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

Math 2022. 9. 2. 20:12
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sin(정현), cos(여현) : 주기신호나 wave등을 나타내는데 사용되는 기본적인 함수.

y(t)=Asin(ωt+θ)y(t)=Acos(ωt+θ)

T : period (주기),

  • 단위 : sec.
  • Time to complete one vibration

ω : Angular frequency (각주파수),

  • 단위 : raidan/sec (보통 기재하지 않음).
  • 오른쪽의 회전운동에서 단위시간(=보통 1sec)당 몇 radian을 움직이는지 를 의미함.
  • ω=2πT=2πf

f : frequency (진동수, 주파수),

  • Hz(=1/sec).
  • How frequently a vibration occurs or # of waves passing any point per second.
  • f=1T=vλ
  • 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.

θ : Phase angle (or phase, 위상각),

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

λ : Wavelength (파장),

  • 단위 : mm (or nm).
  • Distance b/w successive identical parts of the wave.
  • λ=vf=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

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