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The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (''t'') is: : where: * ''A'' = the ''amplitude'', the peak deviation of the function from zero. * ''f'' = the ''ordinary frequency'', the ''number'' of oscillations (cycles) that occur each second of time. * ''ω'' = 2π''f'', the ''angular frequency'', the rate of change of the function argument in units of radians per second * '''' = the ''phase'', specifies (in radians) where in its cycle the oscillation is at ''t'' = 0. * * When '''' is non-zero, the entire waveform appears to be shifted in time by the amount ''''/''ω'' seconds. A negative value represents a delay, and a positive value represents an advance. The sine wave is important in physics because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique. == General form == In general, the function may also have: * a spatial variable ''x'' that represents the ''position'' on the dimension on which the wave propagates, and a characteristic parameter ''k'' called wave number (or angular wave number), which represents the proportionality between the angular frequency ω and the linear speed (speed of propagation) ν * a non-zero center amplitude, ''D'' which is :, if the wave is moving to the right :, if the wave is moving to the left 〔Resnick Halliday Walker, Fundamentals of Physics〕 The wavenumber is related to the angular frequency by:. : where λ (Lambda) is the wavelength, ''f'' is the frequency, and ''v'' is the linear speed. This equation gives a sine wave for a single dimension; thus the generalized equation given above gives the displacement of the wave at a position ''x'' at time ''t'' along a single line. This could, for example, be considered the value of a wave along a wire. In two or three spatial dimensions, the same equation describes a travelling plane wave if position ''x'' and wavenumber ''k'' are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed. 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「sine wave」の詳細全文を読む スポンサード リンク
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