The
frequency and amplitude parameters of a sine wave are completely independent.
When sound
is
heard, however, there is interaction between loudness and pitch. Lower-
frequency sounds decrease
in
loudness much faster than high-frequency sounds.
The
third attribute of a sound, timbre, depends on the presence
or
absence of overtones,
or
harmonics. Any complex waveform
is
actually a mixture of sine waves of different
amplitudes, frequencies, and phases (the starting point of
the
waveform on the time
axis). These component sine waves are called harmonics. A square waveform, for exam-
ple, has an infinite number of harmonics.
In summary, all steady sounds can
be
described by their frequency, overall amplitude,
and relative harmonic amplitudes.
The
audible equivalents of these parameters are
pitch, loudness, and timbre, respectively. Changing sound is a steady sound whose
parameters change over time.
In electronic production of sound, an analog device, such as a tape recorder, records
sound waveforms and their cycle frequencies as a continuously variable representation of
air pressure.
The
tape recorder then plays back the sound by sending the waveforms
to
an amplifier where they are changed into analog voltage waveforms. The amplifier sends
the voltage waveforms
to
a loudspeaker, which translates them into air pressure vibra-
tions
that
the listener perceives as sound.
A computer cannot store analog waveform information. In computer production of
sound, a waveform has to be represented as a finite string of numbers. This transforma-
tion is made by dividing the time axis of the graph of a single waveform into equal seg-
ments, each of which represents a short enough time so the waveform does not change a
great deal. Each of the resulting points is called a sample. These samples are stored in
memory, and you can play them back
at
a frequency
that
you determine.
The
computer
feeds the samples
to
a digital-to-analog converter (DAC), which changes them into an
analog voltage waveform.
To
produce the sound, the analog waveforms are sent first
to
an amplifier, then to a loudspeaker.
Figure 5-2 shows an example of a sine wave, a square wave, and a triangle wave, along
with a table of samples for each. Note
that
the illustrations are not
to
scale and
that
there are fewer dots in the wave forms than there are samples in the table.
The
ampli-
tude axis values
127
and -128 represent the high and
low
limits on relative amplitude.
134 Audio Hardware
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