### Pure Tones

A pure tone is described by a **sine wave**, a mathematical function based on the circle.
The sine wave for each tone has a specific **frequency** (hertz [Hz], or cycles
[repetitions] per second), **amplitude** or **power** (size, strength) in decibels (dB),
and **phase** (time relation to other the sound waves). The graph below shows four sine
waves that represent three pure tones (each containing only one frequency) and the mixture of
the three.
Air pressure is plotted on the X axis (vertical) and time in milliseconds (1/1,000 seconds)
on the Y axis (horizontal). The top line of the drawing represents a 1-kHz (1,000
cycles/second) tone. It has one complete cycle each millisecond and 1,000 complete cycles in
each second.

The second line is also 1 kHz, but it is half the amplitude (up-and-down size) of the first
and is shifted in phase (time relation) relative to the first. This means that the second line has
exactly the same number of cycles (or peaks) per second, but its size is half the size of the
top line, and its peak pressure comes slightly later than the peaks of the top line. The third line
represents a 2-kHz tone, which has exactly twice the peaks per second as the first two. Its
amplitude is the same as the amplitude of the top line.

Pure tones are rare in nature. Natural sounds can be described as mixtures of many sine
waves with different frequencies and amplitudes. The fourth line of the graph above shows
such a mixture: the top three lines combined to form a complex wave. This mixture is still
much simpler than most natural sounds, which have many more than three pure tones in
them.

The three frequencies in this graph are simple multiples of each other, so the sum shows a
regular repetition, like the individual sine waves. Such a mixture is called harmonic, and the
sound it would make would have a musical quality.

The drawing below represents three sine waves
that are not simple harmonics: 1.0, 1.7, and 2.4 kHz
are not simple multiples of each other. The sum is
quite irregular and would sound harsh and noisy.

E10_06h, E10_13c