2007.

Haines, D. W., “On musical instrument wood”, Catgut Acoust. Soc., Newsletter 31, pp. 23-32, 1979.

Hutchins, C. M., Research Papers in Violin Acoustics 1975-1993, Acoust. Soc. of Am., New York, 1997.

Jansson, E. V., “Experiments with the violin string and bridge”, Appl. Acoust., Vol. 30, pp. 133-146, 1990.

Jansson, E. V., Frydén, L. and Mattsson, G., “On tuning of the violin bridge”, Catgut Acoust. Soc. J., Vol. 1, No. 6 (Series II), pp. 11-15, 1990.

Jansson, E. V., “Acoustics for violin and guitar makers”, Dept. of Speech, Music and hearing, 2002.

Jansson, E. V., “Violin frequency response – bridge mobility and bridge feet distance”, Appl. Acoust., Vol. 65, pp. 1197-1205, 2004.

Kishi, K. and Osanai, T., “Vibration analysis of the cello bridge by the finite element method”, J. Acoust. Soc. Jap., Vol. 47, No. 4, pp. 274-281, 1991.

Müller, H. A., “The function of the violin bridge”, Catgut Acoust. Soc. Newsletter, 31, pp. 19-22, 1979.

Moral, J. A. and Jansson, E. V., “Eigenmodes, input admittance, and the function of the violin”, Acustica, Vol. 50, No. 5, pp. 229-337, 1982.

Müller, H. A., “How violin makers choose wood and what the procedure means from a physical point of view”, paper presented at Catgut Acoustical Society International Symposium on Musical Acoustics, Hartford, CT, 1986.

Rodgers, O. E. and Masino, T. R., “The effect of wood removal on bridge frequencies”, Catgut Acoust. Soc. J., Vol. 1, No. 6(Series II), pp. 6-10, 1990.

Saldner, H. O., Molin, N. and Jansson, E. V., “Vibration modes of the violin forced via the bridge and action of the soundpost”, J. Acoust. Soc. Am., Vol. 100, No. 2, Pt. 1, pp. 1168-1177, 1996.

Strobel, H. A., “Art & Method of the Violin Maker”, Aumsville, Oregon, 2006.

Strobel, H. A., “USEFUL MEASUREMENTS FOR VIOLIN MAKERS”, Aumsville, Oregon, 2006.

Trott, W. J., “The violin and its bridge”, J. Acoust. Soc. Am., Vol. 81, No. 6, pp. 1948-1954, 1987.

Weinreich, G., “What science knows about violins – and what it does not know”, Am. J. Phys., Vol. 61, No. 12, pp. 1067-1077, 1993.

Stowell, R., “The cambridge companion to the violin”, 湯定九譯，小提琴指南，世界文物出版社，台北市，13-72頁，1996。

王松永、國立編譯館，木材物理學，財團法人徐氏基金會，台北縣，271-292頁、730-736頁，1993。

安藤由典，鄭德淵譯，樂器的音響學，幼獅文化事業股份有限公司，台北市，1-18頁、103-126頁，1989。

陳元光，提琴的制作與修復，上海教育出版社，上海，2005。

劉成群、張超群，汽車振動與噪音(第二版)，新文京開發出版股份有限公司，台北縣，2006。