Periodic Motion

Periodic motion of some source object is necessary to produce a sustained musical sound (i.e., one with definite pitch and quality). For example, to produce a standard musical A (440 Hz), the source object must sustain periodic motion at 440 vibrations per second with a tolerance of less than 1 Hz -- the normal human ear can detect the difference between 440 Hz and 441 Hz. The conditions necessary for periodic motion are

  1. elasticity - the capacity to return precisely to the original configuration after being distorted.
    • a. a definite equilibrium configuration
    • b. a restoring force to bring the system back to equilibrium
  2. A source of energy.

Fortunately, it is not hard to find vibrators which meet these conditions, hence the richness in variety of musical sound sources.

Terms for describing periodic motion.

A mass on a spring is an example of periodic motion with a single frequency called simple harmonic motion.

Periodic motion concepts

Elasticity and musical sources
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Description of Periodic Motion

Motion which repeats itself precisely can be described with the following terms:

  • Period: the time required to complete a full cycle, T in seconds/cycle

  • Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)

  • Amplitude: the maximum displacement from equilibrium A

and if the periodic motion is in the form of a traveling wave, one needs also

Traveling wave relationshipTraveling wave parameters
Example: vary the parameters for a sine wave

Periodic motion concepts
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Period, Frequency and Amplitude

In a plot of periodic motion as a function of time, the period can be seen as the repeat time for the motion. The frequency is the reciprocal of the period.

If the period T = s
T = ms
T = x 10^ s

then the frequency f = Hz
f = kHz
f = MHz
f = x 10^ Hz

Simple harmonic motionEquilibrium condition

Periodic motion concepts
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