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II.
Physical Characteristics
Any
simple sound, such as a musical note, may be completely described by
specifying three perceptual characteristics: pitch, loudness (or
intensity), and quality (or timbre). These characteristics correspond
exactly to three physical characteristics: frequency, amplitude, and
harmonic constitution, or waveform, respectively. Noise is a complex
sound, a mixture of many different frequencies or notes not harmonically
related.
A.
Frequency
Sounds
can be produced at a desired frequency by different methods. For example,
a sound of 440 Hz can be created by actuating a loudspeaker with an
oscillator tuned to this frequency .
An air blast can be interrupted by a toothed wheel with 44 teeth, rotating
at 10 revolutions/sec; this method is used in operating an ordinary siren.
The sound of the speaker and that of the siren at the same frequency are
very different in quality, but will correspond closely in pitch,
equivalent to the A above middle C on a piano. The next higher A on the
piano, the note one octave above, has a frequency of 880 Hz. Similarly,
notes one or two octaves below have frequencies of 220 or 110 Hz,
respectively. Thus, by definition, an octave is the interval between any
two notes the frequencies of which are in a two-to-one ratio.
A
fundamental law of harmony states that two notes an octave apart, when
sounded together, produce a euphonious combination. A fifth and a major
third produce successively less euphonious combinations. Physically, an interval
of a fifth consists of two notes, the frequencies of which bear the
arithmetical ratio three to two, and a major third, the ratio five to
four. Fundamentally, then, the law of harmony states that two or more
notes sound euphonious when played together if their frequencies bear the
ratio of small, whole numbers; if the frequencies do not bear such ratios,
a dissonance is produced. On a fixed-pitch instrument, such as a piano, it
is not possible to arrange the notes so that all of these ratios hold
exactly, and some compromise is necessary in tuning, called the meantone
system, or tempered scale.
B.
Amplitude
The
amplitude of a sound wave is the degree of motion of air molecules within
the wave, which corresponds to the extent of rarefaction and compression
that accompanies the wave. The greater the amplitude of the wave, the
harder the molecules strike the ear drum and the louder the sound that is
perceived. The amplitude of a sound wave can be expressed in terms of
absolute units by measuring the actual distance of displacement of the air
molecules, or the pressure differential in the compression and
rarefaction, or the energy involved. Ordinary speech, for example,
produces sound energy at the rate of about one hundred-thousandth of a
watt. All of these measurements are extremely difficult to make, however,
and the intensity of sounds is generally expressed by comparing them to a
standard sound, measured in decibels (see Sensations of Tone below).
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