[MATH] A periodic representation of wave : sine and cosine

$\sin$(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

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$\omega$ : Angular frequency (각주파수),

• 단위 : raidan/sec (보통 기재하지 않음).
• 오른쪽의 회전운동에서 단위시간(=보통 1sec)당 몇 radian을 움직이는지 를 의미함.
• $\omega = \dfrac{2\pi}{T} = 2\pi f$

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$f$ : 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

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$A$ : Amplitude (진폭).

• Distance from the midpoint to the crest (or to the trough) : sound wave에서 소리의 크기와 관련됨.

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$\theta$ : Phase angle (or phase, 위상각),

• 단위 : radian.
• Wave(or sinusoid)'s start point (at $t=0$).

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$\lambda$ : Wavelength (파장),

• 단위 : mm (or nm).
• Distance b/w successive identical parts of the wave.
• $\lambda = \dfrac{v}{f}=vT$

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$v$ : Vecocity(or speed) of wave,

• 단위 : mm/s (or nm/s).

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Crest : 마루, High points of the wave
Trough : 골, Low points of the wave