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.

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

• Velocity of propagation: v



• Wavelength: repeat distance of wave λ.

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