University of Taipei:Item 987654321/5083
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    Please use this identifier to cite or link to this item: http://utaipeir.lib.utaipei.edu.tw/dspace/handle/987654321/5083


    Title: 電腦輔助分析小提琴、聲帶在聲學、波動學中的數值分析之研究
    Computer Assisted to Analysis Numerical Values of Vocal Cord and Violin Waveform in acoustics and Wave
    Authors: 陳義勳
    Date: 1982-06
    Issue Date: 2011-12-07 11:34:20 (UTC+8)
    Publisher: 臺北市立師範專科學校
    Abstract:   在週期性的波動中,理論上可以藉無限多項的傅立葉級數展開(Fourier series expansion)處理,但實際上,只要將傅立葉級數展開取到一定的有限項,就可以在所希望的誤差範圍內,做相當完美的傅立葉級數展開。本文針對人類聲帶發出的週期性樂音Do,Re,Mi,Fa,Sol,La,Si,Do'及小提琴發出的週期性的樂音Do,Re,Mi,Fa,Sol,La,Si,Do'以傅立葉級數展開,並藉著電腦的快速、正確地運算來輔助分析,期能由電腦分析的結果來探討週期性波動的一些性質與現象,本篇論文發現(1)週期性波動的Fourier series expansion的數值分析中的係數有│√a<sub>n</sub><sup>2</sup>+√b<sub>n</sub><sup>2</sup>/√a<sub>1</sub><sup>2</sup>+√b<sub>1</sub><sup>2</sup>│隨著n的增加其值有愈來愈小之趨勢,此乃聲學中高次諧振波振幅有愈來愈小的現象(2)同頻率,不同樂器,波形與樂器有關,小提琴的波形較聲帶的波形來得不平滑,此說明了小提琴振動較聲帶來得激烈。(3)相同的樂器,在不同的頻率下,發現低頻週期波的寬度較高頻週期波來得寬,且高頻的高次諧振波振幅比低頻的高次諧振波振幅來得大即│√a<sub>n</sub><sup>2</sup>+√b<sub>n</sub><sup>2</sup>高頻/√a<sub>n</sub><sup>2</sup>+√b<sub>n</sub><sup>2</sup>低頻│>1的趨勢
    Relation: 北市師專學報
    第14期
    總502-396
    Appears in Collections:[Office of Academic Affairs] 北市師專學報(12-18期)

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