Acoustics: Sounds Right


Fundamentals of Sound
Sound can be viewed as a wave motion in air or other elastic media. In this case,
sound is a stimulus. Sound can also be viewed as an excitation
of the hearing mechanism that results in the perception of
sound. In this case, sound is a sensation. These two views of sound are familiar to those
interested in audio and music. The
type of problem at hand dictates our approach to sound. If we are interested in the disturbance in
air created by a loudspeaker, it is a problem in physics. If we are interested
in how that disturbance sounds to a person near the loudspeaker, psychoacoustical
methods must be used. Because this course addresses acoustics in
relation to people, both aspects of sound will be treated. Sound is characterized by a number of basic
phenomena. For example, frequency is
an objective property of sound; it specifies the number of waveform repetitions per unit
of time (usually one second). Frequency can be readily measured on an oscilloscope
or a frequency counter. On the other hand, pitch is a subjective property
of sound. Perceptually, the ear hears different pitches
for soft and loud 100-Hz tones. As intensity
increases, the pitch of a low-frequency tone goes down, while the pitch of a high frequency
tone goes up. Fletcher found that playing pure tones of
168 and 318 Hz at a modest level produces a very discordant sound. At a high intensity, however, the ear
hears the pure tones in the 150 to 300-Hz octave relationship as a pleasant sound. We
cannot equate frequency and pitch, but they are analogous. A similar duality exists between intensity
and loudness. The relationship between
the two is not linear. Similarly, the relationship between waveform
(or spectrum) and perceived quality (or timbre) is complicated
by the function of the hearing mechanism. A complex waveform can be described in terms
of a fundamental and a series of harmonics of various amplitudes and phases. But perception of timbre is complicated by
the frequency-pitch interaction as well as other factors. The interaction between the physical properties
of sound, and our perception of them, poses delicate and complex issues. It is this complexity in audio and acoustics
that creates such interesting problems. On one hand, the design of a loudspeaker or
a concert hall should be a straightforward and
objective engineering process. But in practice, that objective expertise
must be carefully tempered with purely subjective wisdom. As has often been pointed out, loudspeakers
are not designed to play sine waves into calibrated microphones placed in anechoic
chambers. Instead, they are designed to play
music in our listening rooms. In other words, the study of audio and acoustics
involves both art and science. The Sine Wave
The weight (mass) on the spring shown in this figure is a vibrating system. If the weight is
pulled down to the −5 mark and released, the spring pulls the weight back toward 0. However, the weight will not stop at 0; its
inertia will carry it beyond 0 almost to +5. The
weight will continue to vibrate, or oscillate, at an amplitude that will slowly decrease
due to frictional losses in the spring and the air. In the arrangement of a mass and spring, vibration
or oscillation is possible because of the elasticity of the spring and the inertia
of the weight. Elasticity and inertia are two
things all media must possess to be capable of conducting sound. The weight in the figure moves in what is
called simple harmonic motion. The piston
in an automobile engine is connected to the crankshaft by a connecting rod. The rotation of the crankshaft and the up-and-down
motion of the pistons beautifully illustrate the relationship between rotary motion and
linear simple harmonic motion. The piston
position plotted against time produces a sine wave. It is a basic type of mechanical
motion, and it yields an equally basic waveshape in sound and electronics. If a pen is fastened to the pointer of this
figure, and a strip of paper is moved past it at
a uniform speed, the resulting trace is a sine wave. The sine wave is a pure waveform
closely related to simple harmonic motion. Sound in Media
If an air particle is displaced from its original position, elastic forces of the air tend to
restore it to its original position. Because of the inertia of the particle, it
overshoots the resting position, bringing into play elastic
forces in the opposite direction, and so on. Sound is readily conducted in gases, liquids,
and solids such as air, water, steel, concrete, and so on, which are all elastic
media. Imagine a friend stationed a distance
away, who strikes a railroad rail with a rock. You will hear two sounds, one sound coming
through the rail and one through the air. The sound through the rail arrives first
because the speed of sound in the dense steel is faster than in tenuous air. Similarly,
sounds can be detected after traveling thousands of miles through the ocean. Without a medium, sound cannot be propagated. In the laboratory, an electric
buzzer is suspended in a heavy glass bell jar. As the button is pushed, the sound of the
buzzer is readily heard through the glass. As the air is pumped out of the bell jar,
the sound becomes fainter and fainter until it
is no longer audible. The sound-conducting
medium, air, has been removed from the source and the ear. Because air is such a
common agent for the conduction of sound, it is easy to forget that other gases as well
as solids and liquids are also conductors of sound. Outer space is an almost perfect
vacuum; no sound can be conducted except in the tiny island of atmosphere within a
spaceship or a spacesuit.

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