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In physics and engineering, the envelope function of an oscillating signal is a smooth curve outlining its extremes.〔 The envelope thus generalizes the concept of a constant amplitude. The figure illustrates a modulated sine wave varying between an upper and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable. ==Example: beating waves== A common situation resulting in an envelope function in both space ''x'' and time ''t'' is the superposition of two waves of almost the same wavelength and frequency:〔 〕 : ::: which uses the trigonometric formula for the addition of two sine waves, and the approximation Δλ<<λ: : Here the ''modulation wavelength'' λmod is given by:〔〔 〕 : The modulation wavelength is double that of the envelope itself because each half-wavelength of the modulating cosine wave governs both positive and negative values of the modulated sine wave. Likewise the ''beat frequency'' is that of the envelope, twice that of the modulating wave, or 2Δ''f''.〔 If this wave is a sound wave, the ear hears the frequency associated with ''f'' and the amplitude of this sound varies with the beat frequency.〔 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「Envelope (waves)」の詳細全文を読む スポンサード リンク
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