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Particle Movement in Sound & Simple Harmonic Motion (2003)

A paper I wrote during my Queens College Undergraduate studies in audiology... I got an A.

If a tree falls in the woods, and no one is around to hear it, does it still make a sound?  Before one can answer this question, one must define what sound is.  Contrary to the egocentric human inclination, sound does not exist because we have ears to hear it (although it helps).  Rather, sound results from its origin; vibrations.  The following will outline certain acoustic terminology and attempt to explain the process through which ears recognize sound.

Sound vibrations can originate from an infinite number of sources; the striking of a tuning fork, the slamming of a door, the blowing of air into a saxophone, the pushing of air through the vocal tract to produce speech, and yes, a tree falling in the woods.  These sounds belong in several different categories; pure tones, complex periodic signals, and complex aperiodic signals.  Each is defined by the pattern of its vibrations (or lack there of).  The simplest, a pure tone is distinct because it has only one frequency.  This means its vibration occurs in a pattern, or cycle, that repeats itself exactly the same number of times each second.  How many times this cycle repeats per second is called frequency.  It is referred to in units named Hertz (Hz).

For instance, a cycle begins with the striking fork which initiates the inward displacement of the tines.  They move in as far as they can, then elasticity restores them to their original point of rest.  However, inertia, the tendency of an object in motion to stay in motion, forces the tines to continue moving, past the resting point, outward.  The cycle ends when elasticity again returns the tines to the resting point.  Of course, inertia again forces the tines to continue moving; inward, outward, and the pattern continues throughout the duration of the pure tone.  The repetition of oscillations is called Simple Harmonic Motion (SHM).

This is often depicted in the form of a wave drawn over a bisecting horizontal line.  If the previous example were thus illustrated, the wave would begin at a point on the horizontal line, a resting point.  The curve would then arch up to its peak, signifying the place of maximum inward displacement of the tines.  Just as elasticity returned the tines to their resting point, the line would likewise curve back down to the horizontal line.  From this resting point, the line would arch down to another peak, marking the place of maximum outward displacement, then again curve back up to the horizontal line.  This is the representation of a complete cycle.

Similarly, the Swing Analogy is often referred to in order to represent the SHM of a pure tone.  Again, the swing begins at its resting point.  Once a swing is set in motion by an external force, it moves from resting to its back-most point, through its resting point, to its front-most point, and finally returns to its resting point.  This pattern repeats itself at the same rate over and over again.  The resting point is where the swing would reach maximum velocity (speed).  The back-most and front-most points are where velocity briefly drops to zero as the swing changes direction, but they are also where the swing reaches maximum acceleration (increase in speed).

Of course none of these things happen in a vacuum.  In the real world there is friction, and moving objects do no remain in motion indefinitely.  Gradually, the back-most and front-most points of the swing become closer and closer together, as do the tines of the tuning fork until the motion ceases altogether.  The frequency, nevertheless, stays the same throughout the duration of the tone.

These descriptions give some idea of how the sound vibration is produced by an object and how the sound can be graphically drawn.  However, we have not addressed the fact that even though sound does not have any weight or mass, it displaces the surrounding particles of whatever medium in which it is being transmitted.  Although we are most familiar with sound travelling through air; anyone who has gone swimming knows it travels through water, and anyone with noisy neighbors knows, that among other things, it travels through wood and plaster as well.

Air is a particularly elastic medium through which sound travels.  When a tuning fork creates vibrations, the air particles around it are also moved.  There are special names for the back and forth motion; compression and rarefaction.  All of the air particles do not move uniformly.  Instead they are more like aisles of baseball fans doing "the wave" in a stadium.  The first aisle stands and as it begins to sit down, the second aisle begins to stand.  The following aisles follow the pattern.  The process is set so that each successive aisle is slightly off in its motion from its neighbors.  Also, like the baseball fans, who never really leave the seats, the air particles are close together and others, where they are far apart but do not cross paths.  This form of motion produced is called longitudinal waves.  This propagation is what creates the vibratory patterns that our ears receive as sound.

It is a very technical process that creates sound, and pure tones are only a fraction of what we hear.  This lengthy explanation only gets one from the striking of a tuning fork to the ear drum.  The process with which reaches our brains and is perceived as sound is whole other complex system!


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