Elastic objects vibrate, or move back and forth, in a repeating motion
when disturbed by some external force. They are able to do this because
they have an internal restoring force that returns them to their original positions
after being deformed by some external force. If the internal restoring
force is opposite to and proportional to the deforming displacement,
the vibration is called a simple harmonic motion. The extent of displacement
is called the amplitude, and one complete back-and-forth motion
is one cycle. The time required for one cycle is a period. The frequency is
the number of cycles per second, and the unit of frequency is the hertz. A
graph of the displacement as a function of time for a simple harmonic
motion produces a sinusoidal graph.Periodic, or repeating, vibrations or the pulse of a single disturbance
can create waves, disturbances that carry energy through a medium. A
wave that disturbs particles in a back-and-forth motion in the direction
of the wave travel is called a longitudinal wave. A wave that disturbs particles
in a motion perpendicular to the direction of wave travel is called a
transverse wave. The nature of the medium and the nature of the disturbance
determine the type of wave created.
Waves that move through the air are longitudinal and cause a back-and-
forth motion of the molecules making up the air. A zone of molecules
forced closer together produces a condensation, a pulse of increased
density and pressure.A zone of reduced density and pressure is a rarefaction.
A vibrating object produces condensations and rarefactions that expand
outward from the source. If the frequency is between 20 Hz and
20,000 Hz, the human ear perceives the waves as sound of a certain pitch.
High frequency is interpreted as high-pitched sound, and low frequency
as low-pitched sound.
A graph of pressure changes produced by condensations and rarefactions
can be used to describe sound waves. The condensations produce
crests, and the rarefactions produce troughs. The amplitude is the
maximum change of pressure from the normal. The wavelength is the
distance between any two successive places on a wave train, such as the distance from one crest to the next crest. The period is the time required
for a wave to repeat itself. The velocity of a wave is how quickly
a wavelength passes. The frequency can be calculated from the wave
equation, v = λƒ.
Sound waves can move through any medium but not a vacuum.The
velocity of sound in a medium depends on the molecular inertia and
strength of interactions. Sound, therefore, travels most rapidly through a
solid, then a liquid, then a gas. In air, sound has a greater velocity in
warmer air than in cooler air because the molecules of air are moving
about more rapidly, therefore transmitting a pulse more rapidly.
Sound waves are reflected or refracted from a boundary, which means
a change in the transmitting medium. Reflected waves that are in phase
with incoming waves undergo constructive interference and waves that are
out of phase undergo destructive interference. Two waves that are otherwise
alike but with slightly different frequencies produce an alternating
increasing and decreasing of loudness called beats.
The energy of a sound wave is called the wave intensity, which is
measured in watts per square meter. The intensity of sound is expressed
on the decibel scale, which relates it to changes in loudness as perceived by
the human ear.
All elastic objects have natural frequencies of vibration that are determined
by the materials they are made of and their shapes. When energy
is transferred at the natural frequencies, there is a dramatic increase
of amplitude called resonance. The natural frequencies are also called resonant
frequencies.
Sounds are compared by pitch, loudness, and quality. The quality is
determined by the instrument sounding the note. Each instrument has
its own characteristic quality because of the resonant frequencies that it
produces. The basic, or fundamental, frequency is the longest standing
wave that it can make. The fundamental frequency determines the basic
note being sounded, and other resonant frequencies, or standing waves
called overtones or harmonics, combine with the fundamental to give the
instrument its characteristic quality.
A moving source of sound or a moving observer experiences an apparent
shift of frequency called the Doppler effect. If the source is moving
as fast or faster than the speed of sound, the sound waves pile up into a
shock wave called a sonic boom. A sonic boom sounds very much like the
pressure wave from an explosion.
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