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
     a. 一个确定的平衡配置
   • b. a restoring force to bring the system back to equilibrium
     b. 一个恢复力，使系统恢复到平衡状态
   弹性——在受力变形后能精确恢复原状的能力。
2. A source of energy.
   一种能源来源

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
  周期：完成一个完整周期所需的时间，记为T，单位为秒/周期



• Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)
  频率：每秒的周期数，用f表示，单位是秒的倒数或赫兹（Hz）



• Amplitude: the maximum displacement from equilibrium A
  振幅：从平衡位置的最大位移

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

• Velocity of propagation: v
  传播速度：v



• Wavelength: repeat distance of wave λ.
  波长：波的重复距离 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. 在时间对周期性运动的图像中，周期可以看作是运动重复的时间。频率是周期的倒数。

If the period T = s T = ms T = x 10^ s then the frequency f = Hz f = kHz f = MHz f = x 10^ Hz 如果周期 T = s T = ms T = x 10^ s 那么频率 f = Hz f = kHz f = MHz f = x 10^ Hz 中文译文中的待填/计算数值依次对应：1：t1 2：t2 3：tb 4：tp 5：f1 6：f2 7：f3 8：fb 9：fp。实际数值以上方原输入框为准。