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* .