以雷射測距儀量測古典吉他弦與音箱結構之共振耦合

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謝宗祐(Tsung-Yu Hsieh) 查詢紙本館藏

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照明與顯示科技研究所

論文名稱

以雷射測距儀量測古典吉他弦與音箱結構之共振耦合
(Study of acoustic coupling between the strings and the body of classical guitars using laser displacement sensor)

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摘要(中)

本研究旨在探討古典吉他弦與音箱結構之共振耦合現象。了解不僅是吉他面板振動頻率與弦音相當時會產生狼音，當弦音與音孔空氣振動頻率接近或相同時同樣會產生強耦合並形成狼音。我們將透過數值模擬及實驗兩種方式來了解當弦音掃頻經過吉他空氣共振頻率時對於吉他音色的影響。
首先，於數學模擬中透過將吉他二自由度系統的耦合數學模型，模擬了吉他音箱的面板和音孔空氣的質量，並由此擴展為吉他弦和音孔空氣間的耦合。透過實際實驗我們使用了雷射測距儀及開發聲音脈衝激發裝置，這兩種設備皆為非接觸式量測及激發，以獲得A、B古典吉他音箱的空氣共振頻率和面板模式頻率響應。接著，我們組合了一套推拉力計和電動移動平台，實現了對吉他弦的定量撥動。實驗結果將針對弦音與空氣共振頻率品質因子、耦合因子、振幅進行討論。最後，結果表明在演奏時根據具體情況選擇合適的撥弦、彈奏方式和琴弦，可以減少狼音對吉他音色的影響。

關鍵字:狼音，二自由度系統，古典吉他，雷射測距儀，非接觸激發，耦合因子。

摘要(英)

This study aims to investigate the resonance coupling phenomenon between classical guitar strings and the structure of the soundbox. It is understood that not only does the occurrence of beat tones happen when the vibration frequency of the guitar′s soundboard matches that of the strings, but also strong coupling and beat tones are formed when the frequencies of the strings and the air piston vibration are close or identical. Through both numerical simulations and experimental approaches, we seek to understand the impact of string frequency sweeping through the guitar′s air resonance frequencies on the instrument′s tone quality.
Initially, mathematical simulations involve coupling models of a two degree of freedom system of the guitar, simulating the mass of the soundboard and the air piston in the soundhole, which is then extended to the coupling between the guitar strings and the air in the soundhole. In practical experiments, laser rangefinders and a sound pulse excitation device, both of which are non-contact measurement and excitation tools, are employed to obtain the air resonance frequencies and soundboard mode frequency responses of Classical Guitars A and B. Subsequently, a combination of a tension gauge and an electrically driven moving platform is used to achieve quantitative plucking of the guitar strings. Experimental results will be discussed regarding the quality factor, coupling factor, amplitude, and spectral energy of string and air resonance frequencies.

Ultimately, the results indicate that selecting appropriate plucking techniques, playing styles, and strings based on specific conditions can mitigate the influence of beat tones on the tone quality of the guitar during performance.
Keywords: wolf tone, two degree of freedom system, classical guitar, laser displacement sensor, non-contact excitation, coupling factor.

關鍵字(中)

★ 狼音
★ 二自由度系統
★ 古典吉他
★ 雷射測距儀
★ 非接觸激發
★ 耦合因子

關鍵字(英)

★ wolf tone
★ two degree of freedom system
★ classical guitar
★ laser displacement sensor
★ non-contact excitation
★ coupling factor

論文目次

摘要 i
ABSTRACT v
目錄 ix
圖目錄 xi
表目錄 xiii
第一章、緒論 1
1-1 前言 1
1-2 吉他音箱的頻率響應 3
1-3 吉他構造與性質 7
1-3-1 吉他起源與各部位名稱及功用 7
1-3-2 吉他各部位木材材質及面板選擇 10
1-4 吉他的聲學原理 13
1-4-1 吉他的發聲方式 13
1-4-2 吉他音箱部件影響吉他音色程度 14
1-5 吉他琴弦與音箱耦合的發展 16
1-6 結論 23
第二章、吉他自由度系統耦合模擬 25
2-1 狼音與強和弱耦合 26
2-1-1 狼音與強和弱耦合介紹 26
2-1-2 強與弱耦合定義 28
2-2 單自由度系統 32
2-2-1 單自由度系統理論 32
2-2-2 單自由度阻尼振盪系統 34
2-2-3 單自由度受迫振盪系統 38
2-2-4 品質因子Q值定義及推導 40
2-3 二自由度系統 45
2-3-1 二自由度系統理論 45
2-3-2 吉他二自由度系統理論 49
2-3-3 吉他弦與空氣模式模擬原理 52
2-4 結論 55
第三章、古典吉他振動實驗 57
3-1 雷射測距儀 57
3-2 撥弦設備 59
3-3 聲音脈衝激發於古典吉他音箱內設備 63
3-4 結論 67
第四章、吉他弦與空氣模式模擬與實驗分析 68
4-1 聲音脈衝激發於古典吉他音箱內頻譜分析 68
4-2 吉他弦與空氣模式模擬 72
4-2-1 吉他弦與空氣模式模擬之物理參數 74
4-2-2 吉他弦與空氣模式模擬結果 76
4-3 吉他弦掃頻 81
4-3-1 吉他弦掃頻實驗與模擬結果 82
4-3-2 吉他弦掃頻對弦音與空氣共振品質因子及耦合因子影響 85
4-3-3 吉他弦掃頻對弦音與空氣共振振幅影響 89
4-4 結論 93
第五章、結論與未來展望 96
5-1 結論 96
5-2 未來展望 99
參考文獻 100

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指導教授

陳啟昌(Chii-Chang Chen)

審核日期

2024-4-11

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