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C.
Intensity
The
distance at which a sound can be heard depends on its intensity, which is
the average rate of flow of energy per unit area perpendicular to the
direction of propagation. In the case of spherical waves spreading from a
point source, the intensity varies inversely as the square of the
distance, provided that no loss of energy is due to viscosity, heat
conduction, or other absorption effects. Thus, in a perfectly homogeneous
medium, a sound will be nine times as intense at a distance of 1 unit from
its origin as at a distance of 3 units; that is, intensity varies
inversely as the square of the distance. In the actual propagation of
sound through the atmosphere, changes in the physical properties of the
air, such as temperature, pressure, and humidity, produce damping and
scattering of the directed sound waves, so that the inverse-square law
generally is not applicable in direct measurements of the intensity of
sound.
D.
Quality
If
A above middle C is played on a violin, a piano, and a tuning fork, all at
the same volume, the tones are identical in frequency and amplitude, but
very different in quality. Of these three sources, the simplest tone is
produced by the tuning fork, the sound in this case consisting almost
entirely of vibrations having frequencies of 440 Hz. Because of the
acoustical properties of the ear and the resonance properties of the ear's
vibrating membrane, however, it is doubtful whether a pure tone reaches
the inner hearing mechanism in an unmodified form. The principal component
of the note produced by the piano or violin also has a frequency of 440
Hz, but these notes also contain components with frequencies that are
exact multiples of 440, called overtones, such as 880, 1320, and 1760. The
exact intensity of these other components, which are called harmonics,
determines the quality, or timbre, of the note.
E.
Velocity of Sound
The
frequency of a sound wave is a measure of the number of waves passing a
given point in 1 second. The distance between two successive crests of the
wave is called the wavelength. The product of the wavelength and the
frequency must equal the speed of propagation of the wave, and is the same
for sounds of all frequencies (if the sound is propagated through the same
medium at the same temperature). Thus, the wavelength of A above middle C
is about 78.2 cm (about 2.6 ft), and the wavelength of A below middle C is
about 156.4 cm (about 5.1 ft).
The
speed of propagation of sound in dry air at a temperature of 0° C (32°
F) is 331.6 m/sec (1088 ft/sec). If the temperature is increased, the
speed of sound increases; thus, at 20° C (68° F), the velocity of sound
is 344 m/sec (1129 ft/sec). Changes in pressure at controlled density have
virtually no effect on the speed of sound. The velocity of sound in many
other gases depends only on their density. If the molecules are heavy,
they move less readily, and sound progresses through such a medium more
slowly. Thus, sound travels slightly faster in moist air than in dry air,
because moist air contains a greater number of lighter molecules. The
velocity of sound in most gases depends also on one other factor, the specific
heat, which affects the propagation of sound waves.
Sound
generally moves much faster in liquids and solids than in gases. In both
liquids and solids, density
has the same effect as in gases; that is, velocity varies inversely as the
square root of the density. The velocity also varies directly as the
square root of the elasticity.
The speed of sound in water, for example, is slightly less than 1525 m/sec
(5000 ft/sec) at ordinary temperatures but increases greatly with an
increase in temperature. The speed of sound in copper is about 3353 m/sec
(about 11,000 ft/sec) at ordinary temperatures and decreases as the
temperature is increased (due to decreasing elasticity); in steel, which
is more elastic, sound moves at a speed of about 4877 m/sec (about 16,000
ft/sec). Sound is propagated very efficiently in steel.
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