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How does a computer produce a frequency?

A computer produces a frequency by repeating a waveform.

$\scalebox {0.6}{\includegraphics*{graphics/square2.eps}}$

If you look carefully at the plot above, you will see that the waveform repeats every 100 samples. There are four complete iterations of the waveform in the above plot.

A waveform's duration determines the fundamental frequency of the sound.

At the sampling rate of 44100 samples per second, this waveform's fundamental frequency is:

44100 / 100 = 441 hertz

So, it is just over 440 hertz, which is a standard, tuning pitch ``A''.

The general formula for converting waveform durations into frequencies is:

$\begin{displaymath} frequency~=~sampling\_rate~/~waveform\_duration\_in\_samples\end{displaymath}$

If the sampling rate were changed to 22050 samples per second, and the very same waveform were sent to the converter, the frequency would be different:

22050 / 100 = 220.5 hertz

Exactly one octave lower than when the sampling rate was 44100 samples per second.

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Arun Chandra
arunc@evergreen.edu