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## Periodic and aperiodic motion

The simplest kind of motion is the sine wave, which is approximately the natural motion of a weight that bobs up and down on a spring swinging at a moderate displacement. In case of an undamped motion, the weight repeats the same activity with every period T.  A related term is frequency,  , the number of periods  in a given interval of time. For instance, a sine wave with a period  of second has a frequency   of 1000Hz or 1kHz (with ``Hertz'' or ``Hz'' for cycles per second, ``kiloHertz'' or ``kHz'' for 1000 Hertz). Other characteristics of a sine wave are its amplitude, which determines the displacement from a reference point, and its phase,  which refers to the relative displacement in time between sine waves of the same frequency . The amplitude as a function of time can be a measure of distance, as in the case of the spring, or of current or voltage in case of an electrical sine wave. The amplitude of a sound wave like speech is measured in sound pressure fluctuations above and below normal atmospheric pressure.

While pure sine waves are very rare in the real world of sound, they are the basic elements for more complex sounds like a bowed string or a sustained vowel: any repetitive (periodic) waveform can be expressed by an ensemble of sine waves, beginning with a fundamental wave  and adding a set of harmonically related sine waves, whose periods  are related as and so on (Fourier's Theorem). Therefore every complex periodic time wave can be represented by the relative strengths of its fundamental wave   and its harmonics, called a frequency spectrum.   Analysis of a complex periodic time wave into its spectral components is known as Fourier analysis, and the procedure involved is the (Discrete) Fourier Transformation (DFT); specially optimised versions of the DFT algorithm are known as Fast Fourier Transformation (FFT) algorithms.

Another kind of sound is of aperiodic nature, like frication noise,   and therefore has neither a period  nor a fundamental frequency . Just as repetitive waveforms can be made up of harmonically related sine waves, noise  can be represented by a continuous band of an unbounded number of sine waves. Sound containing all frequency  components up to a limiting frequency with equal energy is called white noise .

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