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The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids (e.g. Fourier series), the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as ''f''0 (or FF), indicating the lowest frequency counting from zero.〔(【引用サイトリンク】title=Fundamental Frequency of Continuous Signals )〕 In other contexts, it is more common to abbreviate it as ''f''1, the first harmonic.〔(【引用サイトリンク】title=Standing Wave in a Tube II - Finding the Fundamental Frequency )〕〔(【引用サイトリンク】title=Physics: Standing Waves )〕〔(【引用サイトリンク】title=Phys 1240: Sound and Music )〕〔(【引用サイトリンク】title=Creating musical sounds - OpenLearn - Open University )〕 (The second harmonic is then f2 = 2⋅f1, etc. In this context, the zeroth harmonic would be 0 Hz.) ==Explanation== All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. A single period is thus the smallest repeating unit of a signal, and one period describes the signal completely. We can show a waveform is periodic by finding some period ''T'' for which the following equation is true: : Where ''x''(''t'') is the function of the waveform. This means that for multiples of some period T the value of the signal is always the same. The largest possible value of T for which this is true is called the fundamental period and the fundamental frequency (''f''0) is: : Where ''f''0 is the fundamental frequency and ''T'' is the fundamental period. For a tube of length ''L'' with one end closed and the other end open the wavelength of the fundamental harmonic is 4''L'', as indicated by the top two animations on the right. Hence, : Therefore, using the relation : , where ''v'' is the speed of the wave, we can find the fundamental frequency in terms of the speed of the wave and the length of the tube: : If the ends of the same tube are now both closed or both opened as in the bottom two animations on the right, the wavelength of the fundamental harmonic becomes 2''L''. By the same method as above, the fundamental frequency is found to be : At 20 °C (68 °F) the speed of sound in air is 343 m/s (1129 ft/s). This speed is temperature dependent and does increase at a rate of 0.6 m/s for each degree Celsius increase in temperature (1.1 ft/s for every increase of 1 °F). The velocity of a sound wave at different temperatures:- *v = 343.2 m/s at 20 °C *v = 331.3 m/s at 0 °C 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「fundamental frequency」の詳細全文を読む スポンサード リンク
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