[Physics] A periodic representation of wave : sin and cos

$\sin$(정현), $\cos$(여현) : 주기신호나 wave등을 나타내는데 사용되는 기본적인 함수.

$$ y(t)= A \sin(\omega t + \theta) \\ y(t) = A \cos (\omega t + \theta)$$

• $T$ : period (주기),
  • 단위 : sec.
  • Time to complete one vibration
• $\omega$ : Angular frequency (각주파수),
  • 단위 : raidan/sec (보통 기재하지 않음).
  • 오른쪽의 회전운동에서 단위시간(=보통 1sec)당 몇 radian을 움직이는지 를 의미함.
  • $\omega = \dfrac{2\pi}{T} = 2\pi f$
• $f$ : frequency (진동수, 주파수),
  • Hz(=1/sec).
  • How frequently a vibration occurs or # of waves passing any point per second.
  • $f=\dfrac{1}{T}=\dfrac{v}{\lambda}$
  • Note
    • AM radio : kHz
    • FM radio : MHz
    • Cell phone or Rader : GHz
    • Medical ultrasound : 1~30MHz
• $A$ : Amplitude (진폭).
  • Distance from the midpoint to the crest (or to the trough) : sound wave에서 소리의 크기와 관련됨.
• $\theta$ : Phase angle (or phase, 위상각),
  • 단위 : radian.
  • Wave(or sinusoid)'s start point (at $t=0$).
• $\lambda$ : Wavelength (파장),
  • 단위 : mm (or nm).
  • Distance b/w successive identical parts of the wave.
  • $\lambda = \dfrac{v}{f}=vT$
• $v$ : Vecocity(or speed) of wave,
  • 단위 : mm/s (or nm/s).
• Crest : 마루, High points of the wave
• Trough : 골, Low points of the wave