In Search of the Missing Fundamental: by Richard K. Jones

# Harmonic Motion

Sound is heard because of fluctuations in air pressure or tiny variations from normal atmospheric pressure caused by a vibrating object, which affects our tympanic membrane (eardrum). If the energy causing the fluctuations is substantial enough, the rise and fall in pressure creates a wave of sound.

Red represents high pressure and Blue represents low pressure.

This rise and fall in pressure can be graphed as a back and forth motion (seen also in the swing of a pendulum or mechanical metronome) and is called simple harmonic motion. Even though its velocity changes when it slows down to change direction and then gains speed in the other direction (as shown by the curve of a single sinusoid) its average velocity from one cycle to the next is the same. Each complete vibratory cycle therefore occurs in an equal interval of time or in a given period of time, so the wave is said to be periodic. The number of cycles that occur in one second is referred to as the frequency of the vibration. For example, if the pendulum or metronome goes back and forth 440 times per second, its frequency is 440 cycles per second, and its period is 1/440 second per cycle. These units of frequency are measured in Hertz (abbreviated Hz).  One Hz means one cycle per second. Hz is named after the German physicist Heinrich Hertz (1857-1894) who made considerable contributions to the understanding of electromagnetism. This simple harmonic motion is the building block for the sounds created by most all of the instruments in a modern orchestra.

Sinusoidal change in air pressure caused
by a simple vibration back and forth where
P = air pressure and t = time

Any object that vibrates in simple harmonic motion is said to have a resonant mode of vibration-a frequency at which it will naturally tend to vibrate when set in motion. However, most real-world objects have several resonant modes of vibration, and thus vibrate at many frequencies at once. Any sound that contains more than a single frequency (that is, any sound that is not a simple sine wave) is called a complex tone. Each individual frequency that goes into the makeup of a complex tone is called a partial. It is one part of the whole complex tone.

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